An Automotive Short Range High Resolution Pulse Radar Network

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AN AUTOMOTIVE SHORT R ANGE

HIGH R ESOLUTION

PULSE R ADAR NETWORK

Vom Promotionsausschuß der

Technischen Universität Hamburg-Harburg

zur Erlangung des akademischen Grades

Doktor-Ingenieur (Dr.-Ing.)

genehmigte Dissertation

von

Dipl.-Ing. Michael Klotz

aus

Ungeny / Moldawien

Januar 2002



1. Gutachter: Prof. Dr. rer. nat. Dr. h. c. Hermann Rohling2. Gutachter: Prof. Dr.-Ing. habil. Paul Walter Baier

Tag der mündlichen Prüfung: 18. Dezember 2001



Zusammenfassung

Der anhaltende Fortschritt in der Entwicklung der Mikrowellentechnik sowie leistungsfähigerProzessoren ermöglicht es heutzutage, Radarsensoren kostengünstig für Anwendungen inKraftfahrzeugen einzusetzen. Das Ziel ist es, durch Unterstützung des Fahrers mit Hilfe von

Radarsensorik den Komfort und die Sicherheit für den Fahrer und andere Insassen desFahrzeugs zu erhöhen. Entwicklungen zu Radarsensoren für den Einsatz in Automobilen sindzurzeit in den Frequenzbereichen 24GHz sowie 77GHz zu sehen. Radarsensoren zeigen

bedeutende Vorteile im Vergleich mit anderer Sensorik und sind sogar bereits serienmäßig fürden Bereich bis 150m in manchen Fahrzeugen verfügbar.

Die vorgestellte Arbeit basiert auf dem Einsatz sehr kleiner und günstiger Puls-Radarsensorenim Bereich 24GHz , die für den Nahbereich eines Fahrzeuges entwickelt wurden. DieSensoren können bis ca. 24m messen, und zwar mit einer Genauigkeit von ca. ±3cm sowieeiner Auflösung von ca. 10cm. Ein einzelner Sensor ist lediglich in der Lage, eine Entfernungzu einem Hindernis zu messen, aber nicht dessen Winkel. Der Winkel kann aber in einem

Netzwerk von Sensoren zusätzlich durch Multilaterationsverfahren gewonnen werden. Ein Netzwerk kann außerdem einen sehr großen Winkelbereich um ein Fahrzeug herumabdecken. Ziel ist es, mit einem Netzwerk von um das Fahrzeug verteilten Radarsensoreneinen geschlossenen Schutzring für das Fahrzeug zu bilden. Alle Hindernisse, die sich imBereich von ca. 24m um das Fahrzeug befinden, sollen erkannt und verfolgt werden.Ergebnisse der Berechnungen werden weiter verwendet zur Einparkhilfe, Abstands- undGeschwindigkeitsregelung im Stop&Go-Verkehr, Überwachung des toten Winkels oder zurAuslösung von Sicherheitsvorrichtungen im Fahrzeug, wenn ein Unfall nicht mehr vermiedenwerden kann (Pre-Crash).

Im Rahmen der Arbeit wurden Pulsradarsensoren verwendet und geeignete Methoden derSignalverarbeitung zur präzisen Messung von Entfernungen eines Einzelsensors entwickelt.Außerdem wurden Möglichkeiten untersucht und experimentell erprobt, mit denen einegleichzeitige Messung von Entfernung und Geschwindigkeit durchgeführt werden kann. DieVorteile einer Veränderung der Pulsbreite wurden ebenfalls untersucht sowie Möglichkeitenzur gegenseitigen Entstörung.

Ein Netzwerk von vier Sensoren wurde in ein Experimentalfahrzeug integriert, das für denEinsatz als Testfahrzeug zur radarbasierten automatischen Abstands- undGeschwindigkeitsregelung ausgerüstet ist. Die Sensoren wurden an einen zentralen Rechnerangebunden, der die Multilateration durchführt, die Stellglieder des Fahrzeugs ansteuert sowie

die Ergebnisse der Berechnung auf einem Display während der Fahrt darstellen oderspeichern kann. Zur Multilateration wurden Least-Squares-Verfahren eingesetzt undVerfahren der Kalman-Filterung entwickelt. Es wurden diverse Situationen untersucht undaufgezeichnet, um damit im Labor die Verfahren der Datenzuordnung, Multilateration undFilterung anhand realer Daten für den praxistauglichen Einsatz des Systems zu optimieren.Ergebnisse statischer und dynamischer Meßsituationen sind dargestellt und zeigen dasPotential dieses Systems für den kommerziellen Einsatz in zukünftigen Seriensystemen.

Neben diversen analytischen Beiträgen zur Signalverarbeitung der Sensoren und zurMultilateration bilden die experimentellen Arbeiten und Ergebnisse einen Schwerpunkt derArbeit.





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Contents

1 Introduction ...................................................................................................................... 1

2 An Automotive Radar Network based on Short Range Sensors ................................. 3 2.1 Radar Network Description........................................................................................ 32.2 Automotive Applications and Radar System Requirements...................................... 6

2.2.1 Applications ....................................................................................................... 62.2.2 Requirements for a Short Range Radar Sensor Network................................... 8

2.3 Advantages of a Sensor Network ............................................................................... 92.4 Required Range Measurement Accuracy for Multilateration .................................. 102.5 Positioning of Sensors.............................................................................................. 13

3 Single Sensor Signal Processing for Pulse Radar Sensors.......................................... 17 3.1 Standard Processing Scheme for Simultaneous Range and Doppler Measurement 173.2 Processing of a High Range Resolution Radar with Ultra-Short Pulses.................. 19

3.2.1 Measurement Principle..................................................................................... 193.2.2 Detection and Range Measurement.................................................................. 243.2.3 Simultaneous Range and Velocity Measurement............................................. 27

3.2.3.1 Processing with Stepped Ramps ..................................................................293.2.3.2 Processing with Staggered Ramp Duration.................................................. 30

3.3 Variable Pulse Width ............................................................................................... 333.3.1 Parameters for Variable Range Resolution ...................................................... 333.3.2 Influences of Variable Pulse Width on the System Performance ....................343.3.3 Example for Pulse Width Variation .................................................................37

3.4 Suppression of Sensor Interferences ........................................................................ 383.4.1 Explanation of Sensor Interference.................................................................. 383.4.2 Constant Detuning of the PRF Oscillator......................................................... 413.4.3 Jittering of the Pulse Repetition Frequency ..................................................... 42

4 Radar Network Processing............................................................................................45 4.1 Coordinate System ................................................................................................... 454.2 Multiple Sensor Network Architectures...................................................................46

4.2.1 Network Architectures ..................................................................................... 464.2.2 Software Architecture: Central-Level Tracking............................................... 484.2.3 Software Architecture: Sensor-Level Tracking................................................ 48

4.3 Single Object Multilateration and Tracking............................................................. 494.3.1 Nonlinear Least Squares Estimation ................................................................ 50

4.3.2 Performance Comparison between Systems of 4 and 6 Sensors......................534.3.3 α - β - Filter...................................................................................................... 544.3.4 Kalman - Filtering ............................................................................................55

4.4 Overview of a Multiple Object Multilateration and Tracking System.....................614.5 Data Association Methods .......................................................................................64

4.5.1 Nearest Neighbor Association Methods........................................................... 654.5.2 Joint Probabilistic Data Association (JPDA) ................................................... 664.5.3 Multiple Hypothesis Tracking (MHT) ............................................................. 66

4.5.3.1 Measurement - oriented MHT......................................................................664.5.3.2 Track - oriented MHT .................................................................................. 684.5.3.3 Comparison between both MHT Implementations ...................................... 69

4.6 Description of an Implemented Radar Network Processing .................................... 70

5 Phase Monopulse Sensor Concept ................................................................................ 73





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1 Introduction

The first RADAR (radio detection and ranging) system was invented by Christian Hülsmeyer(1881-1957) in 1904 to avoid vessel collisions on the river Rhine even in bad weather

conditions. The first radar application in road traffic situations was started intensively in theearly 1970s. Long before being realistically ready for the automotive market, experimentswith microwave technology were carried out to understand the potential of microwaves to beused as a robust sensing technique for vehicles. Different applications are desired forautomotive radar systems. The main idea is to avoid vehicle collisions in very muchincreasing traffic density, e.g. to use it as an ACC (adaptive cruise control) system for drivingcomfort and passenger security. The use of radar sensors as a parking aid system and for a

pre-crash application are further useful applications. Unlike airbag systems which react whenan accident already happened, a radar system can even detect collisions before they happenand react very early to avoid an accident or minimize the consequences. Systems at the very

early stage of development in the 1970s exceeded the acceptable geometrical product size fora passenger car, the target price for one unit and had a performance which was not yetconvincing enough.

Approximately 20 years later at the beginning of the 1990s this situation changed in manyaspects. Microwave technology was now very much improved concerning cost and

performance and a radar front-end became small enough to be integrated into a car.Additionally cost for processing hardware like DSPs (digital signal processors) decreasedwith still increasing processing power. Small and cheap electronic control units were nowreality as well as the required low cycle times of a few milliseconds for a security system.Earlier experiences were picked up again and a very dynamic market of automotive radar

system development was formed. Today almost all automotive companies and automotivesystem suppliers work on radar systems. It is important to be one step ahead in such a promising market. With a first forward looking 77 GHz pulse radar system of 150 m range,sold in cars since 1999, a leading car manufacturer broke the ice and showed that all key

parameters e.g. like small cost at large volume production, size, performance can be fulfillednowadays and that customers accept the functionality of an adaptive cruise control system asa security and comfort system. Many publications describe the application of radar technologyin modern passenger vehicles to meet the growing interest in security and safety systems.Until today most of the systems are narrow beam long range radars which are capable ofmeasuring even targets of small radar cross section up to 150 m in front of the vehicle. Fromthe complete surrounding of the car only a very narrow section is monitored by these systems.

Requirements for additional and future automotive radar applications (e.g. parking aid, pre-crash, stop & go) cannot be fulfilled by typical ACC radars, due to some system limitations inangular coverage, range accuracy and range resolution, respectively. For this reason acompletely new automotive radar system development has been started years ago based onhigh powerful short range pulse radar sensors in the 24 GHz domain. These sensors aredistributed in the front bumper for example and measure target range with very high precisionin a large angular observation area. A central processor reads all sensor target lists andcalculates the complete object positions in multiple object situations by multilaterationtechniques. As a contribution for further improvement in future automotive radar applicationsthis thesis describes the implementation of a short range radar sensor network in the 24 GHz

domain and discusses some key topics of the system design. This work should encourage tofurther improvement of these radar networks. It is quite sure that after showing feasibilitywith one of the few worldwide first working systems of this radar network type described in



2

this thesis, large volume production of very similar radar networks will be started. Such a newsystem approach with its advantages can even support ACC radars in the short range up to20 m or may be introduced to the market as a multifunctional radar system for the short rangeof passenger cars or trains.

The radar network described in this thesis is based on short range radar sensors of very highrange resolution and accuracy. By means of ultra-short pulses of a pulse length below 1 ns,technically achieved by high speed switches, a range resolution of a few centimeters can berealized. Range accuracy is below 3 cm (≈0.15%) for all targets in a maximum range up to20 m. Due to the fact that the technology is very cheap, numerous of these small sensors can

be integrated into a single car and connected to a network of sensors surrounding even thecomplete vehicle. Radars of this performance were never used before in a sensor network forautomobiles and a network of this kind is also a very new development.

An experimental vehicle was equipped with this type of radar network of four sensorsintegrated into the front bumper to get experimental experiences with such a new radar system

in real traffic situations. Different applications were tested with the presented radar system.Many parking aid and stop & go situations were tested and data files were recorded to achievefurther improvements in the laboratory. The experimental vehicle is additionally equippedwith an electronic brake and a cruise controller to use the system for adaptive cruise control.Algorithms for distance and velocity control are integrated into the radar network processingand tested in normal traffic situations. A system description and technical descriptions of veryuseful measurement equipment are included in this work to show important tools for anefficient system development. Theoretical aspects e.g. about velocity measurement with theused sensors are explained and ideas for further system improvements are developed. Theobjectives of this thesis are a radar network description, quantitative simulation andexperimental results to validate the system concept and to show the high potential of the radarnetwork for future automotive applications.



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2 An Automotive Radar Network based on Short Range Sensors

This thesis is based on applications of automotive microwave radar sensors and this chaptershows some general aspects of sensor network design for use in a vehicle bumper as an

automotive short range sensor network. A radar network based on short range radar sensorswith wide coverage in azimuth angle and a maximum range up to 20 m shows additionalimportant features not yet introduced into automobiles. When planning a sensor network tocontribute to the mentioned applications, several questions rise and will be discussed in thefollowing chapters. Publications on short range radar networks can be found in [KLO99],[KLO00] and [MEN00].

2.1 Radar Network Description

The general idea of a radar network for automotive applications is to surround a vehiclecompletely with very small and cheap, but quite powerful radar sensors to build a kind ofsafety shield around the vehicle which means that e.g. up to 16 single radar sensors arerequired (Fig. 2-1) to develop a 360 degree protection for each individual car.

The radar sensors must not be uniformly distributed around each car. Fig. 2-2 (right side)shows the result of a long term statistic taken from [ULK94] and describes the percentage ofwhich parts of a vehicle are mostly involved in car accidents. The percentage of accidents of

passenger cars depends very much from the different directions. The vehicle front side and thefront corners are the most critical directions for possible impacts, but also a wider coverage upto a system surrounding the complete car can be of importance. All radar sensors have a very

wide opening angle in azimuth of approximately ±30 degrees and the sensor beam patternsoverlap each other to enable angle estimation of detected obstacles by means of rangemeasurements. According to [IEEE96] the correct term for this processing scheme ismultilateration.

Multilateration (as defined in [IEEE96]):

“The location of an object by means of two of more range measurements from different

reference points. It is a useful technique with radar because of the inherent accuracy of

radar range measurement. The use of three reference points, trilateration is common

practice.”

Surrounding the complete vehicle with a multifunctional radar network is a challenging newidea which can be realized today at affordable cost. The vehicle front side can be covered byintegrating four forward-looking radar sensors within the front bumper and one additionalradar sensor on each front bumper corner especially for supporting cut-in collision warningsituations. That means and results into a total number of six sensors integrated into the front

bumper. Three sensors to each side can be used for pre-crash and blind spot detection. Thatmeans one subsystem of three sensors on each vehicle side. In the rear bumper four sensorsfor parking aid and rear-end collision warning should be sufficient. The sensors can begrouped into subsystems. All subsystems can be handled separately to divide the complete

processing into independent parts. The radar signal processing part in each radar sensor will

be the same and the interface between radar sensors and the radar network processor will bedescribed by target lists containing range and if possible velocity of each detected target. Thesignal processing procedure in each radar network subsystem will be nearly the same fordifferent radar sensor settings and consists mainly of data association and multilateration



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processes and target tracking procedures. Although the developed radar sensor networkconsidered in this thesis consists of an equipped front bumper with four individual radarsensors in the 24 GHz domain, it is possible to validate the complete functionality of futureautomotive applications. A system of four sensors showed to be an excellent platform forexperiments and feasibility studies. Practical experiences at the Technical University of

Hamburg-Harburg showed the high potential of new radar technology in the 24 GHz domainfor future automotive applications. All analytical results can be validated by the experimentalcar equipped with a first radar sensor network integrated into the front bumper.

Front Subsystem

LeftSubsystem

RightSubsystem

Rear Subsystem

Fig. 2-1: Sensor network with four subsystems monitoring the complete car environment

With increasing use of cheap and flexible embedded systems in all aspects of modern life, thenumber of used microprocessors in vehicles is also still increasing. New applications toincrease passenger safety and comfort are nowadays possible with cheap and powerfulcomponents and therefore of economic interest for automotive companies. These new car

applications of radar sensor technology in automobiles are defined today and theirrequirements are discussed and specified by automotive companies. Even very complex streetsituations can be handled with additional sensors, more applications can be introduced intothe vehicle and a wide field of view around the vehicle can be monitored. Sensors like videocameras, infrared lasers, ultrasonic sensors or microwave radar sensors are in discussion to beused in vehicles. All of them have their own advantages and disadvantages and are able tocontribute information to a data fusion processor for traffic situation assessment. Microwaveradar sensors in general show different advantages making them attractive for automotiveapplications. These are:

• A distance measurement can be accomplished with high precision.• The sensors are capable of measuring relative velocities.• The sensors are capable of detecting multiple targets.





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Sensor 1

(x1,y1)

Sensor 2(x2,y2)

Sensor 3(x3,y3)

Sensor 4(x4,y4)

L1L1

L2 L2

DSP 1

Radar decision unitCAN 1

CAN 2 CAN 3

CAN 4

CAN

Application

DSP 2 DSP 3 DSP 4

Fig. 2-3: Network implementation in the experimental vehicle

2.2 Automotive Applications and Radar System Requirements

Starting with an explanation of future automotive radar applications, the system requirementswill be discussed in this chapter.

2.2.1 Applications

The current status of modern commercially available automotive radar systems coversadaptive cruise control applications for highway traffic situations. Numerous automobilemanufacturers and automotive part suppliers as well as RF part producers are engaged in thisdevelopment and try to bring their products to the market or are at least interested in themarket development to keep up with their competitors. Large volume production will one day

be the future of automotive radar systems which cover many different applications.

A multifunctional sensor system is able to detect the complete surrounding of the vehicle asshown in Fig. 2-2 (left figure). Due to the very wide field of view of the individual sensors,their maximum detection range has to be kept low up to e.g. 20 m. A multifunctional radarsensor network is able to support parking aid, pre-crash, stop & go applications for example

and can also support the long range ACC radar in the near distance area with large angularrange. But it is absolutely clear that this radar sensor network should not be seen as areplacement of an ACC radar system due to very different properties.

Possible applications of a short range radar network are illustrated in Fig. 2-2 (left figure).The different applications can be characterized as follows:

Parking Aid:

As a comfort application for the driver and to increase security for people walking onthe streets the use of a high range resolution radar network for parking aid applicationsshould be mentioned. The demands on system reliability and safety is not as high as in

the other applications. A replacement of today’s ultrasonic sensors by amultifunctional radar sensor network with more potential and better performance is theidea. It is intended to warn the driver in situations at very low vehicle speed. An



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acoustic warning can be initiated if the distance between the vehicle and an obstacle orhuman being is below a critical value. An optical display is useful to display directionof an obstacle and exact distance between vehicle and obstacle. Active braking is

possible to prevent the vehicle from hitting obstacles or injuring people in parkingsituations.

Stop & Go:

The warning of or reaction on cut-in collisions is a significant task for adaptive cruisecontrol systems. Vehicles cutting in from adjacent lanes have to be detected very earlyto reduce speed in time. In very dense traffic situations this application can surelyreduce a large amount of accidents.The support of a long range radar sensor for adaptive cruise control and CA (collisionavoidance) is possible. Long range radars show limitations e.g. in their angularcoverage in azimuth. With such very narrow beam radars it is usually not possible tomonitor the vehicle front corners which are also critical directions for accidents (Fig.2-2). Range accuracy and resolution in the very near range in front of the vehicle are

also better if high resolution radars are used.

Blind Spot Surveillance:

Overseeing passing vehicles or vehicles on adjacent lanes by an inattentive driver can be avoided by a blind spot detection function of the sensor network. At least anacoustic warning for the driver in a critical situation would be very helpful.

Rear End Collision Warning:

Rear end collision warning can also be used like all other applications to initiatesystem reactions early in case of an accident, e.g. activating the airbags inside thevehicle or the brakes if a collision with a fast vehicle from the back can not beavoided. This application can be seen as a special case of a complete pre-crash systemmonitoring only the rear of the car.

Pre-Crash:

Last but not least the application of a radar sensor network surrounding the vehicle fora so-called pre-crash application is an important development target of such a network.The main idea is to react very fast with a pre-crash sensor network and activate allnecessary active components (brakes, or even steering) in the car to avoid an accidentor at least minimize consequences of an impact with reduction of the vehicle’s kineticenergy. Early activation of airbags is very important.

When talking about a sensor network it is not yet clear how many sensors are really requiredto cover the complete surrounding of a passenger car and manage all the mentionedapplications. For the sensors used in this thesis a number of up to 16 sensors was discussedfor a complete multifunctional high resolution short range radar network. This large numberof sensors raises immediately the question how much a single sensor can cost to be still cheapenough to be introduced into such a network assuming mass production of millions per year.The prize for a single sensor can not be more than a few dollars, otherwise the completesystem will be too expensive for the market and would not be accepted by the customer.



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2.2.2 Requirements for a Short Range Radar Sensor Network

For all applications described above, automotive companies have already developed specificrequirements for the radar sensor networks which should be fulfilled. The following aspectsand numbers give an overview to understand the main requirements for the specific

applications and should give an overview about the technical challenge. All applicationsevolve different system dynamics and situations and therefore different requirements. A goodsurvey for long range and short range sensor requirement suggestions and differentapplications independent from the specific form of a radar system realization is also given in[MEN99]. In each application case the technical requirements are separated into range,velocity and azimuth angle estimation accuracy and resolution. Additionally the cycle time isan important requirement.

Accuracy and resolution for distance, velocity and angle are defined as follows:

••

••

••

Distance accuracy is the absolute accuracy of a distance measurement.Distance resolution is the ability to distinguish between two targets in a two targetsituation only by range measurement.Velocity accuracy is the absolute accuracy of a relative velocity measurement.Velocity resolution is the ability to distinguish between two targets in a two targetsituation only by velocity measurement.Angular accuracy is the absolute accuracy of an angle measurement.Angular resolution is the ability to distinguish between two targets in a two targetsituation only by angle measurement.

For different applications Table 2-1 shows suggested realistic requirements. The main items

are update rate (cycle time), distance, velocity and azimuth angle. The values for parking aid,stop & go / ACC support and pre-crash detection are assumed for a system installed in avehicle’s front bumper. Blind spot surveillance is seen as a mere presence detection to thevehicle sides and low requirements on distance accuracy are assumed. Some values are seenas not required in this table.

A parking aid needs low update rates due to very slow movements. Velocity is unimportant inthis case, but a wide angular range in azimuth has to be covered with limited accuracy e.g. fora bargraph display as man-machine-interface. Distance accuracy to the nearest object is themost important information. Distance resolution of targets in multiple target situations is lessimportant.

The stop & go / ACC support update rate of a sensor network has to be as high as the updaterate of an ACC radar sensor, i.e. 10 - 20 ms. Distance measurement parameters are similar tothose of an ACC system. For correct distance control a wide range in velocity has to becovered with good precision and a wide area in azimuth angle as well. The most importanttask is to identify a vehicle lane position correctly for ACC support in normal traffic and stop& go situations. Accidental braking for vehicles in adjacent lanes has to be avoided. Twovehicles or objects on both adjacent lanes to the own vehicle’s lane at same distance have to

be identified as different objects (angular resolution in azimuth).

Pre-crash is used for very fast initiation of security mechanisms (e.g. airbag). To reactefficiently, the cycle time has to be very low. Parameters resemble those of ACC support dueto very similar assumed situations.



