The Pennsylvania State University
The Graduate School
Department of Electrical Engineering
TRILATERATION-BASED LOCALIZATION ALGORITHM
FOR ADS-B RADAR SYSTEMS
A Dissertation in
Electrical Engineering
by
Ming-Shih Huang
2013 Ming-Shih Huang
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
May 2013
The dissertation of Ming-Shih Huang was reviewed and approved* by the following:
Ram M. Narayanan
Professor of Electrical Engineering
Dissertation Advisor
Chair of Committee
James K. Breakall
Professor of Electrical Engineering
Julio Urbina
Associate Professor of Electrical Engineering
Dennis K. McLaughlin
Professor of Aerospace Engineering
Kultegin Aydin
Professor of Electrical Engineering
Head of the Department of Electrical Engineering
*Signatures are on file in the Graduate School
iii
ABSTRACT
Rapidly increasing growth and demand in various unmanned aerial vehicles (UAV) have
pushed governmental regulation development and numerous technology research advances
toward integrating unmanned and manned aircraft into the same civil airspace. Safety of other
airspace users is the primary concern; thus, with the introduction of UAV into the National
Airspace System (NAS), a key issue to overcome is the risk of a collision with manned aircraft.
The challenge of UAV integration is global. As automatic dependent surveillance-broadcast
(ADS-B) system has gained wide acceptance, additional exploitations of the radioed satellite-
based information are topics of current interest. One such opportunity includes the augmentation
of the communication ADS-B signal with a random bi-phase modulation for concurrent use as a
radar signal for detecting other aircraft in the vicinity. This dissertation provides detailed
discussion about the ADS-B radar system, as well as the formulation and analysis of a suitable
non-cooperative multi-target tracking method for the ADS-B radar system using radar ranging
techniques and particle filter algorithms.
In order to deal with specific challenges faced by the ADS-B radar system, several
estimation algorithms are studied. Trilateration-based localization algorithms are proposed due to
their easy implementation and their ability to work with coherent signal sources. The centroid of
three most closely spaced intersections of constant-range loci is conventionally used as
trilateration estimate without rigorous justification. In this dissertation, we address the quality of
trilateration intersections through range scaling factors. A number of well-known triangle centers,
including centroid, incenter, Lemoine point (LP), and Fermat point (FP), are discussed in detail.
To the author’s best knowledge, LP was never associated with trilateration techniques. According
our study, LP is proposed as the best trilateration estimator thanks to the desirable property that
the total distance to three triangle edges is minimized. It is demonstrated through simulation that
iv
LP outperforms centroid localization without additional computational load. In addition, severe
trilateration scenarios such as two-intersection cases are considered in this dissertation, and
enhanced trilateration algorithms are proposed.
Particle filter (PF) is also discussed in this dissertation, and a simplified resampling
mechanism is proposed. In addition, the low-update-rate measurement due to the ADS-B system
specification is addressed in order to provide acceptable estimation results. Supplementary
particle filter (SPF) is proposed to takes advantage of the waiting time before the next
measurement is available and improves the estimation convergence rate and estimation accuracy.
While PF suffers from sample impoverishment, especially when the number of particles is not
sufficiently large, SPF allows the particles to redistribute to high likelihood areas over iterations
using the same measurement information, thereby improving the estimation performance.
v
TABLE OF CONTENTS
LIST OF FIGURES ................................................................................................................. vii
LIST OF TABLES ................................................................................................................... xi
LIST OF ACRONYMS ........................................................................................................... xii
ACKNOWLEDGEMENTS ..................................................................................................... xiv
Chapter 1 Introduction ............................................................................................................ 1
1.1 Background ................................................................................................................ 1
1.2 Motivation .................................................................................................................. 4
1.3 Organization of the dissertation ................................................................................. 5
Chapter 2 Evolution of Surveillance Technologies ................................................................ 7
2.1 Ground-based air surveillance system........................................................................ 7 2.1.1 Primary surveillance radar .............................................................................. 8
2.1.2 Secondary surveillance radar........................................................................... 9
2.2 Traffic alerting and collision avoidance system ......................................................... 10 2.3 Automatic dependent surveillance - broadcast (ADS-B) ........................................... 11
2.3.1 Principal operation .......................................................................................... 12
2.3.2 ADS-B signal format ....................................................................................... 13
2.3.3 Remaining issues ............................................................................................. 14
2.4 Other ADS-B related systems .................................................................................... 16
2.4.1 Hybrid surveillance ......................................................................................... 17
2.4.2 Wide-area multilateration ................................................................................ 18
Chapter 3 ADS-B Radar Systems ........................................................................................... 20
3.1 Overview .................................................................................................................... 20
3.2 System design ............................................................................................................ 22 3.2.1 Signal waveform ............................................................................................. 23
3.2.3 System configuration ....................................................................................... 25
3.3 Interference analysis................................................................................................... 26
3.4 Link budget analysis .................................................................................................. 29
3.5 Signal specification comparison ................................................................................ 29
Chapter 4 Estimation and Tracking Algorithm for ADS-B Radar Systems ........................... 31
4.1 Overview .................................................................................................................... 31
4.2 Signal coherence problem .......................................................................................... 31
4.3 Trilateration-based localization algorithms ................................................................ 34
4.3.1 Time of arrival ................................................................................................. 36
4.3.2 Trilateration modes ......................................................................................... 37
4.3.3 Triangle center approaches .............................................................................. 42
4.3.3.1 Centroid ................................................................................................ 43
vi
4.3.3.2 Incenter ................................................................................................. 44
4.3.3.3 Lemoine ................................................................................................ 44
4.3.3.4 Fermat ................................................................................................... 46
4.3.3.5 Range-based weighted centroid ............................................................ 51
4.3.3.6 Performance comparisons .................................................................... 53
4.3.4 Enhanced algorithms for severe trilateration scenario .................................... 58
4.3.4.1 Weighted trilateration ........................................................................... 59
4.3.4.2 Range-adjusted weighted trilateration .................................................. 60
4.3.4.3 Estimation error over range .................................................................. 60
4.4 Particle filter algorithm .............................................................................................. 65 4.4.1 Simplified resampling mechanism .................................................................. 68
4.4.2 Supplementary particle filter algorithm ......................................................... 70
4.4.3 Performance comparisons ............................................................................... 71
Chapter 5 Conclusions and Future Work ................................................................................ 78
5.1 Conclusions ................................................................................................................ 78
5.2 Future work ................................................................................................................ 79
Bibliography ............................................................................................................................ 81
vii
LIST OF FIGURES
Figure 2-1: Principle of PSR operation. ................................................................................... 8
Figure 2-2: Increased uncertainty over distance. . ................................................................... 9
Figure 2-3: SSR relies on onboard transponder, which receives interrogation from ATC
and transmits replied message. ........................................................................................ 10
Figure 2-4: Principle of operation for the ADS-B systems in an air traffic network. ............. 13
Figure 2-5: ADS-B Mode-S Extended Squitter message format. ............................................ 14
Figure 2-6: Illustration of WAM. ............................................................................................. 18
Figure 3-1: Comparison of surveillance principles between ADS-B and ADS-B radar
systems.. .......................................................................................................................... 22
Figure 3-2: Illustration of random phase modulation added onto ADS-B messages. ............. 24
Figure 3-3: Illustration of the ADS-B waveform (blue) versus the ADS-B radar waveform
(red). ................................................................................................................................ 24
Figure 3-4: Conceptual architecture of the proposed ADS-B radar system. ............................ 26
Figure 3-5: Autocorrelation of standard ADS-B signal and autocorrelation of phase
modulated ADS-B signal. ................................................................................................ 27
Figure 3-6: Cross-correlation of one phase modulated ADS-B signal with another
standard ADS-B signal and another phase-modulated ADS-B signal. ........................... 28
viii
Figure 3-7: A simulated range profile based on autocorrelation of a randomly bi-phase
modulated ADS-B signal. ................................................................................................ 28
Figure 4-1: Using trilateration to determine target location..................................................... 37
Figure 4-2: Illustration of trilateration modes. ........................................................................ 39
Figure 4-3: Illustration of the error due to arc-line approximation. ........................................ 40
Figure 4-4: Occurrence probability of each mode under various noise variances. ................. 41
Figure 4-5: The distances between dashed and solid lines are equivalent to RSFs. ............... 45
Figure 4-6: 1E , the difference of the first element of normalized FP and LP barycentric
coordinates. ..................................................................................................................... 49
Figure 4-7: 2E , the difference of the second element of normalized FP and LP
barycentric coordinates. ................................................................................................... 49
Figure 4-8: 3E , the difference of the last element of normalized FP and LP barycentric
coordinates. ..................................................................................................................... 50
Figure 4-9: Distance between FP and LP in Cartesian coordinate. Green triangles are two
fixed triangle vertices, with edge length as 1 m, and the third vertex moves in FOV. ... 51
Figure 4-10: Comparison between centroid and RWC. Numerical values are the
computed weights for each intersection. .......................................................................... 53
Figure 4-11: Average errors of 1000 Monte Carlo simulations with random noise
variance and fixed target location. .................................................................................. 55
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Figure 4-12: RMSE of 1000 Monte Carlo simulations with random noise variance and
fixed target location. ....................................................................................................... 56
Figure 4-13: Average errors of 1000 Monte Carlo simulations with random noise
variance and random target location. .............................................................................. 57
Figure 4-14: RMSE of 1000 Monte Carlo simulations with random noise variance and
random target location. ................................................................................................... 58
Figure 4-15: The extended intersections define an overlapping area. .................................... 61
Figure 4-16: Average errors of WT and RAWT for mode 4 and mode 2. ............................... 62
Figure 4-17: RMSE of WT and RAWT for mode 4 and mode 2. ............................................ 62
Figure 4-18: Average errors of all trilateration techniques under different map sizes. .......... 64
Figure 4-19: RMSE of all trilateration techniques under different map sizes. . ...................... 64
Figure 4-20: Resampling mechanism for multiple targets. ..................................................... 69
Figure 4-21: Transmitted ADS-B radar signal waveform........................................................ 71
Figure 4-22: Transmitted ADS-B radar signal and received signals from four sensors. ........ 72
Figure 4-23: Tracking trajectories of PF and SPF methods against true target (20 MC
trials). .............................................................................................................................. 73
Figure 4-24: Range errors during each iteration (one trial). ................................................... 74
Figure 4-25: RMSE for a target with constant velocity, as well as Gaussian distributed
acceleration and heading direction (20 MC trials). .......................................................... 74
x
Figure 4-26: Tracking performance for a maneuvering target (20 MC trials). ....................... 75
Figure 4-27: Range errors during each iteration (one trial). ................................................... 76
Figure 4-28: RMSE for a maneuvering target (20 MC trials). ................................................ 76
Figure 4-29: Tracking performance for multiple targets (20 MC trials). ................................ 77
xi
LIST OF TABLES
Table 3-1: Effects of random bi-phase modulation on correlation results. ............................. 25
Table 3-2: Link budget analysis. ............................................................................................. 30
Table 3-3: Comparison of signal specification for various air surveillance technologies. ..... 30
Table 4-1: Comparison of various triangle center approaches for fixed target and standard
deviation = 5 m. ............................................................................................................... 54
Table 4-2: Comparison of various triangle center approaches for random target and
standard deviation = 5 m. ................................................................................................ 57
Table 4-3: Estimation error comparison. ................................................................................ 75
xii
LIST OF ACRONYMS
ADS-B Automatic dependent surveillance - broadcast
ATC Air traffic controller
ATM Air traffic management
C2 Command and control
CARATS Collaborative actions for renovation of air traffic systems
CL Centroid localization
DF Direction finding
DOP Dilution of precision
FAA Federal aviation administration
FOV Field of view
FP Fermat point
FRUIT False replies unsynchronized with interrogation transmissions
GNSS Global navigation satellite systems
ICAO International civil aviation organization
LP Lemoine point
MC Monte Carlo simulations
MUSIC Multiple signal classification
NAS National airspace systems
NexGen Next generation air transportation system
PF Particle filter
PM Phase modulation
PPM Pulse position modulation
PSR Primary surveillance radar
xiii
RAWT Range-adjusted weighted trilateration
RCS Radar cross section
RF Radio frequency
RMSE Root mean squared error
RWC Range-based weighted centroid
SAA Sense and avoid
SESAR Single European sky air traffic research system
SPF Supplementary particle filter
SSR Secondary surveillance radar
SWAP Size, weight, and power
TOA Time of arrival
TDOA Time difference of arrival
UAT Universal access transceiver
UAV Unmanned aerial vehicle
WAM Wide-area multilateration
WSN Wireless sensing network
WT Weighted trilateration
xiv
ACKNOWLEDGEMENTS
First and foremost, I am extremely grateful and thankful to my advisor, Dr. Ram M.
Narayanan, for his guidance and patience throughout my entire course of my life at Penn State.
Dr. Narayanan has inspired me with his enthusiasm, positive attitude, and hard-working nature.
I would also like to thank my committee members, including Dr. Dennis K. McLaughlin,
Dr. James K. Breakall, and Dr. Julio Urbina, for their insightful comments and suggestions that
are incredibly helpful for my research work. Special thanks are due to Dr. Yan Zhang of
University of Oklahoma and Dr. Randy Haupt of the Colorado School of Mines for numerous
discussions that helped shape my research work.
I would like to acknowledge the constant support from my fellow labmates and friends
Chieh-Ping Lai, Jack Chuang, Shrawan Surender, Zhixi Li, Wei-Jen Chen, Pin-Heng Chen,
Mahesh Shastry, Surendra Bhat, Russ Vela, Yangsoo Kwon, and many others.
I thank Dr. Chujen Lin and Dr. Alexander Davydov from Intelligent Automation Inc. for
the research internship opportunity. I would also like to thank Dr. Stefan Schwarzer, Dr.
Sebastian Kunkel, Dr. Ulrich Loewen and Carolin Haussner in Corporate Research and
Technologies in Siemens AG for giving me hands-on industrial experience.
Last, but definitely not the least, I would like to express my personal appreciation to my
parents, my loving wife, and my joyous daughter. Without their support and encouragement, my
“Happy Valley” journey would not have been nearly as rewarding as it was. I thank you from the
bottom of my heart for always being there for me.
xv
DEDICATION
To Hsin-Ling and Abigail.
Chapter 1
Introduction
1.1 Background
Over the past few decades, the continuous expansion in air traffic volume and demand
has created substantial problems in terms of capacity and safety for the air traffic management
(ATM) system. In the very near future, we will soon face more increasing aviation challenges, out
of which possibility of aircraft mid-air collisions needs special attention, especially in busy
airport areas. In addition, rapidly increasing growth in various UAVs have pushed governmental
regulation development and numerous technology research activities toward integrating
unmanned and manned aircraft into the same civil airspace.
To enable the transformation of the ATM to a new paradigm that can meet the demand
for the next 20 years and beyond, several developmental programs are underway, such as Single
European sky air traffic research system (SESAR) in Europe [1], next generation air
transportation system (NextGen) in U.S.A. [2] – [4], and collaborative actions for renovation of
air traffic systems (CARATS) in Japan [5]. The philosophy is to move away from legacy ground
based technologies to a new and more dynamic satellite based technology. A key element of
SESAR and NextGen is automatic dependent surveillance - broadcast (ADS-B), which uses the
global navigation satellite system (GNSS) signals to provide air traffic controllers and pilots with
precise position information in space, in contrast to the traditional surveillance radar derived data.
Aircraft transponders receive GNSS signals and use them to determine the aircraft’s precise
location in the sky, which is combined with other relevant data and broadcast out via a digital
data link to other aircraft and air traffic control facilities. Besides ADS-B’s wide acceptance in
2
Europe and U.S.A, NAV CANADA commenced operational application of ADS-B as a means of
providing aircraft surveillance information to air traffic controllers (ATC) [6], and AirServices
Australia commissioned the ADS-B Upper Airspace Project (UAP), providing ADS-B coverage
across the whole continent [7]. In addition, ADS-B is being used as the key solution for UAV
integration in the National Airspace System (NAS). When properly equipped with ADS-B, both
pilots and controllers will see the same real-time displays of air traffic, substantially improving
safety and minimizing collision probability.
There has been much discussion regarding the concept of equivalent level of safety and
whether UAVs can be shown to achieve a collision avoidance performance equivalent to that of
manned aircraft. In accordance with Federal Aviation Administration (FAA) regulations, all
pilots are responsible for seeing and avoiding other aircraft. As the UAV operator is physically
removed from the “cockpit,” airborne sense and avoid (SAA) capability becomes the focus of
technological efforts for UAV [8]. In addition, UAV mid-air collision avoidance capabilities must
be interoperable and compatible with existing collision avoidance and separation assurance.
Small UAV are difficult to see visually and sense electronically owing to the small size and/or the
diversity of the platform size, weight, and power (SWAP). Many approaches, including camera-
based sensing [9], [10], traffic alerting and collision avoidance system (TCAS), and ADS-B have
been considered; however, none of the proposed techniques is convincing enough to be adopted
by FAA. A few major drawbacks are highlighted below.
Centralized flight control system, e.g. ATC, will soon reach its limit for high capacity of
manned aircraft, let alone the airspace comprising manned and unmanned aircraft. Moreover, the
command and control (C2) link between ATC and the flight system introduces a number of
significant issues to aircraft in a fly-by-wireless system, such as link vulnerabilities due to radio
frequency (RF) interference and potential latency of flight control messages. Without the onboard
3
pilot to make a spontaneous decision, the delay in the control message delivery from ATC to
UAV is a very severe problem.
Safety analysis of TCAS on medium to large sized UAV has been carried out [11],
despite its cost and system requirement. Because aircraft are required to be equipped with
altitude-reporting transponder in Class A, B, C airspace and Class E airspace above 10,000 feet,
in low-altitude Class E and uncontrolled airspace through which UAV may fly, TCAS would not
work. In addition, the safety studies conducted to certify TCAS assumed that aircraft would have
a pilot onboard. Due to the bearing error and update rate of TCAS, the FAA and International
Civil Aviation Organization (ICAO) have stated that TCAS display alone is not sufficient to
provide the operator with enough situational awareness to avoid the threat.
In order to reduce the risk of collision, it is essential to make UAV more conspicuous to
other aircraft, and one simple way is through the electronic broadcast of the aircraft’s state vector
data (i.e. position, velocity, aircraft type, etc.). With the proposed rulemaking by FAA that would
mandate ADS-B out equipage by 2020, it appears that ADS-B transceivers will most likely
become critical pieces of an airborne SAA system for UAV operating in the NAS. The ITT
Corporation, chosen in 2007 as the prime contractor for ADS-B ground stations, will implement
the infrastructure covering the entire nation by 2013. Certainly some modifications would be
required to successfully adapt the ADS-B system into UAV due to its high cost, the differences in
aircraft characteristics, and the nature of possible collisions. A lightweight, low-cost and low-
power ADS-B beacon radio developed by The MITRE Corporation [12], [13], and a radio data
system (RDS) proposed in [14] makes it promising to deem ADS-B technology as a key enabler
to integrate UAV into NAS. A flight test of UAV utilizing the ADS-B transceiver [15] was tested
in 2009, and it demonstrated the possibility to use an ADS-B transceiver for UAV as an entry into
NAS.
4
In the environment covered by both ADS-B and radar stations, the fusion of radar and
radio communication fusion provides improved tracking accuracy and system integrity [16], [17]
at a costly expense. However, similar to the first issue to employ TCAS on UAV, many UAVs
operate in airspace not covered by radar.
1.2 Motivation
Before the ADS-B implementation and operation is fully complete, there will be a
transition period involving coexistence of ADS-B equipped and non-equipped aircraft. In
addition, ADS-B systems have several remaining concerns, such as vulnerability to spoofing,
backup system needed at loss of satellite signals, and inability to see non-cooperative targets. It
has been pointed out that the limited use of ADS-B as the sole means of surveillance may lead to
a reduction of the integrity of the entire ATC system [16], [17]. Localized problems, such as less
than the required four visible satellites, will confuse not only aircraft pilots but also ATC [18],
[19]. Hence, it is desired to find a way to cope with the non-cooperative targets while retaining
the benefits of the ADS-B system.
Since the emergence of ADS-B concept, some researchers have considered the utilization
of existing and installed infrastructure of the surveillance radar to combine with the satellite-
based ADS-B system within the perspective of ATC. More interestingly, the use of the ADS-B
signal itself to detect non-cooperative targets from the ADS-B message and from the radar
processing, as an onboard collision avoidance system was first described in a patent disclosure
[20] and the concept subsequently developed further [21] –[26]. The novelty of the ADS-B radar
system lies in that the system insightfully exploits the ADS-B out signal, which is primarily
designed for communication purposes, as a radar signal to perform multiple target estimation and
tracking, thereby creating a multifunctional waveform. With the affordable Universal Access
5
Transceiver (UAT) Beacon Radio developed by The MITRE Corporation [12], [13] and the
hybrid estimation approach for resource-limited UAVs, the ADS-B radar concept appears to be
an economically viable solution to facilitate integration of UAV into NAS.
As a communication system, the ADS-B system has fundamental drawbacks, such as
vulnerability to signal interception and spoofing and inability to see non-cooperative targets.
There has been ongoing research collaboration between The Pennsylvania State University and
Intelligent Automation, Inc. to develop a radar system, named the ADS-B radar, based on the
original ADS-B system to go beyond the natural limitation of the communication system.