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Blind spot surveillance as a mere presence detection (see also [REE98]) with limited distancemeasurement performance does not require velocity and angle measurement.

Parking Aid Stop & Go /

ACC Support

Pre-Crash Blind Spot

Surveillance

Cycle Time [ms] 100 10 – 20 5 100

Distance:

Range [m]Accuracy [m]Resolution [m]

0.05 - 50.05n. r.1

0.5 - 200.51

0.5 - 200.51

0.2 – 50.5n. r.

Velocity:

Range [km/h]

Accuracy [km/h]Resolution [km/h]

n. r.

n. r.n. r.

-360 … +180

15

-360 … 0

15

n. r.

n. r.n. r.

Azimuth Angle:

Range [°]Accuracy [°]Resolution [°]

-90 … +905

n. r.

-60 … +6025

-60 … +6025

n. r.n. r.n. r.

Table 2-1: Suggested realistic system requirements for different applications

2.3 Advantages of a Sensor Network

The use of a multiple sensor network has some advantages compared to the use of a singleintegrated sensor, but it also evolves additional practical issues, a system designer has toconsider when choosing a sensor network architecture. The advantages of a multiple sensornetwork using the described sensor technology are as follows:

1. Very high resolution pulse radar sensors with only a single beam frontend and wideangular coverage in azimuth are described in chapter 3. These sensors are only able tomeasure multiple target ranges with high accuracy and high resolution. Only presence

detection and radial range measurement is possible, but no angular information can beobtained with a single sensor. In a network, a target angle can be calculated by using morethan one sensor in a data fusion processor which combines measured target information(e.g. propagation delay times).

2. The use of a sensor network improves situation assessment capabilities.3. A broader coverage in azimuth can be achieved. So the field of view in front of a vehicle

can cover the front and also the vehicle corners.4. The estimation of target state variables with higher precision is possible if information of

e.g. four sensors is used (see e.g. chapter 4.3.1).5. The number of false tracks can be reduced although the individual sensor’s false alarm

rate may be high. An example is a possible stochastic interference between sensors which

1 n. r.: not required



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can cause false alarms in the single sensor detection algorithms, but not false tracks at theoutput of the data fusion.

6. The suppression of single sensor false alarms by the data fusion allows a reduction ofdetection thresholds within the separate sensor detection algorithms. The result is anincrease in sensitivity when using a sensor network compared with using a single sensor.

Thresholds can also be adapted by the data fusion algorithms or high-level processing inthis case.7. Having redundancy in the system allows the implementation of self-diagnosis routines in

each sensor and in a central processor by comparing the individual results.8. A failure of a single sensor in a network of four sensors reduces the system performance,

but practical tests showed that it can still produce acceptable results. Nevertheless withmore than one broken sensor of four the resulting level of reliability is not any moreacceptable and the system must be switched off.

All these considered arguments are advantages and emphasize the positive aspects of using asensor network instead of a single sensor. On the other hand many additional practical issues

have to be taken into consideration when planning an automotive sensor network:

1. The sensor network time synchronisation is an important aspect for target state estimationand filtering. In many cases asynchronous data and data transfers have to be handled.Delay times are especially important when short system cycle times are asked.

2. Distributed sensors in a network need communication interfaces, i.e. additional electronicsand cabling. Field bus solutions (e.g. CAN [ETS00]) are nowadays widely used invehicles.

3. To minimize data transfer rates within the network it is important to find out where and towhich minimum the transfer rate can be reduced without serious performance degradation.

4. Depending on the used sensor, alignment and recognition of misalignment can beimportant.

5. The positions of the sensors e.g. on a vehicle bumper effects the performance and must beknown very precisely to guarantee precise angle estimation results.

6. Possible crosstalk and undesired microwave propagation behind a vehicle bumper must beavoided.

7. Computation complexity is increased in a sensor network. All sensor signals have to beevaluated and a data association and fusion has to be performed. Which is the optimalallocation of processing resources within the network?

8. Which is the preferred network structure? Complexity should always be kept as low as possible. A high number of components and increased system complexity reduces the

mean time between failures and in automotive applications also the price constraints haveto be met.9. Integration space in modern vehicle bumpers is very small. The number and size of

components both have to be small.10. The quality of the sensors should be similar. This assumes very precise reproducibility in

large volumes. Otherwise differences have to be considered in the signal processing.

2.4 Required Range Measurement Accuracy for Multilateration

There are different ways for target angle estimation using radar sensors. [WAG97] presents an

interesting overview of angle estimation techniques. Some interesting concepts make use ofmechanically scanning sensors, e.g. [ERI95] showing a forward-looking ACC radar with wideangular coverage in azimuth. While mechanically scanning concepts are viewed skeptically



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by automotive companies, electronically scanning systems are too expensive for automotiveapplications. In the network discussed in this thesis an estimation of object angles is achieved

by multilateration techniques based on target range information only. This requires very precise range measurement of each individual sensor. Fig. 2-4 shows a single objectmultilateration situation. Four sensors measure different ranges between the sensor positions

as reference points and the obstacle. From each sensor the true object position is assumed to be located on a circle around the sensor with the radius being the measured range. Rangemeasurement with high precision is absolutely required for precise estimation results. Thefollowing simple analysis shows the required accuracy of range measurement to be achieved

by a single sensor in the network.

R 1

R 2 R 3

R 4

Sensor 1Sensor 2 Sensor 3

Sensor 4

1 23

4

Fig. 2-4: Multilateration situation with a single object

By considering a system of two sensors, the angle error due to an error in range measurementis observed first (Fig. 2-5). The range measurement error (ε 1 for sensor 1 and ε 2 for sensor 2)assumed in this calculation is ±10 cm for both sensors. The resulting maximum object angleerror is approximately 24 degrees. Obviously small errors in the measured range result inlarge errors for the object angle. The sensor distance d of 50 cm is taken from an experimental

bumper as a realistic value. For a distance r = 10 m in front of the sensors the equations forthe object position including errors ε ( oo y x , ) 1 and ε 2 are:

( )

d

r y

o 2

2 22

2121

−

−+−=

ε ε ε ε

( )

2

0

2

1 2

−−+= yd

r xo

ε

(2-1) 22

11

ε

ε

+=

+=

r R

r R

Due to the fact that the lateral distance error depends not only on the error of azimuth angle,

but also on the longitudinal distance of an object, Fig. 2-6 is shown to give a brief overview ofthe quantities. Fig. 2-7 shows the lateral distance error as a function of the object angle errorfor different distances.



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d=50cm

R 1 R 2

Fig. 2-5: Error of object angle using only two sensors

Fig. 2-6: Lateral distance error as a function of longitudinal and angle error

Simple calculations show that for a maximum sensor range error of 3 cm in a situation whereonly two sensors detect the object, the lateral error at a distance of 10 m is approximately60 cm. The error in azimuth angle is approximately 3.4°. For this reason the single sensorrange measurement accuracy should not be worse than 3 cm. In a network with more than twosensors detecting the object, accuracy can be significantly improved by the existingredundancy. In Fig. 2-8 the inner sensors in the network measure with an error of up to±10 cm while the outer sensors measure the correct distance. The results can be comparedwith Fig. 2-5 showing that the error of the object angle is significantly reduced with a

nonlinear least squares solution of four sensors (see chapter 4.3.1).



13

Fig. 2-7: Lateral distance error as a function of angle error

4 d=50cm

R 1 R 2 R 3 R 4

S1 S2 S3 S

Fig. 2-8: Sensor network accuracy with distance errors up to ±10cm of only two sensors

2.5 Positioning of Sensors

The sensor mounting positions on a vehicle bumper have an influence on the measurementaccuracy and on the system performance. To decide where to locate the sensors, the followingaspects have to be considered:

• For a parking aid system blind spots between sensors in front of the car or in the rear haveto be avoided. A target might not be detected if the vehicle stands e.g. very close to a polethat is at a position where the adjacent sensor’s antenna patterns do not reach it. To findout where detection gaps might occur, the antenna patterns are important.

• The sensor constellation effects the accuracy of a nonlinear least squares positionestimation (see chapter 4.3.1).



14

• If only a subset of sensors detected the target, the results are different from the case thatall sensors detected the target. It is obvious that with more information and evenredundancy precision of results can be improved.

For a system consisting of four radar sensors (see Fig. 2-9) the accuracy to be expected with

modelled sensor properties will now be evaluated. The distance of the outer sensors is bestchosen to be as large as possible to minimize the angle estimation error and symmetric to thevehicle axis. The inner sensors are also assumed to be symmetric to the vehicle axis. It is nowimportant to know which value for the distance of the inner sensors L x is the best selection toachieve a minimum angle estimation error. Additionally it is interesting how the resultsdepend on the position of the detected object in the systems field of view.

The following assumptions are made:• The outer sensors are located at L1 = 60.5 cm from the center line like in the real equipped

bumper of the experimental vehicle.• The sensors are assumed to measure the target ranges with uncorrelated Gaussian

distributed noise of variance 5 cm.• It is assumed that all sensors detect the target in each cycle.


Sensor 4

L1L1

LX LX

Fig. 2-9: Bumper geometry

The sensor distances L x from the center line were varied from 5 cm up to 60 cm with steps of5 cm. The object whose position has to be estimated was assumed to be at 15 m with adistance to the center line of 0 m, 5 m and 10 m. A set of 10000 quadruples of measurementswas generated for each situation and after calculation of the object’s least-squares positionsolution the standard deviation of the estimated angles distribution was evaluated. The resultsare shown in Fig. 2-10. A minimum of the estimated angle’s standard deviation is reached ifthe sensors are at 60 cm from the center line. But this result assumes that all sensors detect thetarget. With two sensors at 60 cm on both sides a passed car on the right side would e.g. only

be detected by the two sensors on the right side. In this case an angle estimation only by

evaluation of measured distances is impossible. For a real system the distance L x has to bechosen to be between 20 cm and 30 cm. In this case an angle estimation of an object on theside that was only detected by the two sensors on this side is still possible.

Fig. 2-10 also shows that the estimated angle’s standard deviation is smaller for objects beingdirectly in front of the vehicle and bigger for objects on the side of the lane. This wasrecognized under the assumption that the distance x in front of the vehicle remainsunchanged.



15

0 10 20 30 40 50 602.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

Distance from center line [cm]

S t a n d a r d d e v i a t i o n o f t h e c a l c u l a

t e d a n g l e [ ° ]

Standard deviation of the calculated angle

0m

5m

10m

Fig. 2-10: Standard deviation of the calculated angle with variable target distance to the vehicle

center axis



16



17

3 Single Sensor Signal Processing for Pulse Radar Sensors

High range resolution radar sensors were used in an experimental system described in thisthesis. The sensors use ultra-short pulses below 1 ns length to achieve a high range resolution

of a few centimeters. The following chapters first describe a standard processing strategy for pulse radars and then the signal processing for the used sensors and a description ofthemselves. Aspects of a variable transmit pulse width are discussed as well as possibilities tosuppress interference effects between sensors if more than one is used in a network. The mainobjective for a single radar sensor is the simultaneous range and Doppler frequencymeasurement even in multiple target situations.

3.1 Standard Processing Scheme for Simultaneous Range and Doppler

Measurement

The basic processing of most pulse radar sensors is quite simple, but requires many Fouriertransforms to be processed for Doppler frequency measurement in each range gate. Usually acomplex processing is preferred using an inphase and quadrature sampling. The transmittedcoherent pulse train is received in the receiver and converted with a cosine signal and a sinesignal taken from the cosine carrier signal phase shifted by 90°. The received RF signal withthe pulsed envelope p(t) can be described as:

with: ( ) ( ) ( )[ t t f t pt u C R ϕ π +⋅= 2cos ] ( ) t f t v

t Dπ λ

π ϕ 22

2 =−= (3-1)

The received signal is then multiplied by a cosine and a sine function in the mixer of thequadrature demodulator:

(3-2) ( ) [ t f t u C C π 2cos= ] ]( ) [ t f t u C S π 2sin=

( ) ( ) ( ) ( )[ ] ( ) ( )[ t t pt t f t pt ut u C C R ϕ ϕ π cos2

122cos

2

1++= ] (3-3)

( ) ( ) ( ) ( )[ ] ( ) ( )[ t t pt t f t pt ut u C S R ϕ ϕ π sin

2

122sin

2

1++= ] (3-4)

After low-pass filtering and sampling with the pulse repetition frequency f PRF the two signalslook as follows:

Inphase signal: ( ) ( ) [ n Dnn t f t pt I π 2cos2

1= ] (3-5)

Quadrature signal: ( ) ( ) [ n Dnn t f t pt Q π 2sin2

1= ] (3-6)

The following baseband signal processing is now continued with complex values:



18

(3-7) ( ) ( ) ( )[ ] ( ) ( )( ) ( ) ( n Dnnnnnn t f jt pt jt pt jQt I t h π ϕ 2expexp2 ==+= )

with: ( ) ( ) ( )nnn t Qt I t p 222 +⋅= and ( ) ( )

( )

=

n

nn

t I

t Qt arctanϕ (3-8)

Fig. 3-1 shows the standard processing for pulsed radars. Depending on the type of radar andits pulse repetition frequency (LPRF, MPRF or HPRF) the sampling frequency is set and allrange gates are sampled in an inphase and a quadrature channel in one complete scan. For asingle range gate the DFT (discrete Fourier transform) is calculated using an implementationof the FFT (fast Fourier transform) (see also [BRI74]).

R a n g e G a t e

123

n

n-1

Inphase

Quadrature

1 2 3 NTime cycle

Fast

Fourier

Transform

R a n g e G a t e

123

n

n-1

Doppler Frequency Binf 1 f 2 f 3 f N

Detections

Fig. 3-1: Signal Processing of a Pulse Radar

The complex discrete Fourier transform

( ) ( )∑−

=

−=1

0

2exp

1 N

n

nm n M

m jt h

N f H

π (3-9)

performs a transformation from N samples of h(t n ) inside a single range gate to M=N discretefrequencies with . The results for one complete measurement cycle is a

matrix of range gates and Doppler frequencies. Window functions are very common forsidelobe suppression when calculating the Fourier transform. After application of detectionalgorithms to each individual range gate, targets can be detected and their velocity can becalculated from the Doppler frequency. As detection algorithms for the Doppler spectrum OS-CFAR (

m f 1,,1,0 −= M m K

ordered-statistic constant false alarm rate) algorithms ([ROH83]) or other CFARalgorithms are usually applied.

It has to be mentioned that in many radar systems the received baseband signal is sampled

with a sampling frequency of P

sample T f 1= with pulse length T P . Due to the extreme short

pulses of the radars used in this thesis, the baseband signal is sampled with a sampling



19

frequency which is much lower. The measurement principle described in the next chapterexplains why this is necessary.

3.2 Processing of a High Range Resolution Radar with Ultra-Short Pulses

A short description of the measurement principle is important to understand how ultra-short pulses are generated in HRR (high range resolution) radars of the used type and how the processing effort, especially the A/D-converter sampling frequency, can be kept very lowwith high range resolution. The subchapter about detection and range measurement coversmedian filtering techniques for time signal baseline estimation and application of OS-CFARalgorithms for target detection. Velocity measurement by Doppler frequency processingusually involves high computation effort if the number of range gates is high. This is the caseif the range gate size is very small due to very short transmit pulses. Approaches for Dopplerfrequency measurement are analysed considering feasibility with limited processing powerand measurement time.

3.2.1 Measurement Principle

The hardware structure of the sensors used in this work is described in [WEI98] and alsoshown in Fig. 3-2. For the RF source a 24 GHz DRO in the ISM band was chosen. The poweris split into transmit and receive path and two high speed GaAs Schottky switches are used in

both paths. The pulses are initiated by a 4 MHz PRF oscillator and trigger the pulse generatorswhich consist of two SRD (step recovery diode) networks. In order to be able to scan thecomplete area of measurement the trigger pulses for the Schottky switches in the receive path

can be delayed by an adjustable delay. With a specific delay time corresponding to a specific propagation distance an associated range gate can be set for measurement. With a sweepingdelay time the complete measurement range can be swept e.g. from minimum to maximumrange. The simplicity of the hardware concept requires a long time for one complete scan. Themeasurement time can be reduced by processing the complete range in parallel channels withdifferent fixed base delays and an additional variable delay. A reduction to half of themeasurement time requires therefore almost twice the hardware components for the secondreceive path. A measurement range from 0 m up to 20 m can then be separated into twosections, one from 0 m up to 10 m and the second from 10 m up to 20 m.

The delayed pulses in the receive paths are applied as LO pulses to the sampling phase

detectors of an inphase and a quadrature channel and the IF outputs result only in the case thatLO pulses are coincident in time with received RF pulses. In the quadrature channel thecarrier wave pulse is shifted in phase by 90°. The IF output results are integrated to increasethe signal to noise ratio. Using an inphase and a quadrature component of the receive signalensures a stable amplitude which is independent from the signal phase.

The sensor antennas are separated 6x1 patch arrays for the transmit and the receive side. Theelevation 3 dB-beamwidth is concentrated to approximately 13 degrees while the azimuth

beam is very wide to ensure a very wide field of view for the sensor in a limited short range.





21

cmT c

R P 62 =

⋅=∆ (3-10)

Range accuracy can be even better with application of a so-called center of mass algorithm. In

this case a range accuracy of 2 cm and better is realistic. The maximum range forunambiguous range measurement depends on the pulse repetition frequency and is in this case(with 4 MHz ):

m f

c R

PRF

5.372

max =⋅

= (3-11)

To have a comparison, the required sampling frequency of an A/D-converter with a normal pulse radar for very short pulses of 400 ps would be too high for a realistic commercialsensor. The converter frequency would in this case be 2.5 GHz . The chosen measurement

principle shows to be a very feasible way to keep effort as low as possible with high sensor performance. In the case of an FMCW radar the required bandwidth to achieve the samedistance resolution of 6 cm would be:

GHz R

c f FMCW sweep 5.2

2, =

∆⋅= (3-12)

The key features of the sensors taken from [WEI98] are listed in Table 3-1 and Fig. 3-4 givesan impression of the absolute value of the output signal taken from the inphase and quadrature

IF output channels. Amplitude versus distance is shown.Parameter Min. Typ. Max. Unit

Range 0.15 20 meterSweep Time 1 20 msecPulse Width 300 350 400 psecDuty Cycle 0.175 %Avg. Power -22 -20 -19 dBmPeak Power 4 5 6 dBm

Table 3-1: Main sensor features



22

200 400 600 800 1000 1200 1400 1600 1800 20000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Distance to Target [cm]

A m p l i t u d e [ V ]

Amplitude: Two closely spaced reflectors

Fig. 3-4: Laboratory situation of two close objects

The following equations give an analytical representation of the sensor signals. The sensortransmit signal consists of the pulsed carrier frequency:

( ) ( ) ((

−∗

⋅+⋅=

∑

+∞

−∞=n PRI P

C T

nT t T

t rect t f At s δ ϕ π

0

2sin )) (3-13)

with:

T A : amplitude of single transmit pulse

C f : transmit frequency (24.125 GHz )

0ϕ : transmit signal phase

P T : pulse width (approximately 400 ps)

PRF PRI f

T 1= : pulse repetition interval (250 ns)

PRF f : pulse repetition frequency (4 MHz )∗ denotes a convolution

A target within the sensor’s field of view is located at range r 0 and moves at time ofmeasurement with a nearly constant velocity v during the measurement interval. The range is:

(3-14) ( ) t vr t r ⋅+= 0

After a propagation time of( )

c

t r ⋅2 the signal received at the sensor can be described as

follows:



23

( )

( )

((

−∗

⋅−

⋅

+−−⋅= ∑∞+

−∞=n

PRI

P

C C C E nT t

T

c

t r t

rect c

r f t

c

v f t f At e δ ϕ

π π π

ϕ

244

2sin

1

00

4 4 34 4 21)) (3-15)

with:signalreceiveof phase :

signalreceiveof amplitude :

1ϕ

E A

The Doppler frequency in the signal is:

c

vf f C

D

2−= (3-16)

The receive signal phase changes due to a relative velocity to:

c

r f C 001

4π ϕ ϕ −= (3-17)

If only a single pulse at n=0 is considered, the equations for transmit and receive signals aresimplified:

( ) ( )

⋅+⋅= P

C T T

t

rect t f At s 02sin ϕ π (3-18)

( ) ( )( )

( )

⋅−

⋅++⋅= P

DC E T

c

t r t

rect t f f At e

2

2sin 1ϕ π (3-19)

The transmit signal pulse delayed by a variable time t d for the conversion process in theinphase channel and in the quadrature channel is:

( ) ( )

−⋅+⋅=

P

d C T d I d

T

t t rect t f At t s 0, 2sin, ϕ π (3-20)

( ) ( )

−⋅+⋅=

P

d C T d Qd

T

t t rect t f At t s 0, 2cos, ϕ π (3-21)

A simplified result of the conversion process in both channels is:



24

( ) ( ) ( )

( ) ( )( )

( )

( ) ( )( )

( )

⋅−

⋅

−⋅

+++−+−⋅

=

⋅−

⋅++⋅⋅

−⋅+⋅

=⋅=

P P

d

C C D E T

P

DC E

P

d

C T

d I d I

T

c

t r t

rect T

t t rect t f t f t f A A

T

c

t r t

rect t f f AT

t t rect t f A

t et t st m

2

24cos2cos2

1

2

2sin2sin

,

1010

10

,

ϕ ϕ π π ϕ ϕ π

ϕ π ϕ π

(3-22)

( ) ( ) (( ))

( )

⋅−⋅

−⋅

+++++−⋅=

P P

d

DC D E T Q

T

ct r t

rect T

t t rect

t f t f t f A At m

2

24sin2sin2

11010 ϕ ϕ π π ϕ ϕ π

(3-23)

The product is only unequal zero in the following range for the signal delay time:

( ) ( ) P d p T

c

t r t T

c

t r +<<−

22

If only the situation at ( )c

t r d

2=t is considered, the signals are:

( ) ( ) ( )( )

( )

⋅−

⋅

+++−+−⋅= P

DC D E T I T

c

t r t

rect t f t f t f A At m

2

24cos2cos2

11010 ϕ ϕ π π ϕ ϕ π (3-24)

( ) ( ) ( )( )

( )

⋅−

⋅

+++++−⋅= P

DC D E T QT

c

t r t

rect t f t f t f A At m

2

24sin2sin2

11010 ϕ ϕ π π ϕ ϕ π (3-25)

After analog integration and low-pass filtering the signals are the baseband sensor outputsignals which can be directly processed by the digital signal processor.

3.2.2 Detection and Range Measurement

Detection and range measurement are the main tasks of a single sensor. Detection meansalways a trade-off between a maximum of probability of detection and a minimum of the

probability of false alarms. The following pages outline these topics for the specific sensorconcept applied in the sensor network.







27

inphase and quadrature signal for each range gate. Before detection, the signal offset wasremoved from the curve of absolute values by median filtering. All 64 values were sorted,amplitude at rank r selected and multiplied by a factor. This method of threshold calculationwithin each single cycle showed to be a good compromise between low effort and robustdetection properties. For an automotive radar application typical clutter scenarios like clouds

in weather radars or airborne systems were not observed. Thus a sliding window for the OS-CFAR threshold calculation is not absolutely required.