1.3 Organization of the dissertation
This dissertation is organized as follows: Chapter 2 renders a general understanding the
evolution of air surveillance technologies over the past few decades. Existing surveillance
techniques are reviewed with a focus on their limitation in order to serve the future ATM. New
air surveillance technologies are introduced in details, and potential issues are pointed out and
discussed.
Chapter 3 describes the ADS-B radar system in terms of system configuration and signal
modulation technique. The feasibility of augmenting the communication ADS-B signals with a
random bi-phase modulation to enhance radar capability is investigated. In addition, the link
budget is analyzed in order to understand the system capability in terms of operational range.
Chapter 4 presents the estimation and tracking algorithms proposed for the ADS-B radar
system. Details of such radar-communication system specifications and problems of low-update-
rate measurement due to the ADS-B system requirement are discussed. Trilateration-based
localization algorithms are studied for resource-limited platforms, such as UAV. Particle filter
algorithm is applied for multi-target estimation and tracking with a simplified resampling
6
mechanism presented. SPF is proposed to improve the estimation accuracy using the waiting time
for the next observation.
Chapter 5 draws the conclusions of the dissertation. A few suggested research directions
for future work are also presented.
Chapter 2
Evolution of Surveillance Technologies
It is foreseen that with rapid expansion of in air traffic volume and demand, the ground-
based technology will face its limitation in the near future. The transition of the surveillance
technologies that ATM is shifting from centralized systems to decentralized systems as the
density of the air traffic continues to increase. Although in its early stage of implementation, the
ADS-B system may soon replace and decommission the conventional radar stations and the
delegation of specific separation responsibilities and associated tasks may need to be transferred
to the flight crew to offer instantaneous situation awareness in airspace.
A brief and comparative review of the existing and new surveillance technologies is
provided in this Chapter. The major advantages and disadvantages for each approach are pointed
out with an emphasis on the non-cooperative surveillance capability. Two traditional ground-
based surveillance radar systems, primary surveillance radar (PSR) and secondary surveillance
radar (SSR) will be covered describing their fundamental operational principles and their
limitations [27]. The signal format and system specification of the ADS-B system will be
provided and the remaining concerns for the new concept are presented. At the end of the
Chapter, two ADS-B related systems, including a hybrid surveillance technique using TCAS and
ADS-B and wide-area multilateration (WAM), are described.
2.1 Ground-based air surveillance system
PSR and SSR are the main two components of an ATC station and are widely used for
the past few decades. PSR has the capability to detect large metal objects, including cooperative
8
and non-cooperative targets, while SSR works only for transponder-equipped aircraft. SSR relies
on aircraft with corresponding transponder, but the report provides aircraft identification. Both
PSR and SSR were designed for low and medium traffic situations.
2.1.1 Primary surveillance radar
PSR detects and reports the position of anything that reflects the transmitted radio
signals. However, PSR only finds the aircraft within operational range without being able to
identify them. In addition, the returned signal strength decays as the fourth power of distance
from the radar station to the target. Figure 2-1 shows how PSR detects targets using reflected
microwave bounced from the metal objects and the signal power after the round trip decreases
dramatically. Moreover, the antenna beam gets wider as the target moves farther away from the
antenna, thus making the measured position information less accurate, as illustrated in Figure 2-2.
Although its coverage and information is more limited, PSR is still used by ATC today as a
backup/complementary system for surveillance purpose.
Figure 2-1: Principle of PSR operation.
Signal strength decays as
9
2.1.2 Secondary surveillance radar
The need to be able to identify aircraft and the impetus to reduce power decay led to the
invention of SSR. SSR relies on a piece of onboard device known as transponder, which receives
interrogation at the frequency of 1030 MHz and replies at 1090 MHz, as shown in Figure 2-3.
With the aid of transponder, identification can be inserted in the replied message, and in the
meantime, the signal power decays only to the second power of the distance and uncertainty issue
is also alleviated due to half of the travelling distance compared to PSR technique.
When there are a number of aircraft in close vicinity in terms of distance or direction,
their SSR replies can overlap, the ground decoder is confused and finally their information is lost.
This situation is known as Garbling, and it makes SSR unsuitable in dense aircraft areas.
Moreover, when there are many SSR stations around the aircraft, replies received by other SSR
stations that did not ask for these replies result in confusion and finally rejection due to errors.
This phenomenon is known as False Replies Unsynchronized with Interrogation
Figure 2-2: Increased uncertainty over distance.
0.5°
uncertainty 1
uncertainty 2
10
Transmissions (FRUIT) [28], resulting from the fact that an aircraft SSR reply is received not
only by the SSR that triggered it but by all the others around. The unexpected replies thus arriving
at these other SSR stations in the area result in inconsistent position measurements. Within NAS,
most of the airspace is under coverage of multiple SSR stations, and FRUIT results in loss of the
aircraft position and inaccurate surveillance information.
2.2 Traffic alerting and collision avoidance system
Due to continuing growth in air traffic, TCAS or other similar devices have been in
various stages of research and development since the early to mid 1950s to serve as a last resort
collision avoidance safety-net. TCAS operates similarly to the ground-based SSR but
independently interrogates surrounding aircraft on a 1030-MHz radio channel. The pilot will be
alerted to the presence of the intruding aircraft replying to the interrogation via 1090-MHz radio
frequency. Current generation TCAS II, jointly developed by the US Radio Technical
Commission for Aeronautics (DO-185B) and European Organization for Civil Aviation
Figure 2-3: SSR relies on onboard transponder, which receives interrogation from ATC and
transmits replied message.
interrogation
response
interrogation
response
11
Equipment (ED-143), issues two types of advisories: the resolution advisory (RA), which
identifies an intruder that is considered a collision threat, and the traffic advisory (TA), which
identifies an intruder that may soon cause an RA. According to the predicted closest point of
approach (CPA), TCAS produces a TA at approximately 45 seconds and an RA at 35 seconds to
CPA. TCAS is designed to reduce the incidence of mid-air collisions and has been very
successful since its introduction. However, the major concern with regard to either TCAS or
ADS-B is that they are not required all the time, and ADS-B Out is not yet mandated in most of
the countries. Aircraft equipped with TCAS and/or ADS-B are still exposed to danger of
collisions in low altitude of Class E and uncontrolled airspace owing to their inability to detect
non-cooperative targets and unawareness of any illegal intruder in transponder-required airspace.
2.3 Automatic dependent surveillance – broadcast (ADS-B)
ADS-B is ‘automatic’ in the sense that it transmits signals automatically without
requiring controller action; it is ‘dependent surveillance’ because the surveillance-type
information depends on onboard navigation sources and onboard broadcast transmission systems
to provide surveillance information. The system constantly ‘broadcasts’ the signal at the rate of
once every second. ADS-B is redefining the paradigm of communication, navigation, and
surveillance in ATM. An ADS-B equipped aircraft determines its own position using GNSS and
periodically broadcasts its four dimensional position (latitude, longitude, altitude, and time), track
and ground speed, aircraft or vehicle identification and other additional relevant data as
appropriate, e.g. intended trajectories [29], to nearby aircraft also equipped with the ADS-B
system and potential ground stations without expectation of an acknowledgement or reply. One of
the most significant advantage of the ADS-B system is that it minimizes radio frequency (RF)
spectral congestion as would be generated by TCAS. Any user, either aircraft or ground stations
12
within broadcasting range, may receive and process ADS-B surveillance information. ADS-B
system provides accurate information and improves situational awareness. Moreover, ADS-B
enables a shift from a centralized, ground-based ATM system to a decentralized network
involving pilots and aeronautical operational control centers. ADS-B also provides greater
coverage, since ADS-B ground stations are so much easier to place than radar. Remote areas
without radar coverage, like the Gulf of Mexico and parts of Alaska, are now covered by ADS-B.
According to the ADS-B implementation timetable in USA, by 2020, the ADS-B Out is
mandatory for all aircraft operating in any airspace that currently requires a transponder, and the
ADS-B In equipment will be based on user perceived benefit. The ADS-B system might
eventually allow pilots to use onboard instruments and electronics to maintain a safe separation
and to reduce their reliance on ground controllers.
2.3.1 Principle of operation
Figure 2-4 shows the role of ADS-B in an air traffic network, including ground station
and surrounding airplanes. It is not difficult to envision that once all flying objects within the
National Airspace System (NAS) are equipped with the ADS-B system, the airspace will be as
clear as transparent for the aircraft to see and avoid imminent collisions, which is the ultimate
goal of extreme aviation safety.
13
2.3.2 ADS-B signal format
There are three different types of link technology suitable for ADS-B technology: Mode-
S Extended Squitter (ES), VHF Data Link (VDL) Mode 4, and Universal Access Transceiver
(UAT). A VDL Mode 4 system has the longest operational range among these three candidates,
but the low bandwidth of the signal renders poor resolution to distinguish multiple targets. While
UAT and Mode S ES both work on L-band, the latter has a larger bandwidth of 6 MHz, which
provides many benefits especially in radar application. In the dissertation, only the Mode S ES
will be discussed in our radar system design.
Mode-S ES is agreed to be the first global datalink for international commercial flight,
and the transponder emits periodically with a frequency up to 6 Hz. The uplink operates at 1030
MHz and the downlink at 1090 MHz. The ADS-B message information is encoded in the time
Figure 2-4: Principle of operation for the ADS-B systems in an air traffic network.
Air to Air Link
Air to Ground Link
GPS
14
delay between pulses in a sequence of signal pulses, known as Pulse-Position Modulation (PPM).
A pulse transmitted in the first half of the bit interval represents “1” while a pulse transmitted in
the second half represents “0”. A complete Mode-S ES is 120 s, including 8 s preamble,
followed by 112 data block in 112 s. Each message contains 56 bits of information inserted
between the 24 bit aircraft address and the parity information, as can be seen in Figure 2-5.
2.3.3 Remaining issues
Ever since FAA released ADS-B technology, there has been an ongoing debate about its
advantages and disadvantages. It is clearly desired from the pilots to be aware of all the nearby
aircraft by the broadcasting techniques, but experts worry about the negative effects when the
broadcast information is used by third parties, e.g. terrorists. In addition, it is very important that
ADS-B is resistant to intentional interference or noisy environment. Furthermore, what is the
Figure 2-5: ADS-B Mode-S Extended Squitter message format.
15
alternative procedure when GPS signal is lost and how does ADS-B deal with airplanes not
equipped with the ADS-B system?
Transparency
The ADS-B system broadcasts in one message both the aircraft identification (ID) and
location, which are the very information that could be misused by adversaries. A good encryption
mechanism for ADS-B has not yet been proposed, and it needs to be developed and tested to
upgrade the ADS-B system before any unwanted incidents happen.
Vulnerability to spoofing
Whenever an incoming ADS-B signal is received, the aircraft ID and location embedded
in the message will be updated on the cockpit display. Even if it is a spoofed message, the
receiving end has no way to find out that the information is not correct. The scenario can be
worse if the aircraft that received a spoofed message makes maneuver to avoid the “nonexistent”
collision and causes a real collision danger to other aircraft. Without additional support, the ADS-
B system is vulnerable to spoofing.
Backup system at the loss of GPS signals
In the case of lost or incorrect GPS information, possibly caused by localized problem or
device malfunction, a fallback solution is necessary before ADS-B has been extensively proven
through operational experience. A few seconds of lost signals for a car GPS may not cause a big
harm because the driver still visually sees the traffic even though he/she loses road guidance.
16
Nevertheless, a flight pilot is dependent upon accurate location information of nearby aircraft to
avoid imminent collision. While en route airplanes fly at the speed of around 500 miles per hour,
or equivalently 224 meters per second, a short period of lost GPS signal could make collision
avoidance even more difficult. Therefore, a certain level of redundancy for aviation surveillance
is needed to prevent casualty in the event the primary system shuts down.
Blind to non-cooperative targets
As described in the beginning of this chapter, the ADS-B systems allow the surrounding
airplanes to be aware of each other and provide a safe airspace. However, a fundamental lack of
capability is about non-cooperative targets, which include the aircraft not equipped with the ADS-
B system, flying objects, and UAVs. It is certainly desirable, or necessary to some extent, for the
ADS-B system to be able to see and avoid not only ADS-B equipped aircraft but also non-
cooperative targets.
2.4 Other ADS-B related systems
The ADS-B system is a promising technology and in May 2010, FAA issued a final
ruling mandating ADS-B equipage. A couple of surveillance systems are incorporating ADS-B to
expand function capability or developing techniques to take advantage of the free broadcast ADS-
B Out signals. For the sake of a complete background study on ADS-B, the hybrid surveillance
and WAM are described in this Section.
17
2.4.1 Hybrid surveillance
TCAS is an aircraft collision avoidance system designed to reduce the incidence of mid-
air collisions between aircraft. Aircraft over 5700 kg or carrying more than 19 passengers are
mandated by ICAO to be equipped with TCAS. The operational principal of the TCAS system is
based on SSR transponder which operates independently of ground-based equipment to provide
advice to the pilot on potential conflicting aircraft that are equipped with SSR transponders. Each
TCAS-equipped aircraft interrogates all other aircraft in a determined range about their position
and all other craft reply to other interrogations. This interrogation-and-response cycle may occur
several times per second. Through this constant back-and-forth communication, the TCAS system
builds a three dimensional map of aircraft in the airspace, incorporating their bearing, altitude and
range. Then, by extrapolating current range and altitude difference to anticipated future values, it
determines if a potential collision threat exists.
The collaboration of TCAS and ADS-B signals, known as hybrid surveillance, has been
implemented. TCAS hybrid surveillance makes use of both active surveillance data from
interrogation reply sequence and passive position estimates from ADS-B so that at the presence
of reception of ADS-B messages from an aircraft the rate at which TCAS interrogates that aircraft
is reduced. When ADS-B and TCAS are both working in the operational range, the surrounding
airspace is under satisfactory surveillance control and the probability of having a collision is
minimized. Hence, it is considered as a safe measure to reduce the TCAS interrogation rate
during hybrid surveillance. Furthermore, with reduced interrogation rate, there will be less
microwave interference in the airspace and the operational life of TCAS system will be extended
over time.
In the future, prediction capabilities may be improved by using the state vector
information present in ADS-B messages. Also, since ADS-B messages can be received at greater
18
range than TCAS normally operates, aircraft can be acquired earlier by the TCAS tracking
algorithms.
2.4.2 Wide-area multilateration
Multilateration techniques have been deployed for airport surveillance for a number of
years, and nowadays, the same techniques are used for larger areas, hence the name wide-area
multilateration (WAM) such as en route or approach areas thanks to many types of aircraft
transmissions [30] – [32]. The concept of WAM is illustrated in Figure 2-6.
Figure 2-6: Illustration of WAM.
WAM can be considered an a form of cooperative surveillance technique, and a WAM
system consists of a number of antennas receiving a signal from an aircraft and a central
19
processing unit calculating the aircraft’s position from the time difference of arrival (TDOA) of
the signal at the different antennas. WAM systems can be deployed without any changes to the
airborne infrastructure because the systems make use of currently existing aircraft transmissions
and passively receive the transmissions in multiple locations to estimate the location of the
source. In the event that the received signals contain identification, the estimated location can be
associated with that aircraft, and the combined information is valuable for surveillance purpose. It
is not hard to imagine that how ADS-B signals could be extremely beneficial to WAM systems.
The fact that an aircraft broadcasts messages, including aircraft tail number and GPS-based
location information, makes the ADS-B signal very suitable for a WAM system [32]. In light of a
complete coverage of ADS-B signal in Australia, a large number of WAM surveillance
applications have been developed at Sydney airport.
20
Chapter 3
ADS-B Radar Systems
3.1 Overview
The ADS-B system has the goal of significantly increasing capacity within NAS, while
maintaining or improving safety, but it can be only considered as a cooperative surveillance ATM
technique. Non-cooperative targets, such as UAVs and private jets, are blind to the ADS-B
systems when not equipped with the ADS-B system, but they pose equal collision danger if not
being detected. ADS-B radar [20] – [25] is intelligently introduced as a modification to the
standard ADS-B system in the interests of a safe backup service without significantly enlarging
the volume of ADS-B equipment. In addition, the radar report from ADS-B radar system could be
also used to compare with the incoming ADS-B message to reject any spoofed information.
The basic idea is that since the ADS-B systems constantly broadcast signals, the
reflective ADS-B electromagnetic energy could be exploited and extended for use as radar
echoes. Figure 3-1 illustrates the operational principal of the original ADS-B system and the
ADS-B radar system. In Figure 3-1 (b), four links in an aviation network include the followings:
o Link 1: Communication between aircraft and ATC through ADS-B signals
o Link 2 & 3: Communication between aircraft equipped with ADS-B systems
o Link 4: Detecting non-cooperative targets through reflected microwave
Nevertheless, in order to utilize of the reflected signals as radar echoes, many challenges
need to be overcome and modification to the original ADS-B system will be required. The ADS-
B signal can be viewed as a narrow-band communication signal, but however a large bandwidth
is generally desired for radar application in order to have high range resolution to distinguish
targets in close vicinity. Furthermore, such radar system needs to work under the interference
21
from many other ADS-B signals transmitted at the same frequency. The key adaptation lies on the
phase modulation added onto the standard ADS-B waveform, and it will be discussed in detail in
the second section of this chapter. The location of the non-cooperative targets can be estimated
using the reflected signals bounced off the targets, and techniques and design concerns will be
mentioned in Chapter 4.
It is interesting to note that the uncertainty, i.e. poor accuracy at long ranges, in the
measured radar reports on the aircraft, will no longer be as a major issue as it is for the ground-
based radar because the distance between a target and own aircraft is much smaller than that
between a target and the ground station. Another significant advantage of exploiting the ADS-B
signal is that it minimizes radio frequency (RF) spectral congestion as would be generated by
introducing other interrogation techniques. ADS-B radar system provides pilots with a system
independent of air traffic control to detect the presence of other aircraft, including both
cooperative and non-cooperative aircraft and anomalous aerial objects, which may present a
threat of collision. The location information of the targets can be estimated from the returned
ADS-B radar signals. Both of the ADS-B In information and the estimated locations for the non-
cooperative targets will be fused and then combined fed into Cockpit Display of Traffic
Information (CDTI) [33].
22
3.2 System design
Before a communication signal can be utilized and treated as a radar signal, many issues
need to be addressed first and a proper amount of modification to the system may be necessary.
The transmitted signal must be suitably modulated so that the returned signals could be exploited
Figure 3-1: Comparison of surveillance principles between ADS-B and ADS-B radar systems.
(b) ADS-B radar: able to detect both equipped and non-equipped aircraft
ADS-B Out
(Blind to ADS-B)
ADS-B Out
(a) ADS-B: communication between equipped aircraft and ATC
Detectable through
reflected microwave
(link 4)
ADS-B Out
ADS-B Out
23
to detect targets and estimate their locations. The modification to the original ADS-B system
should be minimized. The constraints from the ADS-B system include long pulse duration,
maximum of peak transmit power, insufficient signal bandwidth, and coherent returned signals,
which all degrade the radar performance. Therefore, one of the primary tasks for ADS-B radar
design is to exam the feasibility of treating ADS-B signal as radar signal and it will be discussed
in a later section with theoretical analysis and simulation results. Then the needed modification to
the system will be described, followed by the link budget analysis.
3.2.1 Signal waveform
Random bi-phase modulation for radar applications is depicted in Figure 3-2. Within the
112 μs message period, 180° phase shift is added pulse-by-pulse in a random manner, and the
random phase keying code is memorized during each message transmission. The bi-phase
modulation will not affect the ability for the ADS-B-in system to interpret the information
because only the envelope of the received signal and the pulse position in the waveform will be
use to decode the ADS-B message. Hence, the aircraft that receives the added phase modulated
signals will still be able to decode the message correctly. This added phase modulation however
provides the modulated signal the radar capability without affecting the decoding of the original
ADS-B message. Figure 3-3 shows the simulated ADS-B waveform and the proposed ADS-B
radar waveform. Both signals are of the same duration and have identical digital messages, except
that the ADS-B radar signal has a random 180° phase shift. By randomizing the transmit signal,
the matched filtering operation can be performed by cross-correlating the reflected signal with a
time-delayed replica of the transmit waveform. The bi-phase modulation renders both positive
and negative products, forcing the autocorrelation to be statistically zero except for zero time-lag.
The effect of the sum of the products in the autocorrelation function is provided in Table 3-1.
24
Figure 3-2: Illustration of random phase modulation added onto ADS-B messages.
Figure 3-3: Illustration of the ADS-B waveform (blue) versus the ADS-B radar waveform (red).
25
3.2.2 System configuration
A conceptual architecture of the proposed ADS-B radar system is depicted in Figure 3-4.
The ADS-B radar system includes the following sub-systems: (a) ADS-B transceiver, (b) ADS-B
encoder/decoder, (c) RF electronics with up and down frequency conversion, crosstalk
cancellation, and filtering capabilities, (d) a phase modulator, and (e) four omni-directional
antennas. Components (d) and (e) are particularly necessary to process the reflected radar signals
and to estimate target locations in real-time. Both of the ADS-B In message and the estimated
target location after processing the reflected signals from the antenna array will be fed into the
CDTI so that the pilot is aware of all surrounding aircraft and more importantly any imminent
collision.
Table 3-1: Effects of random bi-phase modulation on correlation results.