3.2.3 Simultaneous Range and Velocity Measurement

To calculate a target Doppler frequency by FFT (fast Fourier transform) equidistant samplesfor the range gate under test have to be acquired. The general processing technique isexplained in chapter 3.1. Each range gate is sampled over time. If enough samples arecollected, i.e. the measurement time is long enough to achieve the required Doppler frequencyresolution, the complex FFT can be calculated and the resulting Doppler frequency spectrum

can be used for target detection and velocity measurement. This can be done for all rangegates separately involving a high computation effort. Especially for a cheap high rangeresolution sensor with a large number of range gates and a digital signal processor of medium

performance, the effort can be too high. This chapter discusses methods for velocitymeasurement for the used high range resolution sensors. Appendix C gives examples ofmemory and timing requirements for a cheap 16 bit fixed-point processor.

Important design parameters are the velocity range to be expected, the maximum Dopplerfrequency to be expected, the A/D-converter sampling frequency, velocity resolution andDoppler frequency resolution which determine the measurement time.

The required sampling frequency depends on the Doppler frequency range which correspondsto the relative velocity range to be covered. The relation between Doppler frequency andrelative velocity is:

c

vf f C

D

2−= (3-29)

with v being the relative velocity, and f C is the transmit carrier frequency.

Assuming a maximum relative velocity of 180 km/h (= 50m/s), the maximum Dopplerfrequency is:

Hz c

f v f C

D 80422 max

max, == (3-30)

The A/D-converter sampling frequency for a single range gate gets in the case of complexFFT processing using I-Q-channel sensors:

and T (3-31) Hz f AD 8042≈ sµ 3.124= The velocity resolution determines the required Doppler frequency resolution:



28

λ

v

c

f v f C

D

∆−=

⋅∆−=∆

22 (3-32)

For the given maximum relative velocity, the required FFT – length is shown in Fig. 3-7 witha velocity resolution range up to 10 km/h. The required measurement time also depends on thevelocity resolution as shown in Fig. 3-7. For an FFT-length of 32 the achievable Dopplerfrequency resolution, velocity resolution and the measurement time can be obtained by:

ms st Hz Hz

l

f f measure

FFT

AD D 43.12432 3.251

32

8042≈µ⋅=⇒===∆ (3-33)

The velocity resolution is in this case 5.6 km/h. The linear relation between required velocity

resolution and Doppler frequency resolution is shown in Fig. 3-8.

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

40

45

Velocity Resolution [km/h]

M e a s u r e m e n t T i m e [ m s ]

Measurement Time as a Function of Velocity Resolution

Fig. 3-7: FFT length versus velocity resolution and measurement time versus velocity resolution

250

300

350

400

450doppler frequency resolution over velocity resolution

e n

c y r e s o l u t i o n [ H z ]

Fig. 3-8: Doppler frequency resolution as a function of the required velocity resolution



29

3.2.3.1 Processing with Stepped Ramps

A concept with very short sweep voltage ramp signals of 124.3 µs duration over the completerange from 0 m up to 20 m for a maximum Doppler frequency of 8042 Hz is not possible dueto the fact that the time per range gate is too short and the A/D-converter sampling frequency

is high. A stepwise processing of the complete measurement range as shown in Fig. 3-9 seemsto be better, but takes more time for a complete scan. The range is scanned using short rampsto sweep the sensor delay and only a few range gates are covered in a block-wise processingscheme. Fig. 3-9 shows a solution of eight steps to cover the complete range and only fourrange gates per step, i.e. 32 range gates over the complete range. This idea is a compromise

between reduced calculation effort and a reduced range resolution which coincides with areduced number of range gates. It is assumed that real targets will not only be seen in a singlerange gate, but are usually extended targets and distributed over more than one range gate.

Sweep Voltage [V]

measurement time [ms]

0.7

4.2FFT

32 ramps per step with 124.3µs each8 steps with 4 range gates in each one

4ms

2. step3. step4. step5. step6. step7. step

1. step8ms 12

Fig. 3-9: Processing with stepped ramps

For an A/D-converter sampling frequency of 8042 Hz per range gate and a Doppler frequencyresolution of 124.3 Hz which corresponds to a relative velocity resolution of 5.6 km/h, 32samples per range gate are required for the FFT. The resulting total A/D-converter samplingfrequency is in this case:

(3-34) kHz Hz f total AD 168.328042432, =⋅=

With 4 range gates per short ramp and 8 consecutive steps of 32 short ramps per step, a totalnumber of 32 range gates of same size are covered. With a total measurement range of 20 m the range gate size is:

cmcm

R RG 52.6431

2000==∆ (3-35)

One measurement step covers .4.27752.644 cmcm =⋅The total measurement time for the complete range is:

(3-36) ms st total measure 82.313.124328, =⋅⋅= µ



30

That means within two cycles of 20ms each the velocity measurement of the complete rangecould be covered.

The range gate size seems to be very large compared with the range resolution of the sensors,

but it is a good compromise between computation effort and performance. Per velocity scanover the complete range only 32 FFTs of 32 complex values have to be calculated.

The integration time per range gate for a single sample is in both cases:

s s

t µ µ

1.314

3.12432int, ≈= (3-37)

3.2.3.2 Processing with Staggered Ramp Duration

This chapter develops a new concept for velocity measurement using the described high rangeresolution pulse radar sensors. The main idea is to decrease measurement time by measuringvelocity ambiguously. Range is measured unambiguously. So the concept is similar to anLPRF processing scheme with ambiguous velocity and unambiguous range measurement. Inthis special case the pulse repetition frequency is unchanged, but the duration of the sweepvoltage ramp signals for the sensor is staggered in two different steps. Short Fouriertransforms are then calculated for both different sections of ramp durations and ambiguitiescan finally be resolved by known algorithms like the Chinese remainder theorem. Theresolution is a problem of number theory. Some solutions can be found in [ROH86] or

[ROT90]. The basic principle of the sweep voltage applied in this concept is shown in Fig.3-10.

Fig. 3-10: Processing with staggered ramp duration

It is obvious that with a ramp duration of e.g. 1 ms a maximum Doppler frequency of 1 kHz

can be measured unambiguously. For the maximum values assumed above (180 km/h), themaximum Doppler frequency to be measured is 8042 Hz . To get unambiguous results thefollowing processing scheme can be applied:



31

• Control of the sensor with voltage ramps of e.g. 1 ms (16 ramps) and accumulation of 16

samples for each range gate to be examined• Calculation of a short FFT only in relevant range gates for the collected samples yields

Doppler spectrum 1

• Detection in Doppler spectrum 1 by application of an adaptive threshold algorithm (e.g.OS-CFAR)

• Control of the sensor with voltage ramps of e.g. 700 µs (16 ramps) and accumulation of 16samples for each range gate to be examined

• Calculation of a short FFT only in relevant range gates for the collected samples yieldsDoppler spectrum 2

• Detection in Doppler spectrum 2 by application of an adaptive threshold algorithm (e.g.OS-CFAR)

• The two received Doppler values for a target within a range gate are ambiguous.⇒ Resolution of Doppler frequency ambiguity. The results are the Doppler frequencies

of the target detected in the range gate.

To reduce the number of FFTs to be calculated the samples can be examined before atransform to find out relevant range gates including real targets.

Example:

For a short example the following values are selected:• Duration of ramp 1: msT R 11 =

• Duration of ramp 2: sT R µ 7002 =

The sensor is controlled by 32 ramps, 16 of each of both types. So the complete time for onecycle is:

(3-38) ms smst cycle 2.2770016116 =⋅+⋅= µ

The sampling frequency under the assumption that 32 range gates are sampled is:

• for the 1st part with ramps of 1 ms: 32.0 kHz

• for the 2nd part with ramps of 700 µs: 45.714 kHz

The resulting sampling frequency for each range gate is:

• for the 1st part with ramps of 1 ms: 1.0 kHz

• for the 2nd part with ramps of 700 µs: 1.43 kHz

For a Doppler frequency of for example 3.2 kHz , the measured frequencies are e.g. 0.2 kHz and 0.34 kHz respectively. These frequencies can be continued with the sampling frequency,

because this is the frequency range of the FFT. The result is:

• ramp 1: 0.2kHz (1.2kHz 2.2kHz 3.2kHz )

• ramp 2: 0.34kHz (1.77kHz 3.2kHz )

If in each of both series the same Doppler frequency is found, the corresponding frequency isthe result of the ambiguity resolution algorithm. Some ideas how these ambiguities can beresolved are described in the Appendix. With an FFT of length 16 the Doppler frequencyresolution and the velocity resolution can be calculated for both parts:



32

• ramp 1: Hz kHz

l

f f

FFT

AD 5.6216

1===∆

h

km

s

m

f

c f v

C

4.139.02

==⋅∆

=∆ (3-39)

• ramp 2: Hz kHz

l

f f

FFT

AD

8916

43.1===∆ h

km

s

m

f

c f v

C 255.02 ==

⋅∆=∆ (3-40)

It can be seen that a high velocity resolution can also be achieved with this method althoughthe measurement time and the A/D-converter sampling frequency are acceptable low.

Comprehension of the concept: • low sampling frequency of A/D-converter• short length of FFT to be calculated• high achievable Doppler frequency and velocity resolution

• By resolution of ambiguities the velocity range that is covered by this concept is very high,although the sampling frequency stays low enough to manage A/D-conversion withcommercial ICs

• It is not expected to have more than one or two obstacles in each range gate. Multi-targetsituations can generate wrong velocities in the resolution of ambiguities, but a trackingalgorithm can check the result for plausibility and find out wrong results easily.

• The estimated velocity by measuring a range rate can be used as an additional informationfor the resolution of ambiguities.

Resolution algorithms for range and Doppler ambiguities are mentioned in [ROH86]. Thesealgorithms can be transformed to the resolution problem of Doppler ambiguities in this

chapter. The easiest approach to this problem is the Chinese remainder theorem [SCH90]. Itfinds solutions for natural numbers. A modified algorithm described in the appendix alsofinds solutions for real numbers. One possible single-target situation is shown in Fig. 3-11.

Fig. 3-11: Doppler frequency resolution

To measure the two ambiguous frequencies two different ramp frequencies have to be usedfor sensor control. The two ramp frequencies are smaller than the maximum Doppler

frequency. For the measured frequencies M1’ and M2’ which differ from each other, the trueDoppler frequency of the detected single object has to be determined by expanding the





34

For a range resolution compared with the value of the pulse radar calculated above (6 cm), therequired frequency hub is 2.5 GHz . Fig. 3-12 shows resulting range resolution versus transmitsignal pulse width using a pulse radar and also versus frequency hub when using an FMCWradar.

500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

45

Pulse Width [ps]

R a n g e R e s o l u t i o n [ c m ]

Range Resolution as a Function of Pulse Width

0 500 1000 1500 2000 2500 3000 35000

5

10

15

20

25

30

35

40

45

Frequency Hub [MHz]

R a n g e R e s o l u t i o n [ c m ]

Range Resolution as a Function of Frequency Hub

Fig. 3-12: Range Resolution as a Function of Pulse Width and Frequency Hub

3.3.2 Influences of Variable Pulse Width on the System Performance

The variation of the transmit pulse width influences different magnitudes which have to beconsidered in order to decide which time range is the optimum for pulse width variation. Theinfluenced parameters are:

• Range resolution• Time on target• Average transmit power• Signal to noise ratio• Probability of detection and probability of false alarms• Sensor to sensor interference (probability of false alarms due to interference)

The influences of pulse width variation on the specific parameters will now be discussed.

Range resolution:

The influence on target range resolution is shown in Fig. 3-12. In this case the pulse widthwas increased from the achievable pulse width of 400 ps with range resolution of 6 cm up to3 ns resulting in a range resolution of 45 cm.

In general very high range resolution makes sense for applications up to 5 m while fordistances of more than 5 m reduced resolution of e.g. up to 40 cm at 20 m may be sufficient.Additionally the received energy increases which is required to detect small targets atdistances of more than 5 m (e.g. safe detection of a person up to 10 m).

The duty cycle is the ratio between pulse width and the length of a PRI (pulse repetition

interval). In both mentioned cases (400 ps and 3 ns) with a pulse repetition frequency of4 MHz the duty cycles are:



35

400 ps → 0.16% duty cycle 3 ns → 1.2% duty cycle

PRI

P

T

T =cycleduty (3-45)

Time on target / average transmit power:

The increase of duty cycle from 0.16% up to 1.2% is equivalent with an increase of time ontarget by a factor of 7.5 in our example. Average transmit power is assumed to be

proportional to the duty cycle. Thus the increase of average transmit power will also beachieved by a factor of 7.5. The peak power is assumed to remain unchanged.

400 ps → -19 dBm (12.6 µW ) 3 ns → -10.2 dBm (94.4 µW )

with: (3-46) [ ] [( mW P dBm P log10 ⋅= ])

The average transmit power can be expressed as the transmitted energy per PRI and thetransmitted energy per interval is the integration of the pulse power per pulse repetitioninterval.

PRI

PRI avg

T

E P = ; ⇒ ( )∫ ⋅==

PRI T

P peak PRI T P dt t P E 0 PRI

P peak avg

T

T P P ⋅= (3-47)

Difference between coherent and non-coherent integration:

Integration of signals within the receiver is separated into coherent and non-coherentintegration. It is clear that the signal-to-noise ratio can be increased by integration ofnumerous pulses in a pulse radar. Integration is often necessary due to the very small energyof single pulses, especially in pulse radar systems with very high range resolution, i.e. veryshort pulses. Coherent and non-coherent integration have different influences on the increaseof signal-to-noise.

Coherent integration means that all pulses to be integrated have the same signal phase. Theso-called SNR-improvement can be expressed as follows for a coherent integration:

( )( )

n N S

N S I n

SNR ==1

(3-48)

The signal-to-noise is increased by a factor of n if n pulses are integrated in the receiver. Thisis the best SNR-improvement that can be reached with the disadvantage that a coherentintegrator requires additional hardware and cost.

Non-coherent integration is a direct integration of pulses without using the phase information.In the case of the HRR radar a non-coherent integration is performed with the following SNR-improvement:



36

with . (3-49) γ n I eff SNR =, 1<γ

The number of integrated pulses depends on the time on target which is in our case a functionof the slope of the sensor delay sweep.

Signal-to-noise ratio:

From the radar equation (see Appendix) the relation between signal-to-noise ratio and pulsewidth can be formed:

( )( )

( P t

atmt n sys

P

aus

T P L L BkT R

GT

N

S ⋅

⋅⋅

⋅⋅=

1

4 43

22

π

σ λ ) (3-50)

The signal-to-noise ratio depends directly on the transmitted power which is the only variablein the radar equation that depends on the pulse width T P . With the transmitted power

expressed as the average power being a function of the pulse width, the radar equation gets:

( ) P t T P

( )( )

P

PRI

P peak

atmt n sys

P

aus

T K T

T P

L L BkT R

GT

N

S ⋅=⋅⋅

⋅⋅

⋅⋅=

1

4 43

22

π

σ λ (3-51)

This is still the signal-to-noise ratio with consideration of only a single pulse. Non-coherentintegration increases the signal-to-noise ratio after integration of n pulses:

( ) ( ) P n T K nn N S N S ⋅⋅=⋅= γ γ

1 (3-52)

Probability of detection ( P D) and probability of false alarms ( P FA):

The probability of detection is a function of the signal-to-noise ratio. A short derivation of the probability density functions (PDF) of the envelope of signal plus noise and noise only can befound in the Appendix. Having the PDFs, the probability of detection and the probability offalse alarms can be derived by integration of the PDFs.

The probability of false alarms depends on the noise variance and on the detection threshold:

−=

−= ∫

∞

222 2exp

2exp

N

T

V N N

FA

V dr

r r P

T σ σ σ

(3-53)

The probability of detection can also be calculated by integration of the Rician PDF:

( ) ∫∫

∞∞

⋅⋅

+−==

T T V N N N V rice D

dr r

N

S I

N

S r r dr r p P

σ σ σ 2

2exp

02

2

2 (3-54)





38

To keep the signal-to noise ratio at an acceptable level for a moving target, the pulse widthshould be changed non-linear. A quadratic increase with range R can be a good solution (seeFig. 3-14):

( )

2

min,max,min,20 ⋅−+= m RT T T T P P P P (3-56)

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

Distance [m]

P u l s e W i d t h [ n s ]

Transmit Pulse Width vs. Distance

0 2 4 6 8 10 12 14 16 18 201

2

3

4

5

6

7

8

Distance [m]

I n c r e a s e o f S i g n a l - t o - N o i s e r a t i o

Signal-to-Noise increase: S/N(wider pulse) to S/N(normal)

Fig. 3-14: Transmit pulse width versus distance and increase of signal-to-noise ratio versus

distance

3.4 Suppression of Sensor Interferences

It is known from pulse radars that two of them transmitting in the same frequency band canvery well interfere each other. This effect can also be observed when using the described highrange resolution pulse radar sensors in a sensor network installed into a vehicle bumper. Thedistance between the sensors is small compared with the maximum measurement range andinterferences between the sensors can be observed. These may be caused by reflections

behind the vehicle bumper and also when a strong reflector is close to the vehicle. Thischapter gives important explanations concerning the origin of interferences and reveals someideas how to avoid interferences.

3.4.1 Explanation of Sensor Interference

An example of sensor interference is shown in Fig. 3-15 in order to see which issues arecaused without any suppression of sensor interference and to understand how necessary it isto avoid this effect. The target distances of a single sensor target list are shown versus time.The situation was an approaching and receding experimental car to the back of anothervehicle which was detected very well. The steep lines indicate that interfering pulses fromother radars were also integrated resulting in artificial target peaks in the sensor IF signal. It isclear that interference renders correct data association and therefore precise angle estimationand also measurements with low false alarm rate very difficult.

In realistic street situations the probability that two sensors report a detection caused bysensor interference at the same time and at a very similar range was observed to be very low.



39

That means that in most cases the tracker deletes the false targets of a single sensor and avoidsfalse objects in the object map. Nevertheless interference is an unwanted effect that may alsocause false tracker outputs and increases computation complexity for the single sensor tracker.

Fig. 3-15: Example of sensor interference

To understand the phenomenon of interference, Fig. 3-16 shows the transmit and receive pulses for a single target situation with a target at 15 m distance to all sensors (delay time100 ns). The small difference of delay time and distance between each other is neglected.Receive pulses are marked by smaller amplitude. A pulse repetition frequency of 4 MHz wasassumed. That is a total unambiguous range interval of 37.5 m. Further it is assumed that thePRF generators are not synchronized and the delay between each other is chosen randomly.

0 ns= 0 m

250 ns= 37.5 m

133 ns= 20 m

Amplitude

Time

S1

S2

S3

S4

Fig. 3-16: Transmit and receive pulses of four sensors



40

Fig. 3-16 shows that receive pulses of sensors S2...S4 are of course also received by sensorS1. If a sweep signal of 15 ms duration is applied, the time per range gate is approximately58.8 µs. In each range gate 235 pulses will be integrated. For a strong reflector, the integrated

pulses received by other sensors than sensor S1 at a constant range (delay) form a peak in theIF signal. If the pulse repetition frequencies of the sensors are very constant and all precisely

4 MHz , much energy from other sensor’s pulses can be integrated and a peak in the IF signalcan be observed. If the PRFs differ from each other by a specific minimum frequency, thereceived pulses of e.g. sensor S2 within consecutive pulse repetition intervals are found indifferent range gates of e.g. sensor S1 within consecutive PRIs. So not many pulses will beintegrated by sensor S1 and no artificial target will be detected in the sensor S1 IF signal. Onthe other hand sensor S2 receives its own pulses all in the same range gate in consecutivePRIs and received pulses from sensor S1 are not all integrated in the same range gate inconsecutive PRIs. So no artificial target will be detected due to sensor S1 transmit pulsesreceived by sensor S2. The minimum value for the difference of the PRF between two sensorswill be calculated later.

The lines of detections crossing the diagram Fig. 3-15 can be explained using the illustrationsof Fig. 3-16. By zooming into the picture, it can be seen that in a time period of approximately6 cycles (120 ms) and probably multiples of 250 ns a peak in Fig. 3-15 crosses the completerange from 20 m down to 0 m. From this information the difference of the PRF of theinterfering sensor to the shown sensor can be calculated. A range of 20 m corresponds to atime delay of 133 ns. For a single cycle of 20 ms a delay of

6

133250

nsnsk T cycle −⋅=∆ ; with k unknown (3-57)

can be calculated between the two PRFs. For 1 s the time is

−⋅⋅=∆6

133250501

nsnsk T s (3-58)

i.e. for one PRF cycle of 250 ns the difference in time is:

6

104

1

6

13325050

⋅

⋅

−⋅⋅=∆ −

nsnsk T cycle PRF (3-59)

So the difference in PRF between the two oscillators is (under the assumption that one ofthem has a PRF of exactly 4 MHz ):

⋅−⋅⋅⋅+

⋅−=∆−

−

6

1013310250501

144

99

k

MHz MHz f (3-60)



41

In the case that two PRF oscillators trigger the transmit switches with exactly the samefrequency, a false target (caused by received pulses from another sensor) with constantdistance to the real target distance would be observed. With a small difference between thePRF oscillator frequencies the false target is moving. With bigger difference of both PRFs the

probability of false alarms caused by another sensor is significantly reduced.

There are three cases to be distinguished for the analysis of false alarm rate caused by sensorinterference. These are:

1. PRFs of two sensors are absolutely identical2. PRFs differ very strong from each other3. PRFs are very similar to each other

These cases will now be discussed in detail:

1. PRFs of two sensors are absolutely identical

This case is unrealistic because the reproducibility of two oscillators can not be done in such a precise manner that the frequencies are absolutely identical. Each reflected transmit pulse ofsensor S1 would be integrated by sensor S2. Therefore the false alarm rate only depends onthe target size and can be calculated using the radar equation. For a reflector of big radar crosssection the probability of false alarms tends to one.

2. PRFs differ very strong from each other

This case occurs if the following difference for the PRFs of two sensors is observed:

cycle PRF T ns MHz f −∆−−=∆ 250

1

4 with: (3-61) P cycle PRF T T >∆ −

This is also the criterion for interference suppression with constant detuning of the PRFoscillator, i.e. in this case the probability of false alarms tends to zero, because only a single

pulse per PRI might be integrated in the same range gate. This criterion assures that thereflected pulse changes the range gate in consecutive PRIs.

3. PRFs are very similar to each other

For this case where the resulting false alarm rate depends on the target radar cross section andon the difference of the two PRFs, the following criterion must be met:

cycle PRF T ns MHz f

−∆−−=∆

250

14 with: (3-62) P cycle PRF T T <∆ −

For this case with slightly detuned PRF oscillators the probability of a false alarm issomewhere between zero and one.