PPM
PPM with random bi-phase PM
same phase
(no phase shift)
inverted phase
(180° phase shift)
(1, 1) or (0, 0) positive
sum-product positive
sum-product
negative
sum-product
(1, 0) or (0, 1) zero
sum-product
zero
sum-product
zero
sum-product
messages
modulation
26
3.3 Interference analysis
As mentioned earlier in this chapter, one important task of the ADS-B radar system
design is to validate the feasibility to use the bi-phase modulated ADS-B signal as radar signal
through interference analysis. In radar applications, when a known signal is sent out, the reflected
signal is examined for common elements of the out-going signal. With the signature of randomly
added phase change, the match filter is capable of determining the received signal that share the
same template as the transmitted signal. The significance of the random bi-phase modulation (0°
or 180°) can be seen clearly in the autocorrelation of the ADS-B radar signal and the ADS-B
signal, as depicted in Figure 3-5. It is clear that the autocorrelation of the ADS-B radar signal
outperforms that of the original modulation-free ADS-B signal and shows an improved
Figure 3-4: Conceptual architecture of the proposed ADS-B radar system.
RF
coherent
transceiver
GPS ADS-B
codec
Radar
processing
CDTI
TCAS receiving circular
array antenna
Standard ADS-B
transceiver
27
correlation peak to noise ratio. In addition, the ADS-B radar signal has to be resistant to other
ADS-B signals coming from nearby aircraft. The cross-correlation between ADS-B radar signal
and other ADS-B signal, as depicted in Figure 3-6, shows that a typical ADS-B radar signal is
uncorrelated with both a standard ADS-B signal as well as another independent ADS-B radar
signal, thereby indicating that the on-board ADS-B radar receiver will not be affected by standard
ADS-B or ADS-B radar transmissions from other aircraft in the vicinity.
With the introduced bi-phase modulation onto the original ADS-B signal, the modulated
signal has wider bandwidth, the range resolution is improved and the range side lobes are also
further suppressed [34]. The autocorrelation is acceptable to detect the existence of targets, and a
range resolution of 75 meters can be achieved, as shown in Figure 3-7.
Figure 3-5: Autocorrelation of standard ADS-B signal and autocorrelation of phase modulated
ADS-B signal.
28
Figure 3-6: Cross-correlation of one phase modulated ADS-B signal with another standard ADS-
B signal and another phase-modulated ADS-B signal.
Figure 3-7: A simulated range profile based on autocorrelation of a randomly bi-phase modulated
ADS-B signal.
29
3.4 Link budget analysis
The link power budget can be calculated based on the radar range equation
2
3 4(4 )
t t rr
PG GP
R
(3.1)
where rP and tP are the received and transmitted power, respectively; tG and rG are the
receiving and transmitting antenna gain, respectively; is the signal wavelength; is the
target’s radar cross section (RCS); and R is the range to the target. We neglect atmospheric
losses since ADS-B operates at a low enough frequency where losses in clear air and precipitation
are negligible. As shown in Table 3-2, for a target having a RCS of 0 dBsm (1 square meter) at a
distance of 4.5 km, the signal-to-noise ratio (SNR) is 5.0 dB, a desirable value. For a large airliner
with a higher RCS of 20 dBsm (100 square meters), the operational range for the same SNR value
could extend to 14 km, which allows more than one minute of reaction time. The link budget
calculation shown in Table 3-2 and does not consider any reduction in reception range that will
result from the presence of interference and clutter as well as actual line-of-sight limitations.
3.5 Signal specification comparison
For the sake of completeness, the signal specification for PSR, SSR, TCAS, ADS-B, and
ADS-B radar is tabulated in Table 3-3.
30
Table 3-3: Comparison of signal specification for various air surveillance technologies.
Carrier Frequency
Carrier Wavelength
Peak Transmit Power
Coverage Range
Signal Repetition Period
PSR (ASR-11) 2700 – 2900 MHz 10 cm 25 kW 60 NM 12 RPM
SSR (ASR-11) 1030 / 1090 MHz 30 cm 160 – 1500 W 60 NM 12 RPM
TCAS (Honeywell CAS 100)
1030 / 1090 MHz 30 cm 400 W 30 NM Once per second.
ADS-B 1090 MHz 30 cm 500 W 200 NM Once per second.
ADS-B radar 1090 MHz 30 cm 500 W 7.5 NM Once per second.
Table 3-2: Link budget analysis.
Receiver Noise Floor = −110.9 dBm Received Signal Power = −105.9 dBm
Noise figure 3 dB Peak transmit power +57 dBm
Bandwidth 1 MHz baseband
Processing gain
(545 samples coherently integrated)
27.4 dB
Antenna gain (omni-directional) 0 dBsm
Assumed RCS 0 dBsm
1/(4π)3 -33.0 dB
1/(Range)4 (@3 km)
−146.1 dBm-
4
Square of wavelength −11.2 dBsm
SNR = 5.0 dB
31
Chapter 4
Estimation and Tracking for ADS-B Radar Systems
4.1 Overview
Due to the limited resources aboard an aircraft, the detection and estimation technique for
ADS-B radar system needs to be computationally efficient. In addition, as the number of targets
within detection range is not known as prior knowledge, it is important for the ADS-B radar
localization algorithm to have the capability to adapt to a sudden increase in the number of
surrounding aircraft under the constraint of fixed number of antennas mounted. Moreover, the
signal coherence problem, as discussed in the next Section, will need to be properly addressed in
the estimation algorithm for the ADS-B radar system.
4.2 Signal coherence problem
The Multiple Signal Classification (MUSIC) technique [35], which has been widely
adopted in many applications, was the first candidate to be employed for ADS-B radar to perform
detection and estimation. However, although MUSIC works well for multiple independent source
signals, it encounters problems when the returned signals from multiple targets are highly
correlated. The returned signals bounced off from different targets are highly correlated because
all the reflected radar echoes are simply the transmitted signal with a slight Doppler shift, i.e. less
than 1 kHz for the speed of 300 m/s.
Moreover, MUSIC has the constraint that the total number of antennas must be larger
than the number of targets. In another word, the number of detectable targets is limited. To
further elaborate the signal coherence problem and limitation of the number of detectable target,
32
let us assume there are L receivers and m signal sources (1 m L ) and the system model can
be formulated as:
or
, (4.1)
where
, (4.2)
( )Ly t is the received signal from the L-th sensor, ( )ms t is the signal from the m-th source, ( )Lv t is
additive white noise with zero mean and standard deviation , d is the distance between sensors,
is the signal wavelength, m is the arrival elevation angle of the m-th signal, m is the arrival
azimuth angle of the m-th signal, L is the angle according to the position relative to the origin of
the coordinate system of the circular array, and ( , )m m a is the m-th steering vector. It is
important to note that the steering vector is a known function of the signal arrival angles and the
array element locations. The element ija in matrix A is dependent on the i-th array element and
1 1 1
1 1
( ) ( ) ( )
[ ( , ),..., ( , )]
( ) ( ) ( )
m m
L m L
y t s t v t
y t s t v t
a a
Y = AS + V
1
2exp{ sin cos( )}
( , )
2exp{ sin cos( )}
m m
m m
m m L
dj
dj
a
33
its response to a signal incident from the direction of the j-th signal. The L L covariance matrix
of the Y vector is
, (4.3)
where I is the identity matrix of size L L .
If the elements of the vector S are uncorrelated, then the term SS will be positive
definite. The angles of steering vectors can be possibly extracted from the eigenvalues and
eigenvectors of the covariance matrix C [35]. The location estimation function can be formulated
as follows:
, (4.4)
where NE is defined to be the matrix whose columns are composed of the noise eigenvectors.
MUSICP will be large when and are both equal to the arrival elevation and azimuth angles of
the targets, respectively. Hence, the peak of this estimation function may be used to estimate the
location of the signal sources. However, if the signal sources are coherent, the received signals
from each sensor will not be independent and hence the rank of the covariance matrix C will be
reduced. Under this circumstance, it is not possible for MUSIC algorithm to obtain the arrival
azimuth and elevation angles of the desired targets. Although there has been research dealing
with correlated signals, such as constrained MUSIC [36], cumulant-based coherent signal
subspace method [37], and focussing matrix for coherent signal subspace processing (for wide-
band signals) [38], these approaches do not apply to ADS-B radar system owing to either
unavailable prior information or limited signal bandwidth. Therefore, for the ADS-B radar
2C = YY = ASS A + VV = ASS A +σ I
1( , ) [ ( , ) ( , )]MUSICP N Na E E a
34
system, MUSIC unfortunately cannot be a good candidate for detection and estimation for
multiple targets.
4.3 Trilateration-based localization algorithms
Similar to MUSIC, most Direction Finding (DF) methods have the constraint that the
number of the antennas has to be larger than the number of the targets, thereby not suitable for the
ADS-B radar system. Other methods, like the least squares and the unscented Kalman filter
approaches, require prior information of the motion model. With thorough exploration, we
propose to use trilateration-based localization algorithms for the ADS-B radar system, which no
longer has the constraint on the number of detectable targets using fixed number of antennas.
Trilateration is a method to determine absolute or relative position of an object based on
simultaneous range measurements received from multiple stations located at known locations.
Due to its ease of implementation, it is extensively used in applications as diverse as robotics,
radar, aerospace surveillance, wireless sensing network (WSN), and automotive applications to
provide location-aware services.
However, trilateration-based localization approaches are facing many challenges since
error is inevitably introduced in all ranging techniques [39], including, but not limited to,
Received Signal Strength (RSS), Time of Arrival (TOA), and Time Difference of Arrival
(TDOA). Although vision-based localization techniques are possible [40] – [43], camera images
are sensitive to weather conditions. In a dynamic system where range measurements are noisy
and fluctuating, the trilateration problem becomes difficult.
A computationally efficient closed-form trilateration solution has been derived in [44],
[45]. However, because of the non-linearity between range and target location, the relationship
between measurement noise and estimation error is also non-linear in the algebraic solution. The
35
ranging error, as well as the sensor placement, caused the Dilution of Precision (DOP) effect, i.e.
the ranging error amplification when the position vector is computed. Moreover, it has been
shown in [44], [45] that the position estimate is biased even under the assumption that the noise
distribution is zero-mean.
In the literature, several hybrid methods [46] – [49] have been proposed. Localization is
done through two phases of estimation processes: in the first phase, a rough location is obtained;
subsequently, the second phase involves an iterative implementation that refines the output from
the first phase. However, the required computational cost for hybrid methods is high. The
motivation of this dissertation is to find a suitable trilateration algorithm that can be adopted by
resource-limited UAVs, and hence computational load is a key factor to consider.
As a simple and commonly used trilateration technique, centroid localization (CL) [50]
exploits the most closely spaced three intersections of constant range loci from three sensors, out
of possible six trilateration intersections. Nevertheless, to the author’s best knowledge, no
research papers have explicitly explained via rigorous analysis why the centroid has been
selected, except by empirical evaluation. Similarly, other triangle centers, e.g. incenter [51] and
Fermat point (FP) [52], have also been explored, but no clear justification has been provided
either. Because position error is most likely embedded in all of the range measurements, which
further results in inaccurate intersections, it is the authors’ belief that the intersections need to be
prudently used. In addition to the locations of the intersections, their associated quality needs to
be taken into consideration since each of the intersections includes different level of location
offset. For example, in an optimistic case when two range measurements are error-free and one of
the intersections happens to be the target location, the other intersections are incorrect.
Rather than finding the location itself, it is interesting to look for the range errors that
would allow the scaled range circles to meet at one point, which indirectly provides the estimated
target location. Then the trilateration problem can be considered as searching the most possible
36
range scaling factors (RSF) based on the measurement noise statistics. Subsequently, the authors
show that RSF can be well represented by the distances from the predicted location to the edges
of the triangle with acceptable approximation error. Therefore, the optimal trilateration estimate
should be related to the distance to the sidelines, instead of the intersections as conventional
thinking. This dissertation investigates several triangle centers, including centroid, incenter,
Lemoine point (LP), and FP, and their associated properties that can be useful to the trilateration
problem. Finally, enhanced trilateration algorithms, i.e. weighted trilateration (WT) and range-
adjusted weighted trilateration (RAWT), are proposed to deal with sever trilateration scenarios,
such as two-intersection case, which triangle center approaches do not work.
4.3.1 Time of arrival
Let us denote the transmitted signal as ( )s t . The distance between the target and the own
aircraft can be obtained by cross-correlating the delayed transmitted signal, ( )ds t , with the
received signal, ( )rs t , where d is the internal delay and 2r R c is the round-trip time to
the target. The target range is R and the speed of light is c . In theory, the cross-correlation peak
occurs when d r , from which the range can be determined. In our simulation experiment, the
peak location may vary a little due to the measurement noise and phase coding scheme. The
actual target location is determined after trilateration of the signals received by different receive
antennas, as shown in Figure 4-1.
37
Ideally, the intersection of the trilateration result should indicate the location of the target.
However, due to noisy measurements, a blurred area, instead of a point, results, which may be
bounded by the circular arcs, or possibly these circular arcs may not even overlap.
4.3.2 Trilateration modes
The challenge encountered by the trilateration problem is the determination of the best
estimate of the target position given the noisy range measurements. For the sake of simplicity, the
trilateration problem is formulated in 2-D, but it can be extended to higher dimension using the
same framework. The equations representing the target location with its distances from each
sensor can be expressed as
Figure 4-1: Using trilateration to determine target location.
38
2 2 2
1 1 1( ) ( )x x y y r (4.5a)
2 2 2
2 2 2( ) ( )x x y y r (4.5b)
2 2 2
3 3 3( ) ( )x x y y r (4.5c)
where ( , )x y is the target location, ( , ), 1,2,3i i ix y i S the coordinates of sensor station i , and
ir the distance from the target to each sensor.
All ranging techniques are subject to additive noise. For example, RSS is sensitive to the
channel noise and device variation, and TOA and TDOA can be affected by time synchronization
or temperature or humidity changes. To incorporate the ranging inaccuracy, the observed ranges
are
measurement true , 1,2,3i i ir r i (4.6)
where the error i has zero-mean but not necessarily having a Gaussian distribution.
Let us define range circle as 3-tuple ( , , )i i ix y r and the coordinates of the intersections
from range circles as intersection intersection( , )I x y . The number of intersections from three range
circles can be six, four, two, or zero. Let us further define mode 6, mode 4, mode 2, and mode 0
according to the number of intersections, as illustrated in Figure 4-2. The triangle 1 1 1PQ R
formed by the most closely spaced three intersections closest intersection intersection( , ), 1,2,3i i iI x y i has
the smallest circumcircle radius in the Delaunay triangulation of the set of six range intersections.
The smallest area of the triangle is not used because the far three intersections can sometimes be
co-linear, which renders the triangle area to be nearly zero, as is the case in Figure 1.
39
Figure 4-2: Illustration of trilateration modes.
As the trilateration problem is viewed in this dissertation as finding the target location
through scaling range circles, some preparation work is provided here to facilitate proper
analysis. Without loss of generality (WLOG), let us assume '2 1S P is the true distance between
target and sensor 2 and the measurement noise '2 1 1P P , as shown in Figure 4-3. When the
measurement range circle 2 2 2 1( , , )x y S P is scaled exactly with negative 2 , the target should
reside on the scaled range circle '2 2 2 1( , , )x y S P . In the event that all three range circles are scaled
with RSFs as negative , 1,2,3i i , the three scaled range circles should intersect at the exact
target location. Although the actual values of measurement noise are not known, the prior
knowledge of measurement noise distribution can be used in estimation algorithm.
40
Figure 4-3: Illustration of the error due to arc-line approximation.
The last piece to complete the analysis tool is line-arc approximation. The relationship
between RSF, which is '
1 1PP in Figure 4-3, and the parallel distance, ' '
1 1 1 1( , )d PQ PQ is simply
' '
1 1 1 12 1 1'
1 1
( , )sin( )
d PQ P QS PQ
PP (4.7)
2 1 1S PQ is an isosceles triangle, and therefore 1P
and 1Q
must lie between 0° and
90°. Since1 1 1PQ R is formed by the most closely spaced points, 1Q and 1R should be located
close to each other, thereby2 1 1sin( ) 1S PQ . As a result, the approximation error of using
' '
1 1 1 1( , )d PQ PQ to describe RSF, is small, usually less than 2%. For the sake of brevity, RSF will
41
be considered equivalently as the parallel shift from edges of 1 1 1PQ R since the concept of RSF
will be used extensively in the analysis.
In order to understand the occurrence probability of each mode under various noise
variances, a simple simulation is set up and the result is shown in Figure 4-4. 10,000 iterations of
trilateration using random target locations are executed under noise standard deviation up to 10
m. According to the probability distribution in the simulation result, mode 6 is the most common
trilateration scenario, especially when the noise variance is small. However, as the noise variance
becomes large, the occurrence probability of mode 4 and mode 2 increases. Specifically, the
chance of having four intersections increases from 4% to 22% when the noise standard deviation
increases from 0.2 m to 10 m. The probability of seeing mode 2 is about 2% under large noise
variance. Finally, the probability of mode 0 is insignificant as none of 10,000 iterations
experiences mode 0.
Figure 4-4: Occurrence probability of each mode under various noise variances.
42
4.3.3 Triangle center approaches
Because of the geometric meaning of its vertices, the triangle 1 1 1PQ R is a good starting
point to estimate the target location. The characteristics of a few triangle centers are discussed in
detail. While no single triangle center can always render the best estimate of target location under
various types of noise, it is nevertheless interesting to study how the properties of each triangle
center correspond to the noise statistical characteristics. To further elaborate this point, let us look
at the trilateration problem from a reverse direction and assume that the range measurements are
given and the intersections are already determined. The target can still reside at any location as
long as the measurement errors satisfy the conditions:
measurement true , 1,2,3i i ir r i (4.8)
While i follows a certain probability distribution, it is stochastic and its realization can
take any value. As long as i provides appropriate compensation, the target can appear at random
location with the intersection locations unaltered. No deterministic methods, to which triangle
center approaches belong, can guarantee success in all probabilistic cases. At the end, it is
important to note that the computational load to find triangle centers is nearly the same, and
hence the best triangle center approach is solely based on the estimation accuracy.
Several well-known triangle centers will be discussed in this Section. Note that all
triangle center approaches work only for mode 6, and an additional step to identify the correct
triangle is critical to the estimation performance.
43
4.3.3.1 Centroid
As the geometric center of the triangle 1 1 1PQ R , the centroid location in Cartesian
coordinate can be found as 1 1 1 1 1 1
,3 3
P Q R P Q Rx x x y y y
, and its barycentric coordinate is
1 1 1: :
3 3 3CB
(4.9)
Using 1 1 1PQ R as an example, the translation between barycentric coordinate, [ : : ]a b c ,
and Cartesian coordinates, Cartesian Cartesian( , )x y , has explicit relationship as follows:
1 1 1 1 1 1Cartesian Cartesian( , ) ( , )P Q R P Q Rx y ax bx cx ay by cy (4.10)
It is straightforward to prove that, given the location of three vertices, the centroid
minimizes the summed norm:
2 2 2 2
vertex 1 1 1ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ( , ) || ( , ), || | ( , ), || | ( , ), || , ( , )e x y x y P x y Q x y R x y (4.11)
As a matter of fact, centroid is the least squares estimator, which finds the estimation
result such that the sum of the squares of the difference between the possible location and the
three vertices is minimized. However, since the vertices may be off from the true target, the
distance from a point to vertices is not always a meaningful metric to the estimation algorithm.
44
4.3.3.2 Incenter
Incenter is the point of concurrence of the interior angle bisectors of a triangle, and the
distances from incenter to three edges are equal. In [51], Ahammed et. al. discussed the potential
to use incenter of 1 1 1PQ R as estimate of target location, but proper reasoning was not provided.
Recall that RSF is equivalent to the distance of the parallel shift from the triangle edges. Equal
distances from incenter to three edges imply three identical RSFs. Stated differently, incenter is a
good candidate of the predicted location if all of the sensors have the same magnitude of
measurement noise. While identical measurement noises are unlikely, it can be statistically true
that, for certain noise distribution, the measurement noises have similar magnitude, especially
when the noise variance is very small. However, the estimation accuracy deteriorates quickly if
noise variance is large or if different levels of systematic errors exist among measurements. The
authors observe through abundant simulation results that the incenter renders acceptable
estimation error, in general better than the centroid, when measurement noise variances are equal
among all sensors.
4.3.3.3 Lemoine
Bearing in mind that the distance of the parallel edge shift, as illustrated in Figure 4-5, is
a more meaningful indicator than the distance from a point to vertices, one can easily see that the
optimal estimator minimizes the sum of the squares of RSFs. Let us denote ˆ ˆ( , ), 1,2,3ir x y i as
the distances from a predicted location to three sensors. Then, in the sense of statistics, the
optimal solution needs to minimize
45
32 2
edge
1
ˆ ˆ ˆ ˆ( , ) ( , )i
i
e x y d x y
(4.12)
where measurementˆ ˆ, ) 1,2,3i i id r x y r i
Figure 4-5: The distances between dashed and solid lines are equivalent to RSFs.
Lemoine point, also known as symmedian point, has the property that the total distance to
three edges is minimal, and, by its own triangle center definition, LP achieves the minimum of
Eq. (4.12). Therefore, the authors propose to use LP as the trilateration estimator, and LP is
expected to be the optimal solution among all triangle center approaches. The barycentric
coordinate of LP is:
2 2 2: :LPB a b c (4.13)
where a , b , and c are the sideline lengths of 1 1Q R , 1 1PR , and 1 1PQ , respectively.
1P
1Q 1R
46
4.3.3.4 Fermat
In [52], Huang et. al proposed to use FP as the estimation location, and the justification
mentioned in [52] is that FP minimizes the total distance from a point in a triangle to three
vertices. An interesting question arises: why does FP outperform centroid as the former
minimizes the sum of the total distance to three vertices and the latter minimizes the sum of the
squared distances? Moreover, one of the FP’s properties is that when a triangle has an angle
greater than 120°, FP is always sited at the obtuse-angled vertex regardless. This property
prohibits FP to well reflect the dynamics of the trilateration model.