3.4.2 Constant Detuning of the PRF Oscillator

One way for interference suppression can be to vary the PRF oscillator frequencies ofindividual sensors. In this case the difference has to be big enough to avoid integration of



42

receive pulses of a second sensor. The time difference in consecutive PRIs has to be at leastone pulse length:

(3-63) psT cycle PRF 400>∆ −

The resulting difference in frequency under the assumption that one sensor is triggered with4 MHz is:

kHz T ns

MHz f cycle PRF

41.6250

14 =

∆−−=∆

−

(3-64)

0 ns 250 ns

Amplitude

Time

S1

S2

500 ns 750 ns

PRF1 = 4 MHz PRF2 = 4 MHz + ∆f

Fig. 3-17: PRF-oscillator detuning for interference suppression

Fig. 3-17 shows the situation with the difference of two PRFs being 6.41 kHz. For a smaller

difference, integration of consecutive pulses will not be absolutely avoided, but the amplitudeof interference peaks in the IF signal can be reduced, i.e. the probability of false alarms due tointerference is reduced.

To maintain unambiguity of range measurement, the PRF should not be increased too much.For the example of ∆ f = 6.41 kHz (400 ps difference) the unambiguous range for distancemeasurement decreases only by 6 cm which is the range resolution for the chosen pulse widthof 400 ps.

It is also possible to vary the PRF slowly depending e.g. on the DSP time counter sincesystem start. It must be avoided that two cars equipped with the system run the samefrequency pattern for PRF oscillator detuning. A random variation of the PRF explained in thenext subchapter can be a safer solution. [MEI01] suggests to vary the transmit signaldepending on the driving direction of the car to avoid interferences.

3.4.3 Jittering of the Pulse Repetition Frequency

A pseudo-noise like variation of the PRFs can be one solution to exclude that two sensorswhose PRFs are changed during the measurement process run the same frequency pattern.This can be accomplished by delaying the minimum time of one PRI (e.g. 250 ns at 4 MHz

PRF) by an additional time of uniform distribution up to a maximum time. The maximumtime has to be set in order to ensure that within one scan cycle of the sensor (e.g. 20 ms)enough pulses will be integrated to form a detectable peak in the IF signal. The distribution of



43

a pseudo-noise like PRF delay time is a uniform distribution and the probability densityfunction is a constant with amplitude 1/∆T from 0 up to ∆T . ∆T should not be larger than e.g.0.1⋅PRI (in our case 25 ns, ) to keep reduction of amplitude due to less energy

that will be integrated as small as necessary.

kHz f 363max ≈∆

It depends on the specific hardware whether it is possible to change the PRF after each PRIwhich should be preferred or to change the PRF after one complete measurement cycle. Iflatter is the only way, it might still be possible that false alarms occur in a single cycle if twosensors have nearly the same PRF during one measurement cycle of 20 ms, but the probabilityfor this case is very low. Furthermore it must be checked how the PRF can be changed,continuously or in discrete frequency steps.

For one sensor the probability that the PRI delay time equals a specific time T 1 up to T 1 + T P is:

( ) ∫+

∆=

∆=+<<

P T T

T

P P S

T

T d

T T T T P

1

1

111111 τ τ (3-65)

This is the same for a second sensor and if both statistic independent results are combined the probability that two sensors have the same PRI delay with discrete size T P is:

( )T

T T T T T T T P P P

P P erfere ∆=+<<+<<= 121111int , τ τ (3-66)

For our case with ∆T = 25 ns and T P = 400 ps the probability is:

(3-67) 016.0400,int = pserfere P

With additional application of pulse width variation up to pulses of 3 ns the probability ofinterference increases

⇒ 12.03,int =nserfere P 5.7400,int

3,int = pserfere

nserfere

P

P (3-68)

This is the probability that a false alarm occurs in the case that the PRF is only changed everymeasurement cycle (e.g. 20 ms). This should be low enough to decide that a change everycycle is sufficient under the aspect that additionally the tracker eliminates such false alarmseasily. To give a number, the probability that in at least L out of M cases a false alarm occursdue to interference is:

∑=

−

∆

−⋅

∆

⋅

=

16

8

, 1 L

L M

Pulse

L

Pulsetrack FA

T

T

T

T

L

M P (3-69)



44

e.g. for M = 16 and L = 8: and P 11400,, 1093.4 −⋅= pstrack FA P 4

3,, 10256.2 −⋅=nstrack FA

If the PRF is changed with each new pulse and with only a few discrete frequency steps forthe PRF, the probability of a false alarm is much lower and the probability of a false tracktends to zero. Major advantages of a change of the PRF after each single pulse are a reduced

probability of false alarms and the possibility to avoid ambiguities in range measurementwhich may occur if the pulse width is changed for measurements at long distances to achievea higher signal-to-noise ratio.



45

4 Radar Network Processing

The introduction of radar data fusion techniques for this specific application is very new andrequires special topics to be considered, because target detection in the extreme short range ofvehicles and fusion of this target data obtained with very high range resolution pulse radarswas never considered before. Especially the very dynamic surrounding of a moving vehicle innormal street or highway traffic situations is a very difficult challenge. To cope with datafusion and filtering techniques in the sensor network is the topic of this chapter. In this case

practical feasibility with limited processing power at high update rate will be an importantaspect to keep the system as cheap and simple as possible, but also more sophisticatedmethods (e.g. multiple hypotheses tracking) will be taken under consideration in order toachieve better performance. It is in fact a very special case that the sensor measurements onlyconsist of range information of high accuracy and resolution. Additional amplitudeinformation may help in some cases of data association.

To understand the explanations in this chapter it is first necessary to define the followingexpressions:

Target: A target is the obstacle that is in a sensor’s field of view.Target List: The target list is the set of targets detected in one cycle including information

for each single target. This set including target range, amplitude and velocity(if measured) is transmitted from each sensor’s digital signal processor to acentral processor (radar decision unit: RDU).

Intersection: An intersection is an estimated object position for the current measurementcycle. It is calculated by associated target ranges from the network sensors tothe real obstacle. Two, three or four target ranges may contribute to one

intersection.Object: An object is the result of the data fusion process. It is obtained by trackedintersections and described by its Cartesian position coordinates and itsCartesian velocity components.

Object Map: The object map is the system output and the relevant information for afollowing application processor.

4.1 Coordinate System

For tracking and data fusion algorithms in an automotive radar network two different

coordinate systems can be defined. On the one hand the use of a polar coordinate systemmakes sense, because measured quantities of radar sensors are usually output in polarcoordinates, i.e. range and if possible angle and radial velocity. A transformation to anothercoordinate system would not be necessary in this case, but many operations of trackingalgorithms would use trigonometric expressions. This is very time-consuming for the tracking

processor. The selection of a Cartesian coordinate system implies a transformation ofmeasured quantities to the Cartesian coordinate system. This step is performed in the systemmodelling where non-linear measurement equations are linearized. It is done as well in non-linear least squares estimation as in the Kalman algorithms described in this work. Coordinatedefinitions for a system integrated into a vehicle front bumper are given in Fig. 4-1. For avehicle consisting of additional subsystems in the rear bumper and on the sides it is a goodsolution to use coordinate systems for each subsystem separately and relate all results to acommon coordinate system with its origin in the vehicle center. In this case the adaptivecruise control and safety algorithms get all data related to one common origin of all



46

subsystems. It showed to be very easy to use the same tracking algorithms for all subsystemsonly with different sensor locations for each individual subsystem.

vx,car

vy,car

αobj

x

y

vx,obj

vy,obj

z

(xobj,yobj)

r obj

Fig. 4-1: Coordinate system

Additionally automotive radar applications show in most cases objects moving along thevehicle symmetry axis or perpendicular to it. So to track in Cartesian coordinates showsadvantages compared with polar coordinates. Automotive radar systems usually track in twodimensions, because height measurement is difficult or impossible with nearly all existingsystems.

4.2 Multiple Sensor Network Architectures

In the following chapters some possible architectures for an automotive sensor network arecompared. It has to be distinguished between the hardware structure with separate controlunits and communication wires and the signal processing structure determining which parts ofthe complete signal processing and tracking will be performed in the specific elements of thenetwork. [BLA99] proposes some architectures divided into central-level tracking and sensor-level tracking which will be discussed in the following sections under the aspects of an

automotive radar sensor network.

4.2.1 Network Architectures

The first possible hardware architecture is shown in Fig. 4-2. In this case all sensors aredirectly connected to a central ECU (electronic control unit) or RDU which is the single

processor in the system. The ECU controls all sensors and converts all analog sensor outputsignals to digital data in parallel for further processing by a DSP. It is always preferable tocontain all important information in a single unit, but the processor load is too high for allnecessary peripheral tasks and the complete detection, data association, estimation and

tracking algorithms. Additionally the wires between the sensors and the ECU should be short, because external noise (e.g. ignition sparks causing electromagnetic compatibility issues) can



47

reduce the signal-to-noise ratio. On the other hand there is no performance degradation bylatency (delay for digital data transmission).


Sensor 4

Radar decision unit

analog 1 analog 2 analog 3 analog 4

CAN

Sensor-DSP &

Application

Fig. 4-2: System architecture 1

The second possible architecture uses separate signal processing hardware for each sensor tocontrol the individual sensor and to sample and convert the sensor output signals to a digitaldata stream (Fig. 4-3). Included detection algorithms process the sensor output and theindividual processors transfer information to a central processor. The used sensor processorscan also be used for sensor self-calibration if located inside the sensor package. In this case asingle sensor is a compact unit with a digital serial field bus interface (e.g. a CAN bus) tocommunicate with other processors. From an analog signal, the remaining information to betransmitted is significantly reduced to a list of observations.


Sensor 4

DSP 1 DSP 2 DSP 3 DSP 4

Radar decision unitCAN 1

CAN 2 CAN 3

CAN 4

CAN

Application

Fig. 4-3: System architecture 2

A system with distributed processing has the disadvantage that latency has to be considered inthe data fusion and tracking algorithms. Synchronization of the network has to be managed bythe central radar decision unit. Synchronization via CAN bus messages on separated buseswas recognized to be not feasible in this system due to delay times between digital datatransmission. The best solution is a prioritised interrupt line from the radar decision unit to thesensors, so that all sensors start their range sweep at the same time. Triggered by the radar



48

decision unit e.g. every 30 seconds, the sensors can be re-synchronized and drift can beavoided. For data transmission the four sensors can also be connected to a single bus ratherthan using separated buses. This depends on the amount of data to be transmitted and on themaximum bus load.

4.2.2 Software Architecture: Central-Level Tracking

Assuming the network hardware structure to be as shown in Fig. 4-3 all sensors have an ownsignal processing unit to preprocess the sensor output signals. The information flow betweenthe sensors and the RDU is reduced to a list of observations (detections of true targets andfalse alarms). For each cycle a complete new shot of the situation is taken and a new list ofobservations is transmitted untracked to the radar decision unit. The RDU performs thefollowing necessary tasks like data association and update of the estimated target states, gatecalculation for the data association and also an initiation of new tracks (see Fig. 4-4).Obviously the sensors do not communicate between each other. All data is collected in the

RDU to perform a data fusion.

[BLA99] also suggests a central-level tracking with partitioned processing. This structurediffers from Fig. 4-4 in the following points. A local data association is already performed inthe single sensor processor considering the calculated gating information received from theRDU. Associations and remaining observations of all sensors are then transmitted to theRDU. The remaining observations are further used for the initiation of new tracks and theassociations are directly considered for the global track update.

ObservationsSensor 1


GlobalAssociation

Track Initiation

GlobalTrack Update

GateCalculation



Fig. 4-4: Central-level tracking with centralized processing

For the system considered in this work a centralised processing is preferred in comparisonwith a partitioned processing due to the fact that the additional effort to be spent for the dataassociation in the RDU is less than the effort needed for the increase in data amount to betransferred. It is the better way to concentrate as much of the processing in the central RDU as

possible.

4.2.3 Software Architecture: Sensor-Level Tracking

Compared to a central-level tracking a sensor-level tracking already performs target trackingwithin each sensor unit. As Fig. 4-5 shows, local sensor observations are associated to localtracks or local tracks are initiated by local data. Local track information can then be used for



49

local data association adaptive gate calculation. Local track data of all sensors performing asensor-level tracking is then transmitted to a central processing unit for central track datafusion. Track to track association methods are necessary in the central processor to initiateand update global tracks. Sensor-level tracking reduces complexity in the RDU and datatransmission between RDU and sensors.

Local DataAssociation

Track Initiation

LocalTrack Update

GateCalculation

Local Observ.Sensor 1

GlobalAssociation

GlobalTrack Update

Other Sensors

Tracks

Fig. 4-5: Sensor-level tracking with centralized track file

Also for sensor-level tracking the distributed track file method is possible. This would looklike Fig. 4-5 with global track to track association and global track initiation and update

performed in each single sensor unit. In this case the interfaces between the sensors are usedto transmit local track information of each sensor to all other sensors. With this strategy allsensors have all local track information of other sensors available and calculate their ownrepresentation of the situation. This involves much redundancy in the system and highercomputation complexity in each single sensor unit. Distribution of track files makes thesystem robust and flexible because it has no central processing unit.

To draw a conclusion of the possible processing structures it should be noted that sensor-leveltracking can be important for networks consisting of many individual sensors. In a network offour sensors central-level tracking with centralized processing should be preferred. This isalso the structure of the network described in this thesis.

4.3 Single Object Multilateration and Tracking

Under the assumption that only a single object has to be tracked by the radar network, thefollowing pages show basic tracking algorithms and their properties in a radar network. Fromthis simple case the handling of multiple objects will be the following step. The least squaresestimation ([LAY97]) as well as the Kalman filter are designed to calculate object positionsfrom range measurements only.



50

4.3.1 Nonlinear Least Squares Estimation

With two measured ranges the object position can be calculated as the intersection of twocircles around the two sensors with the radius being the measured range. With three and evenfour measured ranges a nonlinear least squares position solution can be calculated to make use

of the given redundancy and to find a more precise solution. An example of such a situation isgiven in Fig. 4-6. Four sensors measure different target ranges in this situation and each sensoris assumed to include a range error. This may be a systematic error, e.g. in the case that thesensor positions in the bumper are only known with limited precision. Another systematicrange error depending on the target range is the remaining range measurement error of asensor for which an absolute maximum value of 3 cm is assumed. Stochastic errors can beseen e.g. in slightly different backscatterer positions on the reflecting object due to differentaspect ratios from the individual sensors.

r 1 r 2r 4r 3

Sensor 1 Sensor 2 Sensor 3Sensor 4

estimated least squaresobject position

xy

Fig. 4-6: Example of an estimated object position by means of a least squares algorithm

This chapter shows an iterative approximation algorithm to find an optimal position solution based on least squares estimation:

Assume that the object position to be estimated is denoted as: (4-1)

=

t

t

y

xt r

The four sensor position coordinates for the sensors s1..4 related to the center of the front bumper are:

=

1

11

s

s

y

x sr

(4-2)

=

2

22

s

s

y

x sr

=

3

33

s

s

y

x sr

=

4

44

s

s

y

x sr

The four differences between the sensors and the object are further denoted as:

Sensor 1: l Sensor 2: l

−

−

=−= t s

t s

y y

x x

t s 1

1

11

rrr

−

−

=−= t s

t s

y y

x x

t s 2

2

22

rrr



51

Sensor 3: l Sensor 4: l

−

−=−=

t s

t s

y y

x xt s

3

333

rrr

−

−=−=

t s

t s

y y

x xt s

4

444

rrr

(4-3)

For the nonlinear equations we get:

( ) ( )

( ) ( )

( ) ( )

( ) ( ) 4

2

4

2

44

3

2

3

2

33

2

2

2

2

22

1

2

1

2

11

n y y x xr

n y y x xr

n y y x xr

n y y x xr

t st sm

t st sm

t st sm

t st sm

+−+−=

+−+−=

+−+−=

+−+−=

(4-4)

with being the measured distances between the object and the sensors while n4...1, =ir mi i

describes the additive noise parts.

We see that the relationship between the measured distances and the object states to beestimated is nonlinear. The measurement equation from above is:

(4-5) ( ) n xh z rrr+=

with being the vector of measurements, is the nonlinear function of the states and

the measurement noise vector.

z r

( ) xhr

nr

The noise parts are assumed to be independent and the noise covariance matrix R is:

(4-6) [ ]

=⋅=

24

23

22

21

000

000

000

000

σ

σ

σ

σ

T nn E R rr

The nonlinear equations can be linearized near an estimated solution using the method of

Newton-Kantorowitsch (see [BRO]):

Using an estimated position denoted as: (4-7)

=

)0(

)0()0(

t

t

y

xt r

the linearization becomes:

( )( )

( ) ( )( )

( ) ( )e F y y y

r x x

x

r r r t t

t t

mit t

t t

mimimi +−

∂

∂+−

∂

∂+= )0(

)0()0(

)0()0(

)0()0( rr

(4-8)

Neglecting the higher order error term F(e) the linearized equations are as follows:



52

x H z

r̂r

∆⋅=∆ ⇔

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

−

−

⋅

∂

∂

∂

∂

∂∂

∂∂

∂

∂

∂

∂

∂

∂

∂

∂

=

−−

−

−

)0(

)0(

)0(4

)0(4

)0(3

)0(3

)0(2

)0(2

)0(1

)0(1

)0(44

)0(33

)0(22

)0(11

)0()0(

)0()0(

)0()0(

)0()0(

t t

t t

t t

m

t t

m

t t

m

t t

m

t t

m

t t

m

t t

m

t t

m

mm

mm

mm

mm

y y

x x

y

r

x

r

y

r

x

r

y

r

x

r

y

r

x

r

r r

r r

r r

r r

rr

rr

rr

rr

(4-9)

( )

( ) ( )

( )

( ) ( )( )

( ) ( )

( )

( ) ( )( )

( ) ( )

( )

( ) ( )( )

( ) ( )

( )

( ) ( )

43421

4 4 4 4 4 4 4 4 4 4 4 34 4 4 4 4 4 4 4 4 4 4 21

43421r

r

x

t t

t t

H

t st s

t s

t st s

t s

t st s

t s

t st s

t s

t st s

t s

t st s

t s

t st s

t s

t st s

t s

z

mm

mm

mm

mm

y y

x x

y y x x

y y

y y x x

x x

y y x x

y y

y y x x

x x

y y x x

y y

y y x x

x x

y y x x

y y

y y x x

x x

r r

r r

r r

r r

ˆ

)0(

)0(

2

4

2

4

4

2

4

2

4

4

2

3

2

3

3

2

3

2

3

3

2

2

2

2

2

2

2

2

2

2

2

1

2

1

1

2

1

2

1

1

)0(44

)0(33

)0(22

)0(

11

∆

∆

−

−⋅

−+−

−−

−+−

−−

−+−

−−

−+−

−−

−+−

−−−+−

−−

−+−

−−

−+−

−−

=

−

−

−

−

(4-10)

)0(mir is the distance between the estimated position t and sensor i. The measurement

residual vector is the difference between the actual measurements and the expectedmeasurements . is the estimated object position error. Matrix H is the measurement

matrix.

)0(r

z r∆)0(

mir x̂r∆

The least squares solution of the system of linearized equations can be obtained byminimization of a weighted sum of squares of deviations (see also [BLA99]):

0ˆ =

∆∂

∂

x

J r with: ) (4-11) ( ) ( x H z R x H z J

T ˆˆ 1 rrrr∆−∆∆−∆= −

The solution is finally:

(4-12) ( ) z R H H R H x T T rr∆⋅⋅=∆ −−− 111ˆ

Assuming that all sensors show similar noise (4.12) can be simplified to:

(4-13) ( ) z H H H x T T rr∆⋅=∆

−1ˆ

Summarized the iteration steps are:







55

The update equations find a new estimated object velocity v and distance x:

( ) ( ) ( )

( ) ( ) ( )( )k x yk xk xT

k x yk vk v

k

k

ˆˆ

ˆˆ

−⋅+=

∆

−⋅+=

α

β

(4-16)

k y is the measurement of the current cycle k (e.g. one coordinate of a least squares

estimation), ∆T is the cycle time between two measurements, α and β are the constant filterweighting factors.

The prediction step calculates a new prediction of state variables for the next cycle:

(4-17) ( ) ( )( ) ( ) ( 1ˆ1ˆ 1ˆ ++=+ =+ k vT k xk xk vk v

)

These filter equations filter only one dimension, for both object coordinates. Two filters haveto be applied in parallel to obtain a filtered position solution and range rate estimations for x-and y-direction. It is important to understand that an α - β - filter assumes movement withconstant velocity, i.e. acceleration equals zero. In contrast to this filter an α - β - γ - filter alsoconsiders changing velocities, i.e. acceleration and deceleration processes.

4.3.4 Kalman - Filtering

As an alternative way of finding a position solution of detected objects by multilaterationcombined with an object tracking, i.e. filtering of object motion and estimation of its statevariables, the use of a Kalman filter will now be shown. With the discussed structure aflexible estimation is possible independent from the number of sensors detecting the object inthe current measurement cycle. In the case that only a single sensor detects the object anestimation of the object position and velocity is still possible. Kalman filters are widelyapplied in estimation and tracking applications. Principles of Kalman filtering are e.g.described in detail in [BRO98] and [BRO97]. The following pages explain the basic equationsand a processing scheme proposed for an automotive radar network consisting of four sensors.

The filter finds a least squares position solution of an object and filters the object state vector.It can be seen as a combination of the nonlinear least squares estimation of chapter 4.3.1 and asmoothing tracking filter (like an α - β - filter) with the difference that the smoothing filtercoefficients are not constant values, but adaptive to system and measurement noise. Filteroutput is a Cartesian object position and a Cartesian object velocity estimation obtained byrange rate estimation.

The object position and velocity vectors are defined as follows in Cartesian coordinates:

Object position to be estimated: (4-18)

= t

t

y

x

t

r



56

Object velocity to be estimated: (4-19)

=

y

x

v

vvr

The sensor locations in the system are defined as:

=

1

11

s

s

y

x sr

(4-20)

=

2

22

s

s

y

x sr

=

3

33

s

s

y

x sr

=

4

44

s

s

y

x sr

The state vector in this case includes the object position errors and the estimated velocityerrors:

(4-21)

=

err y

err x

err

err

s

v

v

y

x

x

,

,

r

The system noise matrix Q including system noise variances is:

(4-22)

=

2,

2,

2

2

000

000

000

000

yv

xv

y

x

Q

σ

σ

σ

σ

The measurement noise covariance matrix R describes the noise properties of measuredvalues (range and range rate):

(4-23)

=

2

2

0

0

v

r Rσ

σ

The a priori state vector estimate error covariance matrix has to be initialized as:

with being the a priori state vector estimate (4-24) ( ) ( )

−⋅−=

T

s s s s x x x x E P ˆˆ rrrr s x̂

r

The state transition matrix as a description of the system dynamics is very simple for theconsidered system. It is in our case:

from: (4-25)

∆

∆

=Φ

1000

0100010

001

T

T

( ) ( ) ( )k qk xk x s s rrr +Φ=+1



57

where is white Gaussian process noise with zero mean and assumed covariance Q. ∆T is

the time interval between consecutive measurements (cycle time).