Surprisingly, FP is in general close to LP, especially when all of the angles are smaller
than or equal to 120°. We will show in the barycentric and Cartesian coordinates the distance
between FP and LP is bounded for nearly all forms of triangles.
The barycentric coordinate for PF of 1 1 1PQ R can be found as:
1 1 11 sec : 1 sec : 1 sec6 6 6
FPB a p u P b q u Q c r u R
(4.14)
where p, q, and r respectively denote the Boolean variables 1boolean( 120p P ,
1boolean( 120q Q , and 1boolean( 120r R , and u p q r .
To reduce the analysis dimension, let us use the normalized lengths 1m ,
2m , and 3m ,
where
1
am
a b c
(4.15a)
47
2
bm
a b c
(4.15b)
3 1 21c
m m ma b c
(4.15c)
As triangle centers are invariant under similarity, the triangle properties are preserved
under the normalization process.
By replacing the variables in Eq. (4.13) and Eq. (4.14) with 1m
and 2m , the barycentric coordinates for LP and FP are dependent only on
1m and 2m :
2 2 2
1 2 1 2: : (1 )LP m m m m (4.16a)
1 1 2 2 1 2 3 1 2( , ) : ( , ) : ( , )FP f m m f m m f m m (4.16b)
We then normalize Eq. (4.16) to obtain the normalized barycentric coordinates for LP
and FP:
normalized normalized normalized normalized
1 2 3
2 2 2
1 2 1 2
2 2 2 2 2 2 2 2 2
1 2 1 2 1 2 1 2 1 2 1 2
: :
(1 ): :
(1 ) (1 ) (1 )
LP LP LP LP
m m m m
m m m m m m m m m m m m
(4.17a)
48
normalized normalized normalized normalized
1 2 3
1 1 2 2 1 2
1 1 2 2 1 2 3 1 2 1 1 2 2 1 2 3 1 2
3 1 2
1 1 2 2 1 2 3 1 2
: :
( , ) ( , ):
( , ) ( , ) ( , ) ( , ) ( , ) ( , )
( , ):
( , ) ( , ) ( , )
FP FP FP FP
f m m f m m
f m m f m m f m m f m m f m m f m m
f m m
f m m f m m f m m
(4.17b)
After two normalization processes, all of the elements in Eq. (4.17) are functions of 1m
and 2m , and hence it is relatively straightforward to see in simulation how close FP and LP are
located. Let us denote the difference between these two normalized barycentric coordinates:
normalized normalized
normalized normalized normalized normalized normalized normalize
1 1 2 2 3 3
1 2 3
, ,
, ,
d
E FP LP
FP LP FP LP FP LP
E E E
(4.18)
The simulation results in Figure 4-6, Figure 4-7, and Figure 4-8 show that the elements in
(14) are smaller than 0.2315, and about 70% of various shapes of triangles are smaller than 0.1.
Another simulation is performed to show the actual distance between FP and LP in
Cartesian coordinate. Two triangle vertices are located at (−0.5, 0) and (0.5, 0), and the third
vertex moves in the field of view (FOV), from (-5, 0) to (5, 5), to create nearly all forms of
triangles. Barycentric coordinates for FP and LP are calculated using Eq. (4.13) and (4.14),
respectively, and their Cartesian coordinates are obtained through coordinate conversion in Eq.
(4.10). The distance between FP and LP is plotted in Figure 4-9. It is shown that the difference of
FP and LP locations in Cartesian coordinates is small, especially when the triangle has no angle
49
Figure 4-6: 1E , the difference of the first element of normalized FP and LP barycentric
coordinates.
Figure 4-7: 2E , the difference of the second element of normalized FP and LP barycentric
coordinates.
50
Figure 4-8: 3E , the difference of the last element of normalized FP and LP barycentric
coordinates.
greater than 120°. When the third vertex moves further away from the initial two vertices, a
slightly increased distance difference is expected. Note that the notch appears when the triangle
has an angle equal to 120°, and it serves as a good indicator that when the triangle has an angle
greater than 120°, the fixed FP position makes the estimation location obsolete.
51
Figure 4-9: Distance between FP and LP in Cartesian coordinate. Green triangles are two fixed
triangle vertices, with edge length as 1 m, and the third vertex moves in FOV.
4.3.3.5 Range-based weighted centroid (RWC)
Similar to the idea in [53] that each trilateration estimates obtained from different set of
beacons have different quality of confidence, each of the intersections represents different
probability of being target location. In [54], [55], the assigned weight is a function of RSS values
of the access points whose corresponding circles intersect at that point. In another word, smaller
range measurements are trusted with higher confidence. This is valid for RSS-based techniques
because channel noise varies tremendously over distance. Nevertheless, when such type of
weightage is used, the estimated location will inherently favor the closer access point locations.
52
Alternative likelihood quantification is sought in this dissertation. The relationship of the
intersection of two range circles with respect to the third circle provides a good indication of the
quality of the intersection because the true target location should not be far from any of the
circles. Therefore, the weighting function is dependent on the range difference between vertex
ir ,
distance from a triangle vertex to sensor i whose range circle does not cross this vertex, and
measurement
ir . Assuming the distance between two points possesses a normal distribution,
representing the probability of one point being the other, the quality of each vertex can then be
evaluated using the weighting function described as follows:
vertex 2vertex
2
1 ( )exp , 1,2,3
22
ii
dw v
(4.19)
where is the variance of the distribution and vertex vertex measurement
i i id r r . The normalized weight,
i.e., 3
vertex vertex vertex
1
i i i
i
w w w
, represents the likelihood of the triangle vertex being the target
location.
Instead of a fixed variance for the weighting function, a dynamic is chosen as one half
of the radius of the circumcircle of the triangle 1 1 1PQ R such that weighting function can adjust
properly on the fly. The final estimated location is the weighted-sum of the triangle vertices given
by
3
RWC RWC vertex closest
1
ˆ ˆ, i i
i
x y w I
(4.20)
53
Figure 4-10 shows an example of a head-to-head comparison between centroid
localization and RWC. The number next to each vertex is the calculated weight using Eq. (4.20),
and it can be seen clearly that the top vertex is far away from the true target and has small weight.
It is not wise to treat all three vertices equally, like centroid localization essentially does. As a
result, RWC outperforms centroid by taking into account the likelihood of each vertex in the final
estimation. It is demonstrated that blind usage of intersections may result in poor estimation
performance, and in addition, RSF is a useful metric in trilateration analysis.
Figure 4-10: Comparison between centroid and RWC. Numerical values are the computed
weights for each intersection.
4.3.3.6 Performance comparisons
To compare the performance of triangle center approaches, including centroid, LP, FP,
and RWC, multiple Monte Carlo iterations are simulated with the following setups: (a) random
54
measurement noise and fixed target location, and (b) random measurement noise and random
target location. Three sensors are located at ( 50 3, 50) , (50 3, 50) , and (0,100) ,which
form an equilateral triangle inscribed in a circle with radius 100 m.
(a) Random measurement noise and fixed target location
One target is located at (30,30) , and the measurements are affected by random noise.
Table 4-1 shows five sets of measurement noise realizations and the subsequently calculated
locations of centroid, LP, FP and RWC obtained using Eq. (4.9), Eq. (4.13), Eq. (4.14), and Eq.
(4.20), respectively. Among the triangle center approaches, centroid has the worst estimation
accuracy.
Table 4-1: Comparison of various triangle center approaches for fixed target and standard
deviation = 5 m.
Test # Target
(m)
Measurement
Noises (m)
Centroid
(m)
LP
(m)
FP
(m)
RWC
(m)
1 (30, 30) (9.9, −1.6, 1.5) (41.7, 34.9) (39.5, 33.6) (39.7, 33.7) (39.9, 33.9)
2 (1.1, 4.1, 8.3) (24.3, 24.5) (29.6, 27.6) (28.5, 27.4) (29.4, 27.3)
3 (−6.5, 9.4, 1.6) (17.1, 27.5) (19.9, 29.3) (19.2, 29.4) (19.9, 29.0)
4 (−2.1, 6.6, -1.3) (22.4, 30.4) (25.0, 31.9) (24.4, 31.9) (24.8, 31.7)
5 (−2.6, 2.7, 8.1) (23.1, 23.1) (27.2, 25.5) (26.3, 25.3) (27.1, 25.3)
1000 Monte Carlo iterations are simulated under different level of noise variance. Since
triangle center approaches require six intersections, cases of mode 0, mode 2, and mode 4 are
excluded from the analysis, but the data will be used later in WT and RAWT to test their
performance under more severe scenarios. As the noise variance increases from 0.1 m2
to 5 m2,
about 4% -20% of the samples are discarded. The number of iterations is selected such that the
number of mode 2 and mode 4 cases is sufficiently large to conduct proper analysis.
55
Localization performance comparison in terms of average estimation error and root-
mean-squared-error (RMSE) are shown in Figure 4-11 and Figure 4-12, respectively. It is clear
that traditional centroid localization renders largest estimation error, and in addition, the average
error between centroid and other approaches is as significant as 25%. Moreover, FP and LP
estimation errors are similar although LP has slightly better estimation accuracy.
Figure 4-11: Average errors of 1000 Monte Carlo simulations with random noise variance and
fixed target location.
56
Figure 4-12: RMSE of 1000 Monte Carlo simulations with random noise variance and fixed
target location.
(b) Random measurement noise and random target location
In this Section, the setup is the same as previous Section, except the target is placed
randomly with uniform distribution in FOV from −200 to 200 m in both x and y directions. It is
important to understand the performance of each trilateration approach at various target locations.
Five sets of measurement noise realizations at different target locations are provided in Table 4-2,
and the calculated locations for each triangle center approach can be directly compared. The
performance trends are similar to fixed target location.
57
Table 4-2: Comparison of various triangle center approaches for random target and
standard deviation = 5 m.
Test
#
Target
(m)
Measurement
Noises (m)
Centroid
(m)
LP
(m)
FP
(m)
RWC
(m)
1 (195.3,
173.3)
(2.2, 1.6,
−10.4)
(180.9,
188.7)
(184.0,
182.0)
(180.6,
181.6)
(181.4,
187.9)
2 (18.2, 40.3) (2.0, 10.4, 7.5) (10.2, 38.2) (13.7, 41.2) (12.7, 42.0) (13.8, 40.1)
3 (−66.5,
147.9)
(−4.7, −4.4,
8.7)
(−77.4,
136.9)
(−75.9,
141.3)
(−78.1,
142.3)
(−75.9,
139.4)
4 (−119.9,
−6.7)
(−9.6, 5.9, 3.6) (−123.9,
−19.8)
(−120.9,
−14.6)
(−118.8,
−16.1)
(−122.2,
−15.8)
5 (174.2,
−26.6)
(−6.2, 4.5, 1.0) (169.7,
−17.1)
(173.5,
−25.3)
(177.2,
−23.1)
(171.1,
−21.5)
Again, 1000 Monte Carlo iterations are simulated. Figure 4-13 and Figure 4-14 indicate
among all triangle center approaches the centroid localization results in worst performance. In
addition, while RWC seems to have the best performance at one fixed target location, LP in
general yields the smallest estimation error at various target locations.