( )k qr

The processing structure of the Kalman filter is shown in Fig. 4-9.

Initialization

Calculation of astarting position

Track stillvalid ?

State transitionmatrix Φ

Error propagation:

Calculation of:1. measurement matrix H i (Eq. 4-29)2. measurement vector (Eq. 4-32)3. correction matrix K i (Eq. 4-33)4. covariance matrix P i (Eq. 4-34)5. new state variable vector (Eq. 4-35)

Sensor dataavailable?

Yes

No

Yes

No

Stop track

Calculation of newobject state:

( ) ( )

( ) ( ) Qk P k P

k xk x

T

s s

+Φ⋅−⋅Φ=

−⋅Φ=

1ˆ

1ˆ

1

1,

rv

new cycle

i s x ,

r

vt rr,

i z r

Fig. 4-9: Processing of the Kalman filter

After track initialization a starting position for the object position estimation has to becalculated. For each cycle it is tested whether the track is still valid or not. If not, the track has

to be stopped. With the known system state transition matrix Φ the object state vector and thestate covariance matrix can be propagated for the current cycle. The result is an estimation forthese values for the current cycle which will be corrected in the following steps of the filter



58

processing. Similar to an α - β - filter the Kalman filter also includes a prediction and anupdate step. The equations for error propagation in order to estimate the state vector and thestate covariance matrix are for the first sensor (i = 1):

(4-26) ( ) ( )1ˆ

1, −⋅Φ= k xk x s s

rr

(4-27) ( ) ( ) Qk P k P T +Φ⋅−⋅Φ= 11̂

As indicated in Fig. 4-9 in the next step the measurement matrix for sensor i is

calculated. The 2-dimensional measurement vector is modeled as:

( )k H i

( )k z ir

(4-28) ( ) ( ) ( ) ( )k nk xk H k z i sii

rrr+⋅=

where is the measurement matrix of dimension 2x4 and vector is a model of theassumed zero-mean white Gaussian measurement noise with covariance R. It is assumed thatall sensors have the same measurement noise characteristics R.

( )k H i ( )k nir

The measurement matrix for the current cycle k and sensor i is calculated as follows

based on object data from cycle k-1:

( )k H i

( )

( )( )

( )( )

( ) ( ) ( )( )

( )

( ) ( ) ( )( )

( )

−

−−−⋅−−−

−

−−−⋅−−−

−−−

−−−

=

001

1111

1

1111

001

1

1

1

,

,

,

,

,

,

,,

k d

k d

yk yk vk v

k d

k d

xk xk vk v

k d

yk y

k d

xk x

k H

io

io

sit i s y

io

io

sit i s x

io

sit

io

sit

i rr

(4-29)

where the direct distance between the specific sensor i and the estimated object position isdenoted as:

( ) ( )( ) ( )( )

22

, 111 sit sit io yk y xk xk d −−+−−=− (4-30)

( )1, −k v i s

r is the projection of the object velocity vector on the direct vector between the

sensor i under consideration and the estimated object location. It is calculated by:

( ) ( ) ( )

( ) ( )

( )( )1

11

1

111

,,

, −−−

⋅−+−−−

⋅−=−k d

yk yk v

k d

xk xk vk v

io

sit y

io

sit xi s

r (4-31)

The measurement of target distances are used to form the measurement vector . Due tothe fact that the errors are estimated in this specific case, the vector is: ( )k z i

r





60

tracking filter makes this algorithm a compact solution and especially suitable for cases whereonly a single sensor reports target detections.

For the situation already described in chapter 4.3.2 the Kalman filter algorithm was simulatedwith the four sensor positions to and the following settings for the noise matrices Q, R

and P :

2 sr

5 sr

=

005.0000

0005.000

00001.00

000001.0

Q

=

50

003.0 R

=

10000

01000

0010

0001

P

The cycle time ∆T was set to 20 ms and all sensor ranges were added with normallydistributed noise of variance 3 cm. Fig. 4-10 shows the error of the object radius and angle

estimated by the least squares algorithm and by the Kalman filter. The Kalman filter curve isthe smooth curve in the diagram. The errors of the Kalman filter results are obviously smallerin both cases due to the smoothing properties of the filter. Fig. 4-11 shows the estimatedCartesian velocity components of the Kalman filter output.

-15 -10 -5 0 5 10 15-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Distance from center line [m]

E r r o r o f c a l c u l a t e d o b j e c t r a d i u s [ m ]

Error of object radius: calculated value - true value

-15 -10 -5 0 5 10 15-20

-15

-10

-5

0

5

10

15

20


E r r o r o f a

z i m u t h a n g l e [ ° ]

Error of azimuth angle: calculated value - true value (four sensors)

Fig. 4-10: Object radius error and angle error for Kalman filter and least squares solution

-15 -10 -5 0 5 10 15-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1


Object velocity in x-direction

O b j e c t v e l o c i t y ( x - d i r e c t i o n ) [ m / s ]

-15 -10 -5 0 5 10 150

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


Object velocity in y-direction

O b j e c t v e l o c i t y ( y - d i r e c t i o n ) [ m / s ]

Fig. 4-11: Object velocity in x – and y – direction (Kalman filter)





62

In a first processing method with all detected sensor targets all possible intersections can becalculated. For one sensor the object position is assumed on a circle with the radius being themeasured range to a detected target. With three or four ranges an iterative least squaresalgorithm can be applied to find an estimated position solution. From the obtained completeset of possible intersections all unlikely intersections can be deleted by a search algorithm.

The set of intersections does not only include representations of real objects, but also falseobjects which have to be deleted for the following tracking. To find out false intersections, itis very useful to consider the situation database of preceding cycles. Deletion of falseintersections without feedback of the situation database is not safe enough. In animplementation of this algorithm a large number of false intersections was observed. To findout correct intersections is very difficult and various false alarms occurred with real measuredsensor data. An additional disadvantage is the large number of intersections which have to becalculated.

Fig. 4-13 shows on the left side an implemented processing with included tracking of singlesensor targets. After association of detected targets to single sensor target tracks the single

sensor targets are tracked by means of an α - β - tracker. All sensor target tracks fromdifferent sensors are then associated to each other to find possible intersections for the objecttracker. With all associations the possible intersections are calculated and fed into the objecttracker. Intersections for three or four associated target tracks can be found by least squaresiteration. It is assumed that a target is only originated by one object. That means that onesingle sensor target track can only be associated with one intersection. Multiple associationsare excluded. Sensor target to target track associations from a previous cycle can be repeated,

because the object was already validated before. This reduces the target lists of all sensors tothe set of targets that possibly belong to a new object. These remaining target tracks can beassociated to form new intersections for new objects. For all association steps the feedback ofthe object map and the intersection list is absolutely necessary to find correct decisions and toreduce effort.



63

Tracking of Single Sensor Data

Association of Targetsto Single Sensor Tracks

Association of Single Sensor Tracks for Intersections

Calculation of Intersections

Tracking of Intersections(Objects)

Observations / Targets

Tracking of Single Sensor Data

Association of Targetsto Single Sensor Tracks

Association of Single Sensor

Tracks for Intersections

Observations / Targets

Kalman - Filtering for Calculation of PositionSolution and Tracking

Feed Back of

Object-Map / Intersection ListFeed Back of

Object-Map / Intersection List

Fig. 4-13: Generalised Processing Overviews ( - - Tracker and Kalman Filter)

A tracking of single sensor targets shows the following advantages and disadvantages:

• Advantages:+ Short gaps of detection of a sensor are bridged by the target tracker. The number

of available sensor target tracks for a calculation of a position solution(intersection) is higher. This increases accuracy of an angle estimation.

+ A radial velocity can be estimated for each sensor track individually from rangerates.

+ Many false targets can be filtered out, e.g. in situations where two sensors show

interferences.+ A pre-filtering of the target list reduces the amount of data to be processed.

Disadvantages:•− Detected targets are passed after a few cycles to the following processing as

confirmed sensor target tracks. Results at the system output are delayed.

A sensor target tracking shows important advantages and is seen as a required processing stepin the radar network data fusion. For applications that require very low reaction times, thedecision criteria for the tracker have to be optimised to achieve a low false alarm rate at lowsystem reaction time. The sensor target association to target tracks is a step with important

influence on the complete system performance. False objects in the object map may result byfalse target data association and the accuracy of measurements can be significantly reduced. Adata association of detected targets to target tracks with consideration of the complete







66

4.5.2 Joint Probabilistic Data Association (JPDA)

Nearest neighbor association methods only consider a single hypothesis for a measurement totrack association. For a track with multiple measurements within the association gate, thereare also other techniques known for an all-neighbors association approach. PDA (for

probabilistic data association see [BLA86], [BLA99] or [BAR88]) forms multiple hypothesesafter a single scan and combines all hypotheses weighted with calculated probabilities. Allneighbors within the gate are considered, but measurements with higher probability areweighted more than measurements obviously caused by clutter. With this strategy allmeasurements contribute to the tracking update. For concrete information how to calculate the

probability of a hypothesis, several publications can be found. The PDA method only assumesa single target while the JPDA method is an extension in order to handle multiple tracks andmultiple measurements.

To the high resolution radar network a probabilistic data association was not applied so far, but can be a technique to improve nearest neighbor method performance with limitedadditional expense.

4.5.3 Multiple Hypothesis Tracking (MHT)

The main idea of MHT (multiple hypothesis tracking) is to form tracking hypotheses for all possible assignments and to propagate these hypotheses in order to resolve uncertainties in alater step of the processing with subsequent data. The advantage compared with simple gatingand nearest neighbour association or JPDA is that a hard decision for the assignment is not

performed until additional information is evaluated. Different hypotheses are tracked as

different possible assignments. JPDA updates the track in the same cycle with a probabilistically weighted composite of all measurements observed within the track gate. Theamount of data and complexity is limited with JPDA whereas in an MHT approach muchinformation has to be tracked and processed from scan to scan. It is necessary to restrict acombinatorial explosion when using MHT. Possible techniques are e.g. clustering, hypothesisand track pruning or a track merging. These techniques are absolutely necessary to make thealgorithm feasible for practical applications with high update rates as required in automotiveradar systems.

An implementation of an MHT algorithm can be accomplished as proposed by [REI79] and[BLA99]. The measurement-oriented approach and the track-oriented approach will be

explained below and a short comparison reveals important features of both. An offline processed application of MHT on an automotive radar network can be found in [HAA00].

4.5.3.1 Measurement - oriented MHT

An implementation of the measurement - oriented approach of MHT was first described by[REI79]. The proposed algorithm includes important features like multiple-scan correlation,clustering and recursiveness. Multiple-scan correlation allows a resolution of uncertainties byusing subsequent as well as previous data. To divide the set of measurements and tracks intoseparate and independent groups is denoted by clustering. This allows the processing of

independent groups of data. The complete problem can be divided into smaller subsets tomake the processing faster and easier. Recursiveness can be accomplished by just using the



67

results of the previous scan and new measurements for a track update. Data from the preceding scan already includes all information from previous scans.

Receive new data set

Perform track update(Kalman-Filter)

Form new clusters:associate tracks and

measurements to clusters

Form new set of hypotheses:calculation of hypotheses

probability and track measurementupdate for each hypothesis of

all clusters

Simplify hypotheses matrixof each cluster; confirm tracks;

create new clusters for confirmed tracks

Reduce number of hypotheses:elimination or combination

return for next scan

Fig. 4-15: Measurement-oriented MHT algorithm

The algorithm described by [REI79] starts with a set of new measurements obtained by thesensor(s) (see Fig. 4-15). A track update for the current cycle is the next step. Usually this isthe extrapolation of the target state variables with the Kalman filter equations:

with Matrix Φ being the state transition matrix( ) ( )1ˆ −⋅Φ= k xk x s s

rr

In the following step recent measurements and tracks are associated with clusters and newclusters are formed for remaining measurements not associated with any existing cluster. As

already explained, a cluster is a separation of the entire set of tracked targets into subsetswhich can be processed independently. For clusters being very close to each other, theindividual clusters can be combined to a super-cluster. This may be the case for crossingtracks or extended objects like a vehicle with numerous backscatterers being very close toeach other.

If possible at this time a reduction of previously found hypotheses will already be carried out.Different possibilities to restrict the total amount of hypotheses are known from the literature.Very suitable techniques are e.g. an elimination of very unlikely hypotheses or a combinationof very similar hypotheses. This reduction procedure is also used by the next processing stagewhich forms a new set of hypotheses from new measurements and the tracked targets.

To form new hypotheses for a new set of measurements the typical measurement-oriented behaviour of the algorithm can be recognized. Starting with the first measurement, all



68

possible associations with existing target tracks in the cluster under consideration are listed.Then the next measurements are examined until the set of all possible hypotheses for allclusters is finished.

For all hypotheses a probability can be calculated. [REI79] gives analytical results for the

probability of a measurement to track assignment in the hypothesis matrix. Based on the probabilities very unlikely hypotheses can be neglected again by simple elimination (or pruning) or by combination of hypotheses. For all remaining hypotheses the track update iscalculated using standard Kalman filtering algorithms. It is worth to reduce before updatingthe target track state variables, because the computational effort for complex Kalman filterequations can be kept as low as possible.

To determine a new hypothesis, different requirements to be explained now have to befulfilled. The measurement under consideration has to be within a specified validation gatearound the track, e.g.:

( ) ( ) 21 ~~ η ≤−− − y yS y y

T (4-41)

with: H S = and R H P T +⋅⋅ ˆ Hx y =~

Furthermore each track should not be associated with more than one measurement in the dataset. Thus ambiguous hypotheses with lower probability have to be eliminated.

After calculation of all possible and probable hypotheses and update of all tracks, thehypothesis matrix is simplified. Tentative tracks can be set to confirmed tracks and will be

eliminated from the hypothesis matrix. With all tracks updated, the processing of a singlecycle is finished and can be restarted with a new data set.

4.5.3.2 Track - oriented MHT

An implementation of a track-oriented approach of MHT is described in [BLA99] andcompared with a measurement-oriented implementation. Track-oriented means that for eachsingle track the possible measurements are associated when forming hypotheses. This chapterdescribes the main processing steps of a track-oriented implementation.

A track-oriented implementation is seen as having an advantage over the conventionalmeasurement-oriented implementation proposed by [REI79]. One main advantage is seen inthe reduced number of hypotheses due to the fact that low probability tracks are immediatelydeleted and only high probability tracks are maintained for further processing steps. The basicalgorithm structure as explained in [BLA99] is shown in Fig. 4-16.

The processing starts by forming and updating tracks for all measurements. All measurementsare checked for possible associations with already existing tracks. This can be established bystandard gating techniques. For possible assignments all combinations are kept disregarding

possible multiple associations of measurements to more than one track. Usually it is assumed

that a measurement can only be caused by a single object. Multiple associations are resolvedlater in the processing. Tracks without any new measurements within their gating region areonly extrapolated. Measurements not associated to any track are recognized as a starting pointof a new track. It is clear that many tracks will be formed and thus pruning techniques are



69

required to restrict the total number of tracks. Therefore the next processing step compares thecalculated probabilities for each track with a fixed threshold and deletes all low probabilitytracks. Tracks sharing common measurements are defined to be incompatible and clustered inthe next step. A cluster includes all tracks sharing common measurements, not only directly,

but also if two tracks share measurements with a third track. The result of clustering is a list

of interacting tracks ranked in order of likelihood.

Track Formationand Maintenance

Track Level PruningConfirmation

Clustering

Hypothesis Formationand Pruning

Global LevelTrack Pruning

Track Updatingand Merging

Tracks

SurvivingTracks

Measurements

TrackingOutput

Deletion Messages

Fig. 4-16: Track-oriented MHT algorithm

After clustering the formation of hypotheses starts. Each hypothesis consists of a set ofcompatible tracks, i.e. a set of tracks that do not share common measurements. The number oftracks within a hypothesis is not limited. For track pruning it is important to find the mostlikely hypotheses, i.e. the most likely set of tracks. This can be established by a search

routine. If the most likely hypotheses are found, those of low probability can be deleted. Theresult is a list of hypotheses with each hypothesis consisting of a set of tracks. In the globallevel track pruning the tracks included only in deleted hypotheses can be deleted. Tracks withvery low probability below a deletion threshold can be deleted, too. If the sum of probabilitiesof hypotheses including a track is calculated, this is also a probability of a given track.

For all remaining tracks which should not be too many, the track updating can be calculatedusing standard Kalman filtering techniques. If track merging of parallel tracks with verysimilar state variable contents is possible, the tracks can be merged. All remaining updatedtracks can now be output to following applications as a result of the MHT algorithm.

4.5.3.3 Comparison between both MHT Implementations

For implementation in an automotive radar network the two possible implementations of themeasurement-oriented approach and the track-oriented approach make sense. The followingshort comparison tries to identify which of both implementations is best suited for thisapplication. The measurement-oriented approach maintains hypotheses from scan to scan andforms a hypotheses tree after more than one scan. A very large number of hypotheses mayresult and the tree has to be pruned. The algorithm proposed by [REI79] may result intracking many hypotheses of low probabilities. The requirements on memory andcomputation power for a system having 10-20 ms cycle time can be quite high. In a track-oriented implementation, hypotheses are formed and reformed within the algorithm.Hypotheses are not maintained from scan to scan. This reduces the required memory space.The number of tracks maintained from scan to scan is also not too high, because tracks of low



70

probability are deleted. As a result the track-oriented approach seems to be more efficient forreal-time applications with limited computer performance.

4.6 Description of an Implemented Radar Network Processing

As shown in Fig. 4-17 in this network of four high resolution pulse radar sensors theindividual target lists of all sensors are the multiple target tracker input. The system input is aset of M k measurements at time k for sensors s:

( ) ( ){ 4...1;,...,2,1, === s M mk Z k Z k m s } (4-42)

The maximum number of observations M k from each sensor is set to ten observations per scan(20 ms) to limit the data to be transferred and to ensure that the processing time for all data is

below the fixed cycle time.

The required system output for following applications is a set of objects listed in an objectmap. Each object is described by its position relative to the car and its velocity components.The system output at time k is defined as:

( ) ( ){ } objectsof numbermaximum:with,...,2,1 ooi nnik Ok O == (4-43)

The first processing step with the sensor target lists is a single sensor target data associationfor the following single sensor target tracking. This observation to track association can use

information of preceding cycles. To consider the previously calculated situation showed verygood results for the data association. One advantage of using a separated single sensor targettracking is that the input to the following multilateration procedures is more continuous thanwithout a single sensor target tracking stage. If omitted, it was observed that results were notsatisfying enough with sensors of reduced sensitivity. The input for the single sensor targettracker has to be selected very accurate to achieve good results in the multilateration.Additionally the number of false targets that are passed to following processing stages withhigher computation complexity is reduced. This is of advantage if sensor interference isobserved or an increased number of false alarms due to clutter. How the sensor target to targettrack association is performed will be described below.

The single sensor target tracking makes usage of an α - β - filter to update the estimation fortarget range and range rate of this sensor target track. After the single sensor target trackingstage all confirmed target tracks are passed to the multilateration procedures. Themultilateration includes target track to track association techniques to find combinations ofsensor target tracks that belong to objects. For all existing objects the sensor target tracks ofthe preceding cycle are used again. It is assumed that the target track is still caused by thesame object and not by another object. These sensor target tracks can be identified by a targettrack identifier which is carried with the target track and which is also stored in the objectdata structure. With this processing all target tracks for existing objects can be associatedagain and removed from the set of target tracks to be associated with other target tracks. It is

important to notice that the algorithm assumes that an object only causes not more than asingle target track. All remaining target tracks have to be associated to each other to form newdetected objects. This is accomplished by an elaborated search algorithm that checks possible



71

combinations first of two tracks and associates a third or even a fourth track if possible. Nearest neighbor gating criteria are used for the data association. This showed to be thefastest way which still produces good results. From all associated sensor tracks a list ofintersections can be calculated. The solution is an intersection of two circle arcs for only twotarget tracks contributing to one object. For three or four target tracks a least squares

algorithm is applied to find an optimal solution. This results in a list of intersectionscalculated from all combinations of sensor target tracks.

This set of intersections gives a representation of the situation only for the current cycle. Asubsequent tracking initiates object tracks from validated intersections observed within a fewcycles. This requires an intersection to object track data association performed in each cycleto update the object track, initiate new object tracks and delete old and not updated objecttracks. For this tracker a two-dimensional α - β - filter is applied to estimate the object

position relative to the vehicle and also the Cartesian object velocity components. The resultof the object tracking is the object map which is the output to the following application

processor, e.g. a parking aid or stop & go algorithm that searches the list for a relevant object

to activate the vehicle brakes or to accelerate if the street in front of the car is empty and thefound objects are located on adjacent lanes.

It was already mentioned that for sensor target to target track association information of the preceding cycle is used. This is the list of intersections and the object map. Each object carriesthe information of the contributing intersection with it as well as the identifier of thecontributing sensor target tracks. From the identifiers the position of the target track in the listof sensor target tracks has to be found. With the found sensor target tracks a prediction of theintersection to the current cycle can be calculated using the estimated target track range rate.The predicted sensor target track ranges are in this case used for calculation of an intersection(using the least squares algorithm) which is denoted as the predicted intersection. From this

predicted intersection the expected ranges for the sensor targets detected in this current cyclecan be determined. With these expected target ranges the target to sensor target trackassociation is performed using a gate depending on the vehicle speed and nearest neighbordata association techniques.



72

Read Target Lists

Find Track Positions

List of TrackedObjects

List of TrackedSensor Targets

Calculate predicted intersectionsTarget to Sensor Target

Track Association

Single Sensor Target Tracking

Association of Tracked Targets

to existing Object Tracks

Multilateration:

Calculation of new Intersections

Association of Intersectionsto Object Tracks

Object Tracking

Output of Object Map

TrackedTarget Lists

List of Intersections

List of TrackedObjects

Associations between Targetsand Sensor Target Tracks

Associations betweenIntersections and Object Tracks

Indices ofused Tracks

Distances between predictedIntersections and Sensors

Fig. 4-17: Radar network processing overview

The main advantage of the described processing with a feedback of information from the previous cycle is that the sensor target tracking is not performed independent from each otherfrom sensor to sensor. A prediction for the intersection is used in the current cycle. Thisincludes contributions for the position estimation from all four sensors. Therefore it is not

possible that one sensor target track range can drift away from the other sensor target trackranges caused by wrong sensor target to track data association. So for each sensor track thedetected target will be associated that fits best to the complete predicted object position. This

processing showed very good results with simulated and also real data. For the existingsoftware a separation of position estimation using least squares algorithms and track filteringwas selected to have a better overview of the system intermediate results with this blockwise

processing. In the case of application of a Kalman filter the optimal position estimation andthe filtering would be one single block in the complete processing (see Fig. 4-13 (right side)).Intersections representing an instantaneous unfiltered object position without respecting the

object position history would not be calculated in this case.



73

5 Phase Monopulse Sensor Concept

With the conventional sensor concept (Fig. 3-2) and the use of e.g. four sensors distributed ina bumper with distances up to 50 cm between each other, all sensors receive reflections from

different backscatterers of a complex target like a vehicle. Angle estimation by means ofsensor to sensor data association of target list data and multilateration is a difficult task in thiscase. Improvements can be achieved by providing more information about single detectedtargets to the data association algorithm. A rough estimation of object angles by each singlesensor and a more precise estimation in a central processor by using data of three or foursensors would be an interesting concept on the way to avoid false objects caused by a wrongdata association. The idea of estimating a target angle already in the single sensor processingstage can be realized by a new concept proposed in this chapter. Important system parametersare discussed to evaluate the performance improvement compared with already existingsystems.

5.1 Concept Overview

On the basis of the conventional concept, Fig. 5-1 depicts the modified radar frontend. Theidea is to use two rather than only one receive path in the sensor while the complete transmit

path remains unchanged. For transmission a patch array antenna on one side of the sensor isused and for signal reception two separated receive antenna patch arrays on the other side ofthe sensor frontend are located with distance dx1 and dx2 to the transmit antenna. The distance∆dx = dx2 – dx1 between both receive antennas in a single sensor has to be less than the carrierfrequency wavelength λ in order to avoid ambiguities for the estimated angle. The distance to

the transmit antenna is a trade-off between low signal crosstalk from the transmit to thereceive antenna and sensor size.

It is assumed that reflected pulses reach the receive antennas in a parallel wavefront. In thiscase the object angle α can be calculated as (see Fig. 5-3):

∆⋅∆⋅

=dxπ

ϕ λ α

2arcsin (5-1)

with a phase difference of between both receive signals and under theassumption that with ∆dx smaller than λ no ambiguities can occur. For small errors of thesignal phase difference the resulting object angle error is proportional to the signal phaseerror. For a distance λ between the receive antennas the resulting object angle error isapproximately one degree for six degrees of phase difference error. The angle estimationaccuracy can be improved with exclusion of ambiguities if a maximum detection angle of e.g.45 degrees is assumed for the sensor. For this case the distance between both receive antennas

can be

21 ϕ ϕ ϕ −=∆

λ ⋅= 2dx∆ . For an error of 8.9 degrees for the signal phase difference the objecterror will be one degree (see Fig. 5-2). Angle estimation can still be better than the result of asingle sensor if a least squares estimation of the object position in the complete network of up

to four sensors is considered.



74

Receive Antenna 2

Transmit Antenna

dx 1

Receive Antenna 1

dx 2

Fig. 5-1: Frontend of the phasemonopulse sensor

-20 0 20 40 60

Signal Phase Error [°]

gle Error vs. Signal Phase Error (dx=1.4*lambda)

O b j e c t P o s i t i o n A n g l e E r r o r [

° ]

Object An

-60 -40

-8

-6

-4

-2

0

2

4

6

8

Fig. 5-2: Object angle error vs. phase error

Transmit

Receive

α∆dx

Fig. 5-3: Wavefront reconstruction with a phase monopulse concept

Fig. 5-4 shows the sensor RF frontend hardware structure in detail. Triggered by the PRFgenerator, the 24 GHz DRO pulses are transmitted as before. Both symmetrical receive paths

are triggered with an adjustable delay set by an external sweep control. Each receive pathconsists of an inphase and a quadrature channel, i.e. the delayed pulses from the DRO are inone case directly provided to the sampling phase detector and in the other case provided witha phase shift of 90 degrees for the quadrature channel. This is done in both receive paths. Itshould be emphasized that both receive paths are triggered with the same adjustable delay.



75

td

PRFGenerator

AdjustableDelay

24GHzDRO

PulseGenerator

PulseGenerator

3dB Power Splitter

High SpeedSwitch

TransmitAntenna

LO/I

IF 1/IOutput

ReceiveAntenna 1

90°

IF 1/QOutput

LO/Q

RF/I

RF/Q

LO/I

IF 2/IOutput

ReceiveAntenna 2

90°

IF 2/QOutput

LO/Q

RF/I

RF/Q

SweepControl

PulseGenerator

High SpeedSwitch

High SpeedSwitch

High SpeedSwitch

Fig. 5-4: Block diagram of the sensor concept

To estimate a target angle it is important to be able to calculate a signal phase within eachreceive path by evaluation of the IQ-signals. The angle estimation can then be accomplished

by phase comparison of both receive paths. Depending on the wavelength which is 1.24 cm with a 24.125 GHz DRO ambiguities may result for the estimated angle depending on thedistance between the receive antenna patch arrays. If necessary, ambiguities have to be

resolved in the central processor.

Within the single sensor an angle estimation using the known multilateration concept oramplitude monopulse techniques would not be feasible due to the very small base length

between the two receive antennas.

It was already shown how the resulting object angle error depends on the signal phase errors(see Fig. 5-2). The required accuracy for phase measurement is different for the possibleapplications with different requirements concerning object angle measurement. An accuracyof one degree for the object angle means a maximum error of approximately 8.9 degrees forthe phase difference which seems to be feasible. One main factor causing phase errors can be

an unsatisfactory orthogonality of I- and Q-channel. In reality there is always an angle slightlydifferent from 90° between both which can be calibrated (see [CHU81]).



76

For automotive applications the frequency band at 77 GHz as well as the ISM band at 24 GHz are considered for future systems. For the idea described in this chapter the ISM band is verysuitable due to the higher wavelength (λ = 1.24 cm) compared with 77 GHz (λ = 3.9 mm).Ambiguities can be avoided. On the other hand a sensor at 24 GHz requires a bigger antennaaperture.

The sensor concept might also allow an estimation of the signal distortion caused by crosstalkfrom the transmit to the receive antenna. Crosstalk is caused by propagation outside the sensorand inside depending on the RF layout and on the sensor design. The distortion can bereduced because real targets have the same amplitude in both receive paths while crosstalkinfluence is different in both paths due to different distances to the transmit antenna.

5.2 Data Fusion in the Phase Monopulse Sensor Network

If a single sensor is only able to give a rough estimation of target angles it is an importantquestion how the angle estimation can be improved in the complete system by using theredundancy when measuring with e.g. three or four sensors. To answer this question theKalman filter modifications of the filter algorithm shown in chapter 4.3.4 will be explainedand some simulations convince how the additional angle estimation within a single sensorimproves the system performance. A data fusion overview shown in Fig. 5-5 includes themain elements of the data association and tracking software running on a central processor.The input vectors from all sensors (e.g. four) include range information as well as anestimated target angle. After target to track association, an individual tracker for all sensorstracks the targets and a following track to track association finds sensor track combinations ofall objects to be tracked. The set of associated sensor tracks is the Kalman filter input. This

extended Kalman filter (see also [BAR93]) is used to find a position solution of the object andtracks the object coordinates. From polar input coordinates of all four sensors with theirindividual aspect to the object, the tracker produces filtered Cartesian output coordinates ofthe tracked object.

r 1,α1 r 2,α2 r 3,α3 r 4,α4

Kalman Filter

x,y,vx,vy

Target to Track Association

& Sensor Tracker

Track to Track Association

r 1T,α1Τ r 2T,α2Τ r 3T,α3Τ r 4T,α4Τ

(r 1T,α1Τ/r 2T,α2Τ/r 3T,α3Τ/r 4T,α4Τ)

Fig. 5-5: Data Fusion Overview



77

The filter equations are very similar to the filter described above in chapter 4.3.4 with thedifference that an extension for measured angles is integrated and the derivation of themeasurement matrix and the state transition matrix is accomplished by calculation of theJacobian matrices. Furthermore not the position and velocity estimation errors are included inthe state vector, but the object position and velocity themselves. It is important to mention

here that the matrices should not be exchanged by mistake with the matrices in chapter 4.3.4. The notation is very similar for better comparison between both methods.

For the sensor locations within the sensor network the following coordinates are used:

=

1

11

s

s

y

x sr

(5-2)

=

2

22

s

s

y

x sr

=

3

33

s

s

y

x sr

=

4

44

s

s

y

x sr

The target ranges and angles are measured by each sensor individually at time k :

with: i = 1…4 for four sensors( ) ( )k k r ii α ,

The initial situation of the algorithm is an estimated object state vector of the previous cycle:

State estimate at time t k-1: (5-3) ( )

( )( )(( )

−

−

−

−

=−

1

1

1

1

1

,

,

k v

k v

k y

k x

k x

o y

o x

o

o

s

r

)

)

A state prediction for the current cycle at time t k can be calculated in nonlinear systems withthe general form represented by a function f :

(5-4) ( ) ( )( 1ˆ −= k x f k x s s

rr

In the specific system modelled in this report the system equations are linear:

( ) ( )1ˆ 1, −⋅= k x F k x s s

rr (5-5)

with the state transition matrix: and (5-6)

∆

∆

=

1000

0100

010

001

T

T

F ( )

( )( )( )( )

=

k v

k v

k y

k x

k x

o y

o x

o

o

s

,

,1,

ˆ

ˆ

ˆ

ˆ

r̂

The derivation of the linear state transition and measurement matrices in this case areobtained by calculation of the Jacobian of a function.

The general form of a Jacobian of a vector-valued function g using the gradientoperator is:

( ) x g x

x∇



78

( ) ( )[ ] ( ) ( )[ ]

∂∂∂∂

∂

∂

∂

∂

=

∂∂

∂∂

=∇=

∂

∂=

n

mm

n

T

m

n

T T

x x

x g

x g

x

g

x

g

x g x g

x

x

x g

x

g x g

L

MOM

L

LM

1

1

1

1

1

1

(5-7)

The Jacobian of the state transition function is in our case the state transition matrix itself dueto the linearity of the system equations. The state transition matrix is linear and time-invariantin this case:

( )

( )

∆

∆

=∂

−∂

= −=

1000

0100

010

001

1

1

T

T

x

k f

F k x x s

r (5-8)

The next step is to find a prediction for the measurements of sensor i. It is a function h of thestate prediction for the current cycle k . The general form is:

( ) ( )k xhk z i si ,ˆˆ rr

= (5-9)

The predicted state vector has to be corrected at the end of the algorithm within eachloop of a single sensor. A measurement residual between the real noise-added measurementsand the predicted measurements for the current cycle and for sensor i is weighted with a filtergain or correction matrix W to compensate errors of the state prediction:

( )k x i s,r̂

( ) ( ) ( ) ( ) ( ))k z k z k W k xk x iiii si sˆˆ

,,

rrrr−⋅+= (5-10)

with the real sensor measurements added with noise :( )k z ir

( )k wr

(5-11) ( ) ( )( ) (k wk xhk z irrr

+= )

The vector with the real measurements is as follows:( )k z i

r

( )

( )( ) ( )

( )

∆−−

=

k T

k r k r

k r

k z

i

ii

i

i

α

1r (5-12)

The three elements of the vector of sensor i are the measured range r , a range rate from thecurrent cycle range and the previous cycle range, and the measured angle.



79

The vector of the estimated measurements is:

( )

( )( ) ( )( )( )( )

( )( ) ( )( )( )

( )( )

( )( ) ( )( )( )

( )( )

−−

−⋅

−+−

−+−⋅

−+−

−−+−

=

sio

sio

y

sio sio

sio x

sio sio

sio

sio sio

i

xk x

yk y

k v yk y xk x

yk yk v

yk y xk x

xk x

yk y xk x

k z

ˆ

ˆarctan

1ˆˆ

ˆ1

ˆˆ

ˆˆˆ

ˆ0,220,22

22

r

(5-13)

The measurement residual for the system under consideration is:( ) ( )k z k z iii

r̂rr−=ν

( ) ( )( ) ( )( )

( ) ( ) ( )( )

( )( ) ( )( )( )

( )( )

( )( ) ( )( )( )

( ) ( )

( )

−−

−

−⋅

−+−

−+−⋅

−+−

−−

∆

−−

−+−−

=

sio

sioi

y

sio sio

sio x

sio sio

sioii

sio sioi

i

xk x

yk yk

k v yk y xk x

yk yk v

yk y xk x

xk x

T

k r k r

yk y xk xk r

ˆ

ˆarctan

1ˆˆ

ˆ1

ˆˆ

ˆ1

ˆˆ

0,220,22

22

α

ν r

(5-14)

The filter gain or correction matrix W for sensor i can be obtained by the followingequations:

( )k i

State prediction covariance matrix at the beginning of a cycle:

( ) ( ) Q F k P F k P T +⋅−⋅= 11̂ (5-15)

State prediction covariance matrix in the loop:

(5-16) ( ) ( ) Q F k P F k P T

ii +⋅⋅= −1ˆ

with the system noise covariance matrix: Q

and the Jacobian of the state transition function f : ( )1−k F

Residual covariance matrix: (5-17) ( ) ( ) ( ) ( ) Rk H k P k H k S T

iiii +⋅⋅= ˆ

with the measurement noise covariance matrix: R

and the Jacobian of the measurement function h: ( )k H i

Filter gain or correction matrix for sensor i: (5-18) ( ) ( ) ( ) ( )k S k H k P k W i

T

iii

1ˆ −⋅⋅=



80

Finally the predicted state covariance matrix has to be updated for the next sensor i+1 of thesame cycle k or for the next cycle:

(5-19) ( ) ( ) ( ) ( ) ( )

k W k S k W k P k P T

iiiii ⋅⋅−= ˆ

For the Jacobian of the measurement equations the following measurement matrix H forsensor i at time cycle k is obtained:

( ) ( )

( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

( )

( )( ) ( )( )

( )

( )( ) ( )( )( )

( )( ) ( )( )

( )

( )( ) ( )( )( )

( )( ) ( )( )( )

( )( ) ( )( )

−+−

−

−+−

−−

−+−⋅∆

−

−+−⋅∆

−−+−

−

−+−

−

=

=

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

=∂∂

==

00ˆˆ

ˆ

ˆˆ

ˆ

00ˆˆ

ˆ

ˆˆ

ˆ

00ˆˆ

ˆ

ˆˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

2222

2222

2222

0,,

0,,

0,,

ˆ

sio sio

sio

sio sio

sio

sio sio

sio

sio sio

sio

sio sio

sio

sio sio

sio

y

i

o x

i

o

i

o

i

y

i

o x

i

o

i

o

i

y

i

o x

i

o

i

o

i

k x x

i

yk y xk x

x x

yk y xk x

y y

yk y xk xT

y y

yk y xk xT

x x

yk y xk x

y y

yk y xk x

x x

k v

k

k v

k

k y

k

k x

k

k v

k v

k v

k v

k y

k v

k x

k v

k v

k r

k v

k r

k y

k r

k x

k r

x

k hk H

α α α α

r

(5-20)

The Kalman filter processing is performed as explained in Fig. 5-6. For each cycle a loop overall sensors is calculated to find an optimal and filtered position solution. At each new cyclethe state and covariance matrix prediction has to be evaluated once (Eq. (5-21) and Eq.(5-22)) before running the loop over all sensors.



81

Initialisation

Calculation of astarting position

Track stillvalid ?

State transition matrix F

State / Covariance prediction:

Calculation of measurementJacobian matrix H i(k)

Calculation of measurementresidual:

Calculation of residual covari-ance S i(k), and filter gain W i(k):

Calculation of updated statecovariance matrix:

Calculation of new state variablevector:

Sensor dataavailable?

Yes

No

Yes

No

Stop track

Calculation of newobjekt position

( ) ( )( ) ( ) Q F k P F k P

k x F k xT

s s

+⋅−⋅=−⋅=1ˆ

1ˆ

1

1,

rr

( ) ( ) ( )k z k z k iii

r̂rr−=ν

( ) ( ) ( ) ( ) ( )k W k S k W k P k P T

iiiii ⋅⋅−= ˆ

( ) ( ) ( ) ( ) ( )[ ]k z k z k W k xk x iiii si sˆˆ

,,

rrrr−⋅+=

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )k S k H k P k W

Rk H k P k H k S

i

T

iii

T

iiii

1ˆ

ˆ

−⋅⋅=

+⋅⋅=

Fig. 5-6: Extended Kalman Filter Processing





83

=

01.0000

001.000

00003.00

000003.0

Q

=

05.000

050

0003.0

R

=

0.10000

00.1000

000.10

0000.1

P

(5-23)

5.4 Combination of Amplitude Monopulse and Phase Monopulse Techniques

Application of phase monopulse techniques showed feasibility of angle estimation already inthe single sensor stage. It is obvious that for the data association as well as for themultilateration and tracking results it is of advantage to get this additional angularinformation. When time synchronization between the sensors is also achieved, the targetamplitudes of all sensors can be used in the central processor to get an additional angleestimation using conventional amplitude monopulse techniques. These methods can beapplied after target to target association in the central processor.

5.5 Conclusive Discussion of a Phase Monopulse Sensor Network

A short comparison of advantages and disadvantages concludes the description of the phasemonopulse sensor concept. The two main advantages are that the angle tracking results with asingle sensor detecting an object is much more precise than before and that data association oftargets to sensor tracks is easier than before. With correct data association the number of false

alarms should be significantly reduced.

Advantages of the concept are:1. Possibility to measure an object position angle with each single sensor and use this

information as a contribution in the central processor to improve system performanceand reliability.

2. The required very precise range measurement with the system described before isrelieved because an additional angle information received by each sensor improvesobject angle estimation in the central processor if ranges are less accurate.

3. Angle estimation in each sensor is independent from non-linearities or temperaturedependent variations of the adjustable delay for the receive paths. For the phase

measurement only the difference of propagation time is of importance.4. Situations with extended targets having multiple backscatterers or changing

backscatterer positions in dynamic situations can be handled easier. The effort for dataassociation algorithms within the software of a central processor can be significantlyreduced.

5. Angular resolution can be accomplished by clustering of targets from the four sensorsin the central processor and tracking of distinguishable clusters.

6. In situations when only a single sensor detects the target, tracking results are of verygood quality compared with a sensor network that only measures target ranges.

Disadvantages of the concept are:1. Increased cost for sensor RF frontend hardware due to the second receive path.2. Larger antenna aperture with a second receive antenna patch array.





85

6 Experimental Short Range Radar Network

Practical feasibility of a short range radar network was studied by means of an experimentalvehicle. The following chapters give a brief system description.

6.1 System Description

For experimental evaluation of theoretical aspects in a short range radar network, a normal passenger car was modified to be used for the safety and comfort applications describedabove. The purpose and importance of the vehicle covers multiple aspects. These are forexample:

• Acquisition of realistic traffic data on normal roads and highways in very different

situations. Realistic data files are an important data base for improvement of detectionand sensor data fusion techniques in the laboratory.• Real-time display capabilities are important to show the system performance and all

vehicle data on a notebook in the car.• In combination with the actual street situation recorded on video tape in parallel to

radar data, the radar results can always be evaluated considering the video reference.• Observing the very complex system’s real-time behavior in real traffic situations and

as a target data source for an adaptive cruise control system with an electronicaddressable brake and cruise controller.

• Observing the reflectivity and complexity of very different real objects with adiversity that can not be replicated in a normal laboratory (e.g. reflectivity of trees,metal fences, crash barriers, bicycles, passengers, traffic signs, bridges or evendifferent road surface conditions).

• Experimental vehicle as a development platform to show feasibility of a system whichwill surely become a new feature in future vehicles.

• With the possibility to simply change the vehicle front bumper the performance ofdifferent sensors and sensor networks can be directly compared.

Without the possibility to have access to real data the development of such a system coulddisregard important practical aspects and conditions while some aspects which might be oftheoretical importance show to be of minor interest in a real system. To stay as close to

practical applications and feasibility as possible was always the intention during the wholedevelopment of this system.The implementation of a short range radar network based on four 24 GHz pulse radar sensorsis shown in Fig. 6-1. The sensors are usually covered in this car and can be mounted behind avehicle bumper to make the car look like any other car. A block diagram of the experimentalvehicle equipment is presented in Fig. 6-2. The car is equipped with an addressable brake

booster and a modified cruise controller for adaptive cruise control applications. Amicrocontroller (SAB 80C167) handles communication between the RDU and the cruisecontroller. It also measures the wheel rotation time of all four wheels. The interface to theRDU is the CAN bus the brake is also connected to. All sensors have a CAN interface to beconnected directly to the RDU in a common bus or each of them separately. The RDU serves

as sensor supply and as a central data fusion processor. The RDU functionality will beexplained in the following chapter.



86

Fig. 6-1: Short range sensor network integrated in a vehicle front bumper

ABS

Cruise

Controller

externalsignals

Notebook/VGA Display

V e h i c l e C A N

Brake-Booster 80C167

Radar Decision

Unit

HRR DSP

HRR DSP

HRR DSP

HRR DSP

E t h e r n e t / C A N o

r V G A

+12V

C A N

a n d S e n s o r S u p p l y

Fig. 6-2: Experimental vehicle equipment



87

6.2 Radar Decision Unit Overview

Processing of all radar data is accomplished in an industrial PC (Fig. 6-3 (left side)) mounted

in the back of the vehicle. Input for this so-called radar decision unit are target lists from eachindividual pulse radar sensor. Output is the so-called object map which is a list of detectedobjects with distance, angle and speed. The sensors integrated in latest developments includeintegrated processing capabilities and distance self-calibration to achieve a distancemeasurement accuracy of less than ±3 cm over the complete range of up to 20 m. This

precision was measured with the automatic self-calibration and test system described inchapter 7.1 and is the key sensor feature to achieve high performance with the system.

The radar decision unit (Fig. 6-4) is a very flexible data fusion processor in the system. Itcovers the following tasks:

• Data acquisition of all sensor target lists from the high resolution radar sensorsmounted in the subsystem under consideration (e.g. front or rear bumper). In this stageof showing feasibility, all sensors have an individual CAN bus to the RDU.

• Sensor target lists are received by a microcontroller which transfers all data to a fastdual ported RAM mounted as a daughter-module on a PCI DSP board(TMS320C6701 evaluation board). The microcontroller CAN board and the PCI DSP

board with DPRAM daughter-module is depicted in Fig. 6-3 (right side).• The task of the DSP is to combine all target lists to get a representation of the real

street situation (object range, angle and speed). The DSP is timer-triggered with 20 ms cycle time and interrupts the microcontroller via DPRAM to start a new cycle of target

data collection.• The microcontroller has an additional own on-chip CAN interface to read vehicle datalike own speed or the current curve radius and to control brake and cruise controller.Control algorithms are included in the data fusion processor (DSP) which calculates arequired brake pressure or vehicle speed. This information is passed to themicrocontroller’s CAN interface.

• For real-time visualization in the drivers cockpit the objects detected by the RDU are passed via PCI bus to an all-in-one PC board which is the main processing board booting the operating system from hard-disk on system start.

• The PC board in this case has all required interfaces on board, like a normalmainboard including an Ethernet interface. With its interfaces, the PC is able to record

data files while driving, to display object map data or vehicle data in real-time usingan external VGA display. A DirectX display running on the PC showed very fastupdate rates of a few milliseconds ([WEN00]). Transmission of all data via Ethernete.g. by means of Client-Server sockets showed to be another very flexible possibilityfor an RDU display.

On system start all sensors boot up individually and unsynchronized to each other. Themicrocontroller starts from its Flash-Eprom and waits for DSP triggers to collect data. The PC

boots automatically and starts a Windows-based application which loads an executable fileto the DSP board, starts the DSP software and transmits all results to a display tool (if

connected as a client application to the server). So the complete system is self-starting andshows much potential for modification of software and experiments in an early stage ofsystem development and feasibility study as well as system performance tuning.



88

Fig. 6-3: RDU industrial PC with data acquisition CAN board and DSP hardware

Fig. 6-4: Radar Decision Unit Overview

The software running on the PC (see Fig. 6-5) includes features which appeared to beimportant for fast signal processing development with the experimental system. All measuredsystem data can be saved on hard-disk. Individual sensor target lists can be saved duringmeasurements and used in the laboratory to improve data fusion algorithms. Target list filescan be loaded and the data fusion can be processed in a very convenient Windows-based

development environment for debugging or on the DSP board to measure execution time ofthe data fusion software on the DSP. This can be used to estimate which maximum processor performance is required in a later serial system. To be able to debug the software in a veryconvenient environment and directly test data fusion software modifications with real datawas a way of very fast progress for the complete system. It is furthermore possible to sendlarge blocks of data from each sensor (up to 512 CAN messages per cycle of approximately100 ms) to directly have a look at the analog sensor output signal which is sampled by an on-chip A/D-converter of the sensor DSP. With this feature raw sensor data can be recorded indynamic street situations.



89

Fig. 6-5: Online display in the driver’s cockpit

6.3 Network Communication Considerations

Communication of data in the sensor network is an important topic and different factorsinfluence the selection of a bus system or protocol. The required data rate is not the onlyaspect. Especially for a radar sensor network in a vehicle, the following points have to beconsidered:

• Safe transmission of all data in an electromagnetic influenced environment• Serial communication with only a few wires to be integrated into the vehicle• Fast bus access of the individual sensors to a common bus interface• Availability of cheap communication controllers (as cheap stand-alone controllers or

as on-chip interface controllers on commercial microcontrollers)• Low amount of overhead for data transmission• Capability to send short messages with low effort and overhead• Extension of the network over a few meters without transmission errors• Flexible number of nodes in the network and correct communication if individual

nodes fail

A very good overview of common transmission protocols and busses and evaluations for avehicle sensor network is given in [KUH00]. The required data rate for a system of foursensors has to be evaluated to find out which communication platform is suitable for a vehiclesensor network. Each sensor transmits e.g. an amount of 10 targets per cycle with 8 Bytes pertarget message and a cycle time of 20 ms. The complete data rate for a bumper equipped withfour sensors is:



90

s

kBit

D ms

12820ms

1Bit64104

TimeCycle

1gthMessageLen NumTargets NumSensorsTargets10,20,Sensors4

=⋅⋅⋅=

⋅⋅⋅= (6-1)

One target message includes distance information, amplitude, velocity (if measured) and atime stamp. If the realistic number of 10 targets per sensor and cycle in a range of up to 20 m is not sufficient, the data rate increases. Additionally the cycle time of 20 ms is too long forapplications with high demand on security. A cycle time of 10 ms would be better. For theserequirements a worst case estimation with 20 targets would be:

s

kBit

ms Bit D ms 512

10

164204Targets20,10,Sensors4 =⋅⋅⋅= (6-2)

It should be noted that this data rate is only relevant data, but no header information. Allheader information has to be added to get the maximum bus load for the communication busto be selected.

In this thesis a maximum number of 10 targets, a maximum cycle time of 20 ms is assumedand a data rate of 128 kBit/s. For a first system all sensors were separated and connected tothe RDU via individual CAN busses. One CAN bus is able to handle a maximum data rate of1 Mbit/s including data and header. To guarantee safe transmission, a maximum bus load of40% is a good compromise. For a CAN bus the header of a 64 Bit data message is 47 Bit(total = 111 Bit). The relevant data rate for one bus with a maximum bus load of 40% is then

approximately 230 kBit/s.

With the capacity of one CAN bus, data compression can be applied to manage four sensorson one CAN bus. The properties of CAN are very attractive to use it in a sensor network andthe price of a CAN node is very low compared with other interfaces, because CAN is widelyused today for many applications. If more capacity is needed different new interfaces areinteresting. These are e.g. MOST (Media Oriented Systems Transport with up to 50 MBit/s),Byteflight (up to 10 MBit/s data rate) or TTP (Time-Triggered Protocol, a system withTDMA protocol).

6.4 Sensor Network Synchronization

It was already explained that precision in range measurement of approximately 3 cm isdesired to achieve good results for angle estimation. With a cycle time of 20 ms Table 6-1shows the obstacle movement for different velocities. For a maximum difference in timesynchronization between two sensors of 20 ms the error for this worst case is shown. Forvelocities of 5 m/s the maximum error can already be 10 cm. It is obvious that timesynchronization between the sensors is absolutely required for dynamic applications, while a

parking aid system can show good results without any synchronization.



91

Velocity 5 m/s 10 m/s 15 m/s 20 m/s 50 m/sDistance 0.1 m 0.2 m 0.3 m 0.4 m 1 m

Table 6-1: Obstacle movement for different velocities

One solution for time synchronization in the network is to use a prioritised interrupt line to allsensors and interrupt the sensor processing in fixed time intervals to avoid drift. This needs anadditional wire in the vehicle. If all sensors are connected to a single bus system, e.g. a CAN

bus, one CAN message is sufficient if the CAN controller gets an interrupt on reception ofthis synchronization message. Due to the fact that CAN is a multi-master bus system, allsensors would receive the message simultaneously. For each sensor connected to a separate

bus the synchronization message will not be transmitted on all buses at the same time. Thereis a fixed time difference. In this case an interrupt line is the best solution.

6.5 Closed-Loop Adaptive Cruise Control

On the base of the high range resolution radar network a closed-loop adaptive cruise controlwas integrated into the experimental car. A block diagram of the cruise control system isdepicted in Fig. 6-6. The control system structure is a typical cascaded control system withcruise controller and brake deceleration controller inside and a distance controller. A distancecontrol algorithm calculates a distance reference for the distance controller. Output is avelocity reference for both the cruise controller and the brake deceleration controller. Due tothe fact that only deceleration or acceleration are active at the same time the controllers areswitched in the software which is also indicated in Fig. 6-6. v is the measured velocity of

the host vehicle and can be measured by means of ABS wheel sensors. v is the velocity of

the selected object to follow for the distance and velocity control algorithms. It is measured by the sensor network or estimated in the tracking filter as range rate. is the currentdistance between the host vehicle and the object to follow. For radar system tests linearcontrol algorithms were implemented. The shown control block diagram was implemented inan adaptive cruise control in the experimental vehicle and tested with the short range radarnetwork with good performance.

host

otf

∆ x

Distance

Controller

∆vref ∆xref

-votf

-

+

+

-

+K

CruiseController

BrakeBooster

Vehicleand

Sensors

votf

∆xvhost

p b,ref

Fig. 6-6: Block diagram of a closed-loop adaptive cruise control





93

7 Single Sensor Experimental Results

This chapter presents some results of the used sensor technology concerning high precisionrange measurement and frequency domain velocity measurement.

7.1 Automatic Sensor Test System

A previous chapter showed the required accuracy of measured target ranges to achieve preciseangular estimation results. In reality non-linearities, e.g. of an analog sensor drive-boardgenerating the delay time for the sensor receive path switch, result in a systematic rangemeasurement error depending on real target range. This error can be measured very precisely.A calibration is then possible with a known range error for the complete range up to morethan 20 m. Manual calibration can be accomplished by placing a reflector at known distances

and comparison of the true distance between sensor and reflector with the sensor output value.To ensure highest precision and a very short measurement time, an automatic sensor testsystem was designed (Fig. 7-1) [HAN00].

The system consists of a linear Gray code over a distance of up to 30 m mounted onto wooden boards. Optical reflex coupler sensors are used to measure the precise position of a railvehicle by scanning the Gray code. The reflex couplers are mounted on the bottom of amoving carrier vehicle equipped with a DC motor, a microcontroller and the radar sensor withits internal digital signal processor or an external sensor control unit. Power supply for thecarrier vehicle is provided from one pair of rails. Digital data communication is performed viaCAN bus using a second pair of rails. Working as a sensor positioning system, a CAN bus

message places the carrier vehicle to the specified distance with a specified velocity. Vehicle positions are measured by the reflex couplers and reported to the notebook each 20 ms.Additionally the sensor mounted on the vehicle transmits a targets list each 20 ms. Truevehicle position and sensor target lists can be saved in data files for each cycle. Multiplemeasurement cycles can be started to scan e.g. the complete sensor range many times andstore all data in separate files. The microcontroller uses pulse width modulated control of theDC motor to move the carrier vehicle along the rails with different velocities. The maximumvelocity is 0.6 m/s. One complete measurement cycle up to 30 m requires about 4 minutes.The used 14 Bit gray code allows a resolution of the true distance to the stationary reflector of5 mm within a range of up to 82 m. Fig. 7-2 gives an impression of a real measurementsituation (30 m length). Very good system performance was noted for automatic sensor

accuracy measurements making the system a very convenient tool for short range radarsystem developments. The measured data can be used to correct the systematic distancemeasurement error by software. This ensures high precision for angle estimation techniques

based on distance information. An example of a measured sensor distance error up to 24 m isshown in Fig. 7-5.

System configurations different from the standard configuration shown in Fig. 7-1 aresuggested in Fig. 7-3 for angle accuracy measurements and in Fig. 7-4 for distance accuracymeasurements with variable temperature.



94

Sensor

DSP

CAN

Micro-controller

CAN

Reflex-coupler

stationaryReflector

Gray Code

PC Notebook

CA N

Motor

Track CAN transmission via tracks

Fig. 7-1: Automatic sensor test system block diagram

Fig. 7-2: Equipped carrier rail vehicle





96

the notebooks serial interface. Measurements can be started in the evening and carried outautomatically until the next morning.

7.2 Measurements of Single Sensor Range Accuracy

Very high range accuracy is the key feature of the short range radar network. Using theautomatic sensor test system described in chapter 7.1 single sensor range accuracy can bemeasured with the system configuration of Fig. 7-1. The ability to check the sensor accuracyand therefore quality automatically brought remarkable progress into the complete systemdevelopment. Changes of sensor hardware can now be evaluated and range accuracy andstability can be assured easily. A complete measurement cycle for one sensor takes only a fewminutes. Thus multiple measurements can be recorded automatically. Fig. 7-5 is the result ofone single sensor range accuracy measurement. It can be seen that the remaining systematicerror of range accuracy is small enough to ensure always good system performance.

200 400 600 800 1000 1200 1400 1600 1800 2000 2200-10

-8

-6

-4

-2

0

2

4

6

8

10

Distance [cm]

D i s t a n c e

E r r o r [ c m ]

Distance Error vs. Distance

Fig. 7-5: Single sensor range accuracy

7.3 Frequency Domain Velocity Measurement

Chapter 3.2.3 already described possibilities for simultaneous range and velocitymeasurement. Fourier transform and Doppler frequency calculation in each range gate gives amatrix including both range and Doppler information for all targets. The following resultsshow a sequence of a test drive with an experimental vehicle. In an indoor garage fixed

objects on the side of the path were passed. Own vehicle speed can be measured by relativevelocity of detected fixed objects and was approximately 8 m/s (28.8 km/h). One highresolution radar sensor was programmed to scan the complete range and sample data



97

according to Fig. 3-9. Data blocks were transmitted via CAN and recorded for offline processing. A representation of the range and Doppler matrices is depicted in Fig. 7-6 to Fig.7-8 as a color plot. Additionally the Doppler frequency spectrum for the range gate includingthe target is depicted on the right figures having a logarithmic scale.

A total number of 32 range gates was sampled with 32 samples per range gate. For thecomplete measurement time, velocity range and resolution the parameters defined in chapter3.2.3.1 were selected. The velocity measurement range and the velocity resolution are in thiscase:

h

km

s

mv 9025max ==

h

km

s

mvrel 6.556.1 ==∆

The peak at frequency zero in the spectrum results from a signal offset of the analog sensoroutput signal. With additional calibration this peak can be removed. Due to non-orthogonalities of inphase and quadrature channel a second peak mirrored at frequency zerocan be observed. [CHU81] presents methods to correct this error. The sequence shows anobject passing the vehicle at three time steps with 200 ms distance from step to step. AHamming window was selected for sidelobe suppression.

In Fig. 7-6 to Fig. 7-8 the complete range was scanned with low resolution of velocity withina total time of 31.8 ms. To achieve higher velocity resolution at same total measurement time,in other measurements a number of 64 samples were collected per range gate with scanningonly half of the complete range (e.g. from 10 m up to 20 m). Results showed that a longermeasurement time per range gate increased the signal to noise ratio and improved velocityresolution and also accuracy. The disadvantage is that the processing time increases as

described in Appendix C (for TMS320F243 digital signal processors).



98

-25 -20 -15 -10 -5 0 5 10 15 20 250

20

40

60

80

100

120

140

160

180

200

220

Velocity [m/s]

A m p l i t u d e [ 2 0 * l o g ( a b s ( F F T ) ) ]

Spectrum for Distance 14.8m

Target

Fig. 7-6: Sequence at time step 1273 and spectrum at 14.8m

-25 -20 -15 -10 -5 0 5 10 15 20 250

20

40

60

80

100

120

140

160

180

200

220

Velocity [m/s]

A m p l i t u d e [ 2 0 * l o g ( a b s ( F F T ) ) ]


Target

Fig. 7-7: Sequence at time step 1275 (200 ms later) and spectrum at 12.9m

-25 -20 -15 -10 -5 0 5 10 15 20 250

20

40

60

80

100

120

140

160

180

200

220

Velocity [m/s]

A m

p l i t u d e [ 2 0 * l o g ( a b s ( F F T ) ) ]


Target

Fig. 7-8: Sequence at time step 1277 (200 ms later) and spectrum at 11.2m



99

8 Experimental System Results for Different Applications

The experimental vehicle described in chapter 6 is an excellent platform to test all softwareand sensor hardware modifications in realistic street conditions. It is very important that such

a system does not only show good results in ideal laboratory situations, but of course also in arealistic environment. Normal street conditions reveal a very high degree of complexity whichnobody would ever expect who only works in a laboratory. But this is the target to get such asystem running with perfect results on normal roads. It is important to find a catalog of manydifferent situations where such a system has to work perfectly and test these situations manytimes and improve the system until the obtained accuracy meets the requirements. Results forsome of these situations can be found in this chapter.

The following measurements show quantitative results of different applications. In most casesexact accuracies of distance and angle measurements are not given, because no other system

existed during these tests which could record the same situation in parallel as a reference forevaluation of the system precision. Angular accuracy can only be measured in staticsituations. Angular resolution is of course also an important topic to distinguish between twoobjects at same distance in front of the car when driving between them. Parking aid andstop & go situations explained in this chapter show that the system is feasible to handledifferent realistic situations. It should be emphasized that the system update rate is 20 ms. Todisplay object trajectories of the measurements has the advantage that position information intwo dimensions and its change over time can directly be seen in a single diagram. This is agood qualitative representation of a complete measurement situation and was often used toevaluate the system performance.

8.1 Measurements of Angular Accuracy

Angular accuracy of a static laboratory situation is the first simple system test to see that anangle estimation by multilateration techniques works quite well. This situation with twodifferent point target reflectors is based on target range measurements only. It is more difficultto determine angular accuracy of extended targets, because the geometrical center and theobject reflection center for microwaves often differ from each other. On the other hand anextended object results in many close detected targets per sensor which have to be associatedto each other to calculate an object position in the multilateration procedure.

8.1.1 Angular Accuracy of Point Targets

Angular accuracy and stability can be measured easily in static situations as shown in Fig.8-1. A cylindrical reflector and a corner reflector were placed in front of the sensor networkand the calculated system intersections were recorded for 62 seconds. For each cycle sensortarget tracks were used for calculation of intersections by means of a least squares algorithm.The position of the cylindrical reflector is (4.5 m,1.5 m) and the position of the cornerreflector is (6.8 m,-1.6 m). The position solutions are of very high stability with low errorvariances.

Cylindrical reflector variances: cm x 57.02 =σ cm y 58.12 =σ



100

Corner reflector variances: cm x 3.02 =σ cm y 67.12 =σ

CylindricalReflector (4.5,1.5)

Corner Reflector (6.8,-1.6)

VehicleBumper

Fig. 8-1: Static multiple object situation

Fig. 8-2: Cylindrical reflector and corner reflector

Another measurement to prove angular accuracy of the radar network is depicted in Fig. 8-3.

An oil barrel of approximately 40 cm diameter was moved on ±2 m from the vehicle centerline and at 8 m in front of the car in a rectangular way. The complete rectangle was movedtwice and the sensor network object map was recorded. It is very impressive that on both lapsthe object map results are very identical. Fig. 8-3 is the plot of the object trajectory in a birdview display, i.e. the picture was not cleared during the measurement. The object position ofthe complete measurement is visualized. Differences from the ±2 m lines on the sides aresystematic errors and reproducible. The maximum deviation to the sides is always less than50 cm. This example also illustrates that small errors of the measured sensor ranges mayresult in significant errors of the estimated object position due to the short baseline betweenthe sensors in the bumper. The barrel was moved with a velocity of approximately 15 - 20 cm

per second. The four small squares below the measured curve indicate the four sensorsmounted in the vehicle bumper.



101

Fig. 8-3: Trajectory of a rectangular movement of an oil barrel (two laps)

The situation in Fig. 8-4 and Fig. 8-5 is a static situation in a corner of a building. The cornersin the building wall (marked by 1…3) are like small corner reflectors and can be seen as pointtargets in the measurements. The door in front of the experimental car is another goodreflector in this situation. Displayed results of the radar decision unit are shown on an onlinedisplay in the car (see Fig. 8-5). The small squares are detected targets of the four sensorsdisplayed directly in front of the specific sensor because a single target of a sensor has onlyrange and no angle information. The arcs indicate sensor target tracks of the individualsensors. These sensor target tracks are used for the multilateration procedures. After targettrack to target track association a least squares algorithm estimates an object position for thecurrent cycle, i.e. intersection marked by small yellow dots in the display. The bigger red dotsare the filtered intersections, i.e. object positions. Fig. 8-5 shows that the three building

corners are well detected by the sensors and the angle estimation works quite well.Additionally the door in front of the car is located in the correct position by the multilateration

procedures.



102

Fig. 8-4: Static multiple object situation

1

2

3

4

Fig. 8-5: Bird view of the calculated static multiple object situation



103

8.1.2 Angular Accuracy of Extended Targets

Extended obstacles include several reflecting centers which are distributed very closely on thevehicle surface. This might e.g. be the rear end of the car in Fig. 8-7 or may result fromreflections from the bottom of the car. It is obvious that numerous targets for each sensor will

be detected in such a situation and all these targets have to be tracked. Individual sensor targettracks are associated to each other to find a correct object position. If this important track totrack association fails, the angle estimation results in a wrong interpretation of the situation.This fact is independent from the kind of processing that is chosen, i.e. a least squares

processing and a Kalman filter both can only give good results if the sensor track to trackassociation is correct. The intention of the following results is to show that angle estimationnot only of point targets, but also of extended targets is possible. Of course a correct angleestimation of extended obstacles is still a challenging topic for radar networks of this kind, butthe results of this work already show some good news that it is not impossible to handle thesesituations with such a network.

Two different distances of the own experimental vehicle’s center axis to the car parked on theside of the street were selected and the distances of the car parked on the side to the centeraxis were calculated in short measurements. The first measurement was 450 cycles long (9seconds) and the results are displayed in Fig. 8-7 together with a photograph of the situationfrom the driver’s seat (Fig. 8-6). Fig. 8-7 shows that the distance to the vehicle center axis isabout 1.5 m. In Fig. 8-8 the car parked on the side is about 3 m away from the vehicle centeraxis. This can also be seen in the diagram (Fig. 8-9). The situation was recorded for 600cycles, i.e. 12 seconds. It can be seen that the curve in Fig. 8-9 is not as stable as in Fig. 8-7due to the fact that the sensor on the outer left corner is detecting the car not as good as

before. If only three sensors detect the car, the results are not as precise as with four sensors

detecting it.





105

Fig. 8-8: Vehicle at 3 m from own vehicle axis

0 2 4 6 8 10 12-10

-8

-6

-4

-2

0

2

4

6

8

10

Time [s]

M e a s u r e d d i s t a n c e f r o m o w n v e h i c l e a x i s [ m ]

Vehicle at 3m from own vehicle axis

Fig. 8-9: Measured distance of vehicle at 3 m from own vehicle axis



106

8.2 Measurements of Angular Resolution

It is not easy to distinguish between two objects with very short distance between each other

and at almost the same distance to the vehicle. Even if the range resolution of the singlesensor is very high to separate two targets, the data association in the multilateration processorhas to be very good to associate the targets correctly to each other to identify the two objectsat their correct positions. One test with the vehicle driving between two corner reflectors atthe same distance to the vehicle located on ±2 m to the sides is shown in Fig. 8-10.

Fig. 8-10: Trajectory when driving between two corner reflectors





108

8.4 Stop & Go Situations

The surrounding of a vehicle driving at e.g. 50 km/h is very dynamic and targets for eachsingle sensor appear only for a short time. Targets have to be picked up by the tracker very

fast to ensure fast reactions of the system in case of an unavoidable accident. So the use of aradar network in stop & go situations requires detection and tracking of all objects with very

precise coordinates. This is a very challenging task concerning the angle estimation. With theexperimental vehicle measurements were recorded on normal streets in Hamburg and also onhighways at very high speed. For the existing system status a maximum relative velocity to

pick up a target for tracking is limited to 50 km/h by the gate for target to track association.For first feasibility tests this limitation was accepted. For higher relative velocities the dataassociation has to be improved.

Fig. 8-12 shows a situation where a lamp pole on the side of the street was passed in a curve.Such a lamp pole is like a cylindrical reflector of very small radar cross section due to thesmall diameter. So as a point target it is easy to estimate an object position for these lamp

poles on the street sides. They can often be observed in measurements and always trackedwith high precision of distance and angle. In Fig. 8-13 the trajectory of the lamp is depicted.The object was first picked up at 14 m.

Passing parked cars is an important task when driving in a town. The system has to be able tolocate the parked objects on the side and not on the road. For an error in position finding, anACC car would immediately activate the brakes which may cause a dangerous situation forother following drivers on this road. Fig. 8-14 shows the situation and Fig. 8-15 shows theobject trajectories when passing the parked cars. Velocity was not more than 20 km/h. The

precision of an angle estimation of these extended objects is not as good as in the case of a point target especially when a car is measured from this aspect angle. Pointing with the radarat the vehicle corner, the side of the vehicle is like a mirror, reflecting emitted energy awayfrom the radar sensor. The same does the back of the car from this aspect angle.

A real stop & go situation is depicted in Fig. 8-16. The object radius for this situation isshown in Fig. 8-17. The diagram shows radial distance versus cycles (1 cycle equals 20 ms).The vehicle in front of the experimental car is seen as an object with slowly changing distance

between 18 m and 10 m. Passed objects (i.e. cars parked on the side) are seen as very steeplines in the diagram. The distance changes very fast. Own velocity can be estimated from thegradient of the lines. Fig. 8-18 shows the corresponding estimated angles in degrees over

cycles. For the car in front a precise angle was estimated around zero degrees. Passed objectsare first seen at small angles at higher distance. With smaller distance these objects moverelative to the own car from the center to the side when being passed. So the angle increasesfor objects being passed. Most fixed objects are detected on the right side (negative angle).From range rate estimation Fig. 8-19 shows relative velocity in x-direction (m/s over cycles).For the objects appearing for a very short time the velocity estimation is not as precise as forthe car in the front. Fig. 8-20 and Fig. 8-21 are presented to show an example of the results ofthe single sensor target tracking. Fig. 8-20 shows the targets detected in each single cycle bythe outermost right sensor. The single sensor target tracker has the task to extract relevantinformation from this picture in each single cycle. Fig. 8-21 is what the target trackerextracted and tracked from the detected target lists. The vehicle in the front was always

detected with very high probability of detection and also many fixed objects were picked upand tracked by this sensor. So the target tracker really extracted the most importantinformation from all the data.



109

Fig. 8-12: Street lamp pole in a curve

Fig. 8-13: Trajectory when passing a street lamp pole



110

Fig. 8-14: Passing parked cars

Fig. 8-15: Trajectories of two passed cars



111

Fig. 8-16: Stop & Go situation

Fig. 8-17: Object radius of stop & go situation (radius [m] vs. cycles (time))



112

Fig. 8-18: Object angle of stop & go situation (angle [°] vs. cycles (time))

Fig. 8-19: Object speed in x – direction (speed [m/s] vs. cycles (time))



113

Fig. 8-20: Target detections of sensor 4 (right vehicle side, range [m] vs. cycles (time))

Fig. 8-21: Sensor target tracks of sensor 4 (range [m] vs. cycles (time))









117

Appendix

A Standard Form of the Radar Equation

Power density at distance R:

24densityPower

R

G P T

π = (A-1)

with: : transmit power R: distance G: antenna gainT P

Isotropic reflected power from target at distance R:

2

4

power Reflected R

G P T

π

σ = (A-2)

with: G: antenna gain σ : effective area of isotropic target

Reflected power density back at the radar:

( )224density powerReflected

R

G P T

π

σ = (A-3)

Basic radar equation (e.g. [LEV88]):

( ) 43

22

4 RG P P T

Rπ

σ λ = with:π λ

4

2

G A = : effective receiving antenna area (A-4)

: received power R P

The effective area of the isotropic target is also called its radar cross section. This is the areaof a target that reflects back isotropically and would have caused the same return power as theoriginal target. The radar cross section is usually very different from the physical dimensionsof a target.

Other form of the radar equation (see e.g. [LUD98]):

( ) atmt n sys

t

aus L L BkT R

G P

N

S

⋅⋅

⋅⋅=

1

4 43

22

π

σ λ (A-5)

with: : noise powern sys BT k N ⋅⋅=

: losses due to the distance between transmitter and antennat L

: losses due to atmospheric attenuationatm L



118

B Basic Equations for Single Pulse Detection

The output signal without noise can be described by:

(B-1)

( ) ( ) ( ) ( )t bt at At s cc sc ω ω ϕ ω sincoscos0 ⋅+⋅=−⋅=

cc s f a

bba A π ω ϕ 2 ;arctan ;22 =

=+=

The output noise of the receiver can be described by:

(B-2) ( ) ( ) ( ) ( ) ( )t t Y t t X t n cc ω ω sincos0 +=

with being the center frequency and X(t), Y(t) are independent random variables with

Gaussian probability density function, zero average and same variance.cω

The combined output of signal and noise gets:

( ) ( ) ( ) ( )[ ] ( ) ( )[ ] ( ) ( ) ( )( )t t t r t t Y bt t X at nt st e ccc ϕ ω ω ω +=+++=+= cossincos000

(B-3)

with: ( ) ( )[ ] ( )[ ] ( ) ( )t Y t X t Y bt X at r 2

1

2

1

22 +=+++= ( )

( )

( )

+

+=

t X a

t Y bt

arctanϕ

The probability density functions of both parts assuming independent Gaussian variables areas follows:

( ) ( )

−−=

2

2

111

2exp

2

1

N N

a X X p

σ π σ and ( )

( )

−−=

2

2

112

2exp

2

1

N N

bY Y p

σ π σ (B-4)

Due to independence from each other the two-dimensional joint probability density functionis the product of both parts:

( ) ( ) ( ) ( ) ( )

−+−=⋅=

2

2

1

2

12121111

2exp

2

1,

N N

bY a X Y p X pY X p

σ πσ (B-5)

The transformation to polar coordinates (r , ϕ ) can be achieved with the relations:

( )ϕ cos1 r X = ( )ϕ sin1 r Y =2

1

2

1 Y X r +=

= 1

1

arctan X

Y

ϕ

(B-6)



119

( ) ( )

( )11

11

,

,,

Y X J

Y X pr p =ϕ with the Jacobian J of the transformation: (B-7)

( )r

Y X

Y

r

X

r

Y X J 1

det,

11

1111 =

∂∂

∂∂

∂∂

∂∂

=ϕ ϕ

(B-8)

The joint probability density function of r and ϕ is:

( ) ( ) ( )( )

−−++−=

2

222

2 2

sin2cos2exp

2,

N N

rbrabar r r p

σ

ϕ ϕ

πσ ϕ (B-9)

The probability density function of the envelope is:

( ) ( ) ( )

( ) ϕ ϕ ϕ σ σ πσ

ϕ ϕ

π π

d rA Ar r

d r pr p s

N N N

−⋅⋅

+−== ∫∫ cosexp

2exp

2,

2

2

02

22

2

2

0

(B-10)

The resulting probability density function of the envelope of signal plus noise gets finally:

( ) ( )

⋅

+−=

202

22

2 2exp

N N N

rice

rA I

Ar r r p

σ σ σ (B-11)

with the modified Bessel function of order zero: ( ) ∫ ⋅=π

ϕ ϕ π

2

0

cos0

2

1d ek I k

(B-12)

The PDF for the envelope of signal plus noise is also called Rician PDF. By setting

2

2

2 N

A

N

S

σ = (B-13)

the PDF can be written in a different form:

( )

⋅⋅

+−=

N N N

rice

r

N

S I

N

S r r r p

σ σ σ 2

2exp 02

2

2 (B-14)

For the PDF of the envelope of the noise the amplitude has to be set to zero. The PDF is:

( )

−

= 2

2

2 2exp N N Rayleigh

r r

r p σ σ (B-15)



120

C FFT Memory and Timing Requirement

For the processing of Fourier Transforms, the processing hardware performance plays an

important role. For a standard FFT library for the TMS320C2000 digital signal processorfamily the memory requirements and the timing requirements are listed below to get anoverview of what is feasible with cheap processor hardware of limited performance. The

processors are 16 bit fixed-point processors running at 20 MHz. Data is taken from [TEX98].

The forward FFT memory requirements are:

Program Memory Words

FFT Size

Data Memory Words for

intermediate storageFunction Size Sine Table Size

N 2N+17 ¾ N32 81 109 2464 145 109 48

128 273 109 96256 529 114 192512 1041 114 384

1024 2065 114 768

Table C-0-1: Forward FFT Memory Requirements

The forward FFT timing requirements are:

FFT Size Clock Cycles Time[ms] (20MHz) Time[ms] (40MHz) N O(N*logN) O(N*logN) O(N*logN)32 7.552 0.3776 0.188864 17.216 0.8608 0.4304

128 38.880 1.944 0.9720256 86.298 4.315 2.157512 238.016 11.90 5.950

1024 522.720 26.14 13.07

Table C-0-2: Forward FFT Timing Requirements



121

D Resolution of Doppler Ambiguities

As already described in chapter 3.2.3.2, the true frequency to be calculated for the ambiguous

measured real values and is:'

1

M '

2

M

222111 M f V M f V M ′+⋅=′+⋅= (D-1)

The solutions for the numbers of the ambiguous intervals V 1 and V 2 are the interesting values.

The two chosen ramp frequencies f 1 and f 2 have to be two numbers with no common divisor.

First both measured values have to be normalised:

10 ; 10 ; 22

2

211

1

1 ≤≤

′

=≤≤

′

= M f

M

M M f

M

M (D-2)

(D-1) is then:

( ) ( 222111 f M V f M V M +=+= )

( ) ( ) 0 222111 =+−+⇒ f M V f M V (D-3)

Both frequency intervals f 1 and f 2 can be divided into J 1 and J 2 subsections. The numbers J 1

and J 2 have no common divisor. This results:

1221

2

1

2

1 J f J f J

J

f

f =⇒= (D-4)

The subsections have all the same length E :

2

2

1

1

J

f

J

f E == (D-5)

With (D-4) equation(D-3) becomes:

(D-6) ( ) ( ) ( ) ( ) 0 0 11221122222111 =−+−⇒=+−+ J V J V J M J M J M V J M V

The first term of (D-6) is known and the second term includes the unknown values V 1 and V 2.

With the following substitution the equation is:

( ) ( Z J V J V J M J M Z =−⇒−= 22111122 )

)

(D-7)

with: (D-8) ( ) ( 11 21 −≤≤−− J Z J

After some steps the solution is (see [ROH86] for a detailed derivation):



122

( ) ( )( )( 211 mod1 J Z V Z V = )

)

(D-9)

( ) ( )( )( 122 mod1 J Z V Z V = (D-10)

with:

( ) ( ) ( ) ( )2

1

211 mod1 2 J J J V J −−= ϕ

(D-11)

( ) ( ) ( ) ( )1

1

212 mod1 1 J J J V J −−= ϕ

(D-12)

ϕ (m) is Euler’s function [SCH90] defined as the number of positive integers r smaller than m

that are coprime to m, i.e., for which 1 ≤ r < m.

Note:ϕ (1) = 1;If m is prime, ϕ (m) is: ϕ (m) = m − 1.

Example: m = 10; r = 1,3,7,9. Thus ϕ (10) = 4.m = 11; ϕ (11) = 10.

The solution can be checked with: ( ) Z J V J V =− 2211

A flow chart of the algorithm is shown in Fig. D-0-1.

Measurement

Normalization:M1 = M1' / f 1M2 = M2' / f 2

Calculation of Z:Z = M2J2 - M1J1

V1(Z), V2(Z)True frequency:M = [M1+V1(Z)]f 1 = [M2+V2(Z)]f 2

V1(1), V2(1)

M1', M2'

M

Resolution algorithm

Fig. D-0-1: Resolution of Doppler ambiguities



123

References

[BAR88] Bar-Shalom, and T. E. Fortmann: “Tracking and Data Association“, Orlando,FL, Academic Press, 1988.

[BAR93] Bar-Shalom, Y. and Li, Xiao-Rong: “Estimation and Tracking – Principles,

Techniques and Software”, Norwood MA, Artech House, 1993.

[BRI74] Brigham, E. Oran: “The Fast Fourier Transform”, Prentice Hall, Inc.,Englewood Cliffs, N.J., 1974.

[BLA86] Blackman, S.: “Multiple-Target Tracking with Radar Applications”, DedhamMA, Artech House, 1986.

[BLA99] Blackman, S., and Popoli, R.: “Design and Analysis of Modern Tracking

Systems”, Norwood MA, Artech House, 1999.

[BRO] Bronstein-Semendjajew: “Taschenbuch der Mathematik”, Teubner, 24.Auflage.

[BRO98] Brookner, Eli: “Tracking and Kalman Filtering Made Easy”, John Wiley &Sons, 1998.

[BRO97] Brown, R. G.: “Introduction to Random Signals and Applied Kalman

Filtering”, John Wiley & Sons, 1997.

[CHU81] Churchill, F.E.; Ogar, G. W.; Thompson, B. J.: “The Correction of I and Q

Errors in a Coherent Processor”, IEEE Transactions on Aerospace andElectronic Systems, Vol. AES-17, No. 1, pp. 131, January 1981.

[ERI95] Eriksson, L. H. and As, B. O.: “A High Performance Automotive Radar for

Automatic AICC”, IEEE International Radar Conference, Alexandria, Virginia,May 1995.

[ETS00] Etschberger, K.: “Controller Area Network“; Carl Hanser Verlag, Munich, 2nd

Edition, 2000.

[HAA00] Haas, G.: “Datenzuordnungsverfahren in einem Automobil - Radarnetzwerk”;Diploma Thesis, TU Hamburg-Harburg, Department of Telecommunications,2000.

[HAN00] Hansen, M.: “Entwicklung eines Systems zur automatischen Kalibrierung von

KFZ – Nahbereich – Radarsensoren”; Diploma Thesis, TU Hamburg-Harburg,Department of Telecommunications, 2000.

[IEEE96] Institute of Electrical and Electronics Engineers, Inc.: “The IEEE Standard

Dictionary of Electrical and Electronics Terms“, 6th Edition, IEEE Std 100-1996



124

[KLO99] Klotz, M. and Rohling, H.: “A High Range Resolution Radar System Network

for Parking Aid Applications”, 5th International Conference on Radar Systems1999, Brest, France, May 1999.

[KLO00] Klotz, M. and Rohling, H.: “24 GHz Radar Sensors for Automotive

Applications”, 13th

International Conference on Microwaves, Radar andWireless Communications, Poland, Wroclaw, May 22-24, 2000.

[KUH00] Kuhlmann, V.: “Entwurf und Performanceanalyse eines Bussystems für

sicherheitsrelevante Anwendungen mit verteilten Radarsensoren im

Automobil“; Studienarbeit, TU Hamburg-Harburg, Department of Tele-communications, 2000.

[LAY97] Lay, David C.: “Linear Algebra and its Applications”; 2nd Edition, AddisonWesley, 1997.

[LEV88] Levanon, Nadav: “Radar Principles”; John Wiley & Sons Inc., 1988.

[LUD98] Ludloff, A.: “Praxiswissen Radar und Radarsignalverarbeitung”, ViewegVerlag, 2. Auflage, 1998.

[MEI01] Meinecke, M.-M.: “Zum optimierten Sendesignalentwurf für Automobil-

radare”; PhD Thesis, TU Hamburg-Harburg, Department ofTelecommunications, 2001.

[MEN99] Mende, R.: “Radarsysteme zur automatischen Abstandsregelung in

Automobilen”; PhD Thesis, TU Braunschweig, 1999.

[MEN00] Mende, R.; Zander, A.: “A Multifunctional Automotive Short Range Radar

System”, German Radar Symposium, GRS2000, Berlin, October 10-11, 2000.

[REE98] Reed, J. C.: “Side Zone Automotive Radar”; IEEE AES Systems Magazine, pp. 3-7, June 1998.

[REI79] Reid, D. B.: “An Algorithm for Tracking Multiple Targets“; IEEETransactions on Automatic Control, Vol. AC-24, Dec. 1979, pp. 843-854.

[ROH83] Rohling, H.: “ Radar CFAR Thresholding in Clutter and Multiple TargetSituations“; IEEE Transactions on Aerospace and Electronic Systems, Vol.AES-19, No. 4, July 1983.

[ROH86] Rohling, H.: “Zur Auflösung von Radialgeschwindigkeits- und Entfernungs-

mehrdeutigkeiten bei der Radarmessung“; ntzArchiv Bd. 8 (1986), H. 2.

[ROT90] Rottler, J.: “Auflösung von Geschwindigkeits- und Entfernungsmehrdeutig-

keiten beim Puls-Radar“; PhD Thesis, Karlsruhe 1990.

[SCH90] Schroeder, M. R.: “Number Theory in Science and Communication“; Springer

Verlag, 1990.



125

[TEX98] Texas Instruments, Application Report SPRA354: “TMS320C2000 C-callable

FFT package”, May 1998.

[ULK94] Ulke, W.; Adomat, R.; Butscher, K.; Lauer, W.: “Radar – based Automotive

Obstacle Detection Systems”; SAE Technical Paper Series, International

Congress & Exposition, Michigan 1994.

[WAG97] Wagner, Klaus-Peter: “Winkelauflösende Radarverfahren für Kraftfahrzeug-

anwendungen”; PhD Thesis, TU Munich, Lehrstuhl für Hochfrequenztechnik,1997.

[WEI98] Weidmann, W. and Steinbuch, D.: “A High Resolution Radar for Short Range

Automotive Applications”; 28th European Microwave Conference 1998,Amsterdam, pp. 590-594.

[WEN00] Weng, W.: “Programmierung einer graphischen Anzeige mit hoher

Updaterate unter MS Windows für ein KFZ - Radarsystem”; Diploma Thesis,TU Hamburg-Harburg, Department of Telecommunications, 2000



126



127

Acronyms and Abbreviations

ACC Adaptive Cruise ControlCA Collision AvoidanceCA-CFAR Cell-Averaging Constant False Alarm RateCAGO-CFAR Cell-Averaging Greatest Of Constant False Alarm RateCAN Controller Area NetworkCFAR Constant False Alarm RateDFT Discrete Fourier TransformDRO Dielectric Resonator OscillatorDSP Digital Signal ProcessorECU Electronic Control UnitFFT Fast Fourier Transform

FMCW Frequency Modulated Continuous WaveHPRF High Pulse Repetition FrequencyHRR High Range ResolutionIF Intermediate FrequencyISM Industrial, Scientific, MedicalJPDA Joint Probabilistic Data AssociationLO Local OscillatorLPRF Low Pulse Repetition FrequencyMHT Multiple Hypothesis TrackingMOST Media Oriented Systems TransportMPRF Medium Pulse Repetition Frequency

OS-CFAR Ordered-Statistic Constant False Alarm RatePDA Probabilistic Data AssociationPDF Probability Density FunctionPRF Pulse Repetition FrequencyPRI Pulse Repetition IntervalRADAR Radio Detection and RangingRDU Radar Decision UnitRF Radio FrequencySRD Step Recovery DiodeTDMA Time Division Multiple AccessTTP Time-Triggered Protocol



128



129

List of Figures

Fig. 2-1: Sensor network with four subsystems monitoring the complete car environment...... 4Fig. 2-2: Applications of an automotive short range radar network and percentage of accidents

from different directions..................................................................................................... 5Fig. 2-3: Network implementation in the experimental vehicle................................................. 6Fig. 2-4: Multilateration situation with a single object ............................................................ 11Fig. 2-5: Error of object angle using only two sensors ............................................................ 12Fig. 2-6: Lateral distance error as a function of longitudinal and angle error.......................... 12Fig. 2-7: Lateral distance error as a function of angle error..................................................... 13Fig. 2-8: Sensor network accuracy with distance errors up to ±10cm of only two sensors.....13Fig. 2-9: Bumper geometry ...................................................................................................... 14Fig. 2-10: Standard deviation of the calculated angle with variable target distance to the

vehicle center axis ............................................................................................................ 15

Fig. 3-1: Signal Processing of a Pulse Radar ........................................................................... 18Fig. 3-2: 24 GHz sensor hardware structure ............................................................................ 20Fig. 3-3: Example of a sensor delay sweep signal and sensor frontend................................... 20Fig. 3-4: Laboratory situation of two close objects.................................................................. 22Fig. 3-5: Probability density functions of noise and signal...................................................... 25Fig. 3-6: Processing of an OS-CFAR detector......................................................................... 26Fig. 3-7: FFT length versus velocity resolution and measurement time versus velocity

resolution.......................................................................................................................... 28Fig. 3-8: Doppler frequency resolution as a function of the required velocity resolution....... 28Fig. 3-9: Processing with stepped ramps.................................................................................. 29Fig. 3-10: Processing with staggered ramp duration................................................................ 30

Fig. 3-11: Doppler frequency resolution.................................................................................. 32Fig. 3-12: Range Resolution as a Function of Pulse Width and Frequency Hub..................... 34Fig. 3-13: SNR versus PD for single pulse detection (Source: [LEV88]) ................................ 37Fig. 3-14: Transmit pulse width versus distance and increase of signal-to-noise ratio versus

distance............................................................................................................................. 38Fig. 3-15: Example of sensor interference ............................................................................... 39Fig. 3-16: Transmit and receive pulses of four sensors............................................................ 39Fig. 3-17: PRF-oscillator detuning for interference suppression .............................................42Fig. 4-1: Coordinate system ..................................................................................................... 46Fig. 4-2: System architecture 1 ................................................................................................ 47Fig. 4-3: System architecture 2 ................................................................................................ 47

Fig. 4-4: Central-level tracking with centralized processing ................................................... 48Fig. 4-5: Sensor-level tracking with centralized track file ....................................................... 49Fig. 4-6: Example of an estimated object position by means of a least squares algorithm...... 50Fig. 4-7: Error of azimuth angle (system with four and six sensors) ....................................... 54Fig. 4-8: Angle error for variable number of sensors............................................................... 54Fig. 4-9: Processing of the Kalman filter ................................................................................. 57Fig. 4-10: Object radius error and angle error for Kalman filter and least squares solution.... 60Fig. 4-11: Object velocity in x – and y – direction (Kalman filter) ......................................... 60Fig. 4-12: Abstract Data Fusion Model.................................................................................... 61Fig. 4-13: Generalised Processing Overviews (α - β - Tracker and Kalman Filter)................ 63

Fig. 4-14: Target to track data association ............................................................................... 64Fig. 4-15: Measurement-oriented MHT algorithm .................................................................. 67Fig. 4-16: Track-oriented MHT algorithm............................................................................... 69Fig. 4-17: Radar network processing overview ....................................................................... 72





131

List of Tables

Table 2-1: Suggested realistic system requirements for different applications ......................... 9Table 3-1: Main sensor features ............................................................................................... 21

Table 4-1: Example of an assignment matrix........................................................................... 65Table 6-1: Obstacle movement for different velocities............................................................ 91Table C-0-1: Forward FFT Memory Requirements............................................................... 120Table C-0-2: Forward FFT Timing Requirements................................................................. 120





Lebenslauf

Name: Michael KlotzGeburtsdatum: 16.08.1971

Geburtsort: Ungeny / Moldawien

Schulbildung:

1977 – 1981: Grundschule in Hildesheim und in Holle (Landkreis Hildesheim)1981 – 1983: Orientierungsstufe in Bockenem1983 – 1990: Scharnhorst – Gymnasium in Hildesheim; Abschluss: Abitur

Studium:

10/1991 – 12/1996: Studium der Elektrotechnik an der TU Braunschweig mitVertiefungsrichtung Meß- Regelungs- und Automatisierungstechnik

11/1995 – 08/1996: Diplomarbeit am Institut für Regelungstechnik der TU Braunschweig08/1996 – 12/1996: Studienarbeit bei der Firma Aerodata Flugmesstechnik GmbH in

Braunschweig

Berufliche Tätigkeit:

12/1996 – 03/1997: Diplom – Ingenieur in der Abteilung Navigationssysteme bei der FirmaAerodata Flugmesstechnik GmbH in Braunschweig

04/1997 – 03/1999: wissenschaftlicher Mitarbeiter am Institut für Nachrichtentechnik der

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An Automotive Short Range High Resolution Pulse Radar Network

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