Figure 4-13: Average errors of 1000 Monte Carlo simulations with random noise variance and
random target location.
58
Figure 4-14: RMSE of 1000 Monte Carlo simulations with random noise variance and random
target location.
4.3.4 Enhanced algorithms for severe trilateration scenario
Depending on the sensor placement, target location, and corrupted range measurement,
three range circles do not always create six intersections, which will make the triangle center
approaches invalid. WLOG, let us assume that the range between the target and sensor 1S , is
small, and there is a possibility that the range circle 1 1 1( , , )x y r lies completely within
2 2 2( , , )x y r ,
or 3 3 3( , , )x y r , or both. The number of intersections is consequently reduced. Therefore, the
localization algorithm cannot solely rely on having six intersections. In addition, an additional
step is required for triangle center approaches to identify1 1 1PQ R correctly. If the chosen three
intersections fail to form the desired triangle, the triangle center approaches may lead to large
estimation error.
59
In this section, two algorithms for severe trilateration scenarios are discussed. WT can be
deemed as an extension of RWC by assigning weight to each of the intersections, regardless of
the number of intersections. RAWT is capable to deal with the extreme case of zero intersection
by adjusting the range circles with appropriate offset and post-generating additional intersections.
WT and RAWT are closely related to particle filtering (PF) with advantages and
limitations. While WT and RAWT are considered coarse-grained due to the small number of
intersections (particles), their computational load is significantly lower than PF.
4.3.4.1 Weighted trilateration
RWC can be readily extended by assigning the weights to all of the intersections, not
merely to the vertices of 1 1 1PQ R . Each intersection is evaluated and assigned with a weight, and
then final estimate location is the weighted-sum of all intersections. Identification of the
trilateration mode and finding 1 1 1PQ R are no longer necessary. Nevertheless, while is
dependent on the radius of the circumcircle of 1 1 1PQ R in RWC, needs to be pre-selected and
is application-specific for different accuracy requirements.
However, it is obvious that WT cannot work in mode 0 although it has been shown in
Figure 4-4 that occurrence of mode 0 is very rare. In mode 2, large estimation error is expected
because of insufficient sample diversity. In fact, most of the time, one intersection is selected as
final estimate because of its dominant weight. Therefore, it is suggested to post-generate
additional intersections in mode 2 and mode 0 through adjusting the range circles, as discussed in
the next section.
60
4.3.4.2 Range-adjusted weighted trilateration
In the extreme trilateration cases of mode 2 and mode 0, it is desired to create additional
range intersections. One straightforward approach is to adjust the range circles with a sufficient
offset, offsetr , that is at least three times of the measurement noise standard deviation. In addition
to the original three measurement range circles with radii, measurement , 1,2,3ir i , another six range
circles with radii as max measurement offset , 1,2,3i ir r r i and
min measurement offset , 1,2,3i ir r r i will be
introduced. Three annuli with inner radius min
ir and outer radius max
ir are then formed, and these
three annuli should overlap, as shown in Figure 4-15. For normal distributed measurement noise,
the probability of the magnitude of the measurement noise being larger than offsetr is only 0.3%
and hence the possibility of obtaining no overlapping area is insignificant.
Out of these nine range circles, there will be at most 54 intersections. The next step is to
find the extended intersections, mI , that satisfy the following condition:
min maxdist( ( , ), ) , 1,2,3 , 54i m i ir I x y S r i m (4.21)
mI defines the overlapping area that the target is likely to reside. Subsequently, each of
the extended intersections will be evaluated and proper weights will be assigned according to Eq.
(4.21).
61
Figure 4-15: The extended intersections define an overlapping area.
Triangle center approaches require six intersections, but WT and RAWT are insensitive
to the number of intersections. While this is an advantage of WT and RAWT over triangle center
approaches, it makes it difficult to perform an absolutely fair comparison. Therefore, the
simulation in this Section is intended to demonstrate how WT and RAWT handle the severe
scenarios like mode 4 and mode 2, which triangle center approaches cannot deal with.
The data used in this Section are those discarded in Section 4.1.2, and the estimation
results are provided in Figure 4-16 and Figure 4-17. It can be seen that WT and RAWT are
capable to provide acceptable estimation results for severe trilateration scenarios although the
estimation error is slightly larger. Furthermore, RAWT has better performance at the cost of
additional computational resources.
62
Figure 4-16: Average errors of WT and RAWT for mode 4 and mode 2.
Figure 4-17: RMSE of WT and RAWT for mode 4 and mode 2.
63
4.3.4.3 Estimation error over range
It is important to know how the trilateration techniques performance deteriorates
over wide FOV. Therefore, the performance results of all techniques under mode 6 are
compared.
1000 Monte Carlo iterations are simulated with various range from 100 m to 1000
m. The noise standard deviation is set as 5 m. It is shown in Figure 4-18 and Figure 4-19
that centroid localization degrades rapidly as distance between target and sensors
increases.
WT and RAWT approaches have the smallest RMSE when the map size is large.
However, when the target range is not large, WT and RAWT provide marginal
improvement. Although average error of RWC is the smallest, its RMSE is larger than
WT and RAWT. As more intersections imply better diversity, WT and RAWT is more
robust at random target location under random measurement noise.
64
Figure 4-18: Average errors of all trilateration techniques under different map sizes.
Figure 4-19: RMSE of all trilateration techniques under different map sizes.
65
4.4 Particle filter algorithm
Recursive Bayesian estimation and particle filter algorithm are briefly reviewed in this section.
Furthermore, a simple multi-target estimation method based on particle filter is proposed for the
application of ADS-B radar system.
A discrete time estimation problem is considered here. The state vector is denoted by tx
whose temporal evolution is given by the state equation:
t t t-1 t-1x = f (x , v ) (4.22)
where tf is the state transition function and 2(0, )t vN v is the process noise with zero mean and
variance 2v . In the ADS-B radar system, the components of the state vector will be target
locations. Without prior information about the target motions via estimating target velocities and
accelerations, the system transition function will be identity matrix with 2v sufficiently large in
order to cover the motion uncertainty.
At each discrete time point an observation ty , related to the state vector, can be represented as
follows:
t t t ty = h (x ,n ), (4.23)
where th is a possibly nonlinear function of the state, tx , and the measurement noise,
2(0, )t vN n is the measurement noise with zero mean and variance 2n . The measurement noise
is uncorrelated with the process noise. In the simulation, ty will be the calculated range
information, and th is the process to obtain the target ranges through TOA technique. Let tD
66
denote all of the available information, 1 t...y , ,y , at time. The non-linear prediction density is
given via the Chapman-Kolmogorov equation:
1 1 1 1 1( | ) ( | ) ( | )t t t t t t tp p p d x D x x x D x. (4.24)
When new measurement inputs arrive, the solution to compute the posterior distribution
( | )t tp x D of the state vector, given past observations, is given by using Bayes theorem:
11 1 1 1
1
( | ) ( | )( | ) ( | ) ( | ) ( | )
( | )
t t t tt t t t t t t t t
t t
p pp p p p d
p
y x x D
x D y x x x x D xy D
(4.25)
Where
1
1
( | ) ( | )t t t t tp p d
y x x D x (4.26)
is a normalizing constant.
Particle filter [56], [57] is recursive Bayesian filter based on Monte Carlo simulations. It
is also known as sequential Monte Carlo methods, bootstrap filtering [58], and the condensation
algorithm in computer vision [59], and is very suitable for non-linear and non-Gaussian
applications as often encountered in the real world. A particle filter is essentially composed of
three stages: prediction, update, and resampling. The prediction stage uses the system model to
predict the state probability density function (PDF) forward from one measurement time to the
next. Since the state is usually subject to unknown disturbances, prediction generally spreads the
state PDF. The update operation takes the latest measurement to modify the prediction PDF using
67
Bayes’s formula. A resampling step was introduced by Gordon et al. [60] in order to discard the
particles with very low weights to improve the algorithm efficiency. When probabilities of many
particles are too small, it is wise to use those particles on other potential target locations during
searching.
Particle filters work by providing a Monte Carlo approximation to the probability density
function (PDF) which can be easily updated to incorporate new information as it arrives. All the
possible locations, i.e. where particles lie, will be assigned with a weighting function
corresponding to how likely a target occurs at the particle location.
An approximate numerical integration method to solve Eq. (4.25) is described below.
(i) Particle generation: Within the field of view (FOV), create N particles and associated
weights 1 1 1,...,( , ( ))n nt t n Nw x x according to the uniform distribution.
(ii) Prediction: Particles propagate according to evolution Eq. (4.22).
(iii) Measurement update: Use the available measurements to compute the likelihood of each
particle and update the weights of all particles with a posteriori density. This is accomplished
using
1( ) ( ) ( | )i i it t t tw w px x y x (4.27)
where the final weights sum to one, viz., 1
( ) 1
Nit
i
w
x .
(iv) Systematic resampling: After a predetermined number of iterations, take N samples with
replacement from the current particle set based on ( )itw x .
(v) Iteration: Letting 1t t , repeat the process until desired estimation error is achieved.
68
For abruptly changing systems, Interacting Multiple Model (IMM) method [61] – [63]
and Generalized Pseudo-Bayesian (GPB) [64] are widely used in the target tracking literature. To
reduce the computational complexity on the ADS-B radar system, these approaches are not
adopted. In fact, we do not even use the motion equation since the dynamic model of the object
cannot be obtained. In the prediction step, particles are simply scattered with a large variance that
is able to cover abrupt motion changes.
Assume there are two targets around the own aircraft equipped with ADS-B radar system.
Each particle will be assigned two weights according to the state PDF. In order to eliminate the
particles with weights that are both low, we first randomly pick a number r within 1[0, ]N .
Then we add 1N to r and select the particle which corresponds to the value of r . If both of the
weights of a particle are lower than 1N , then they are very likely to be neglected when we jump
to the next pick. By repeating this procedure, all the particles that have both low weights will be
discarded and only those particles with at least one high weight will survive. Parts of the particles
will be representing Target 1 if their first weights are clearly larger than the second ones. After
resampling, the number of particles remains unchanged. Figure 4-2 depicts the idea of resampling
for multiple targets. The resampling step removes particles that are improbable to be targets, but
it requires additional processing latency. Hence, we would like to intelligently pick up the right
time to do the resampling step. The parameter effN , the effective sample size, can be used to
measure the degeneracy of the algorithm [65], [66]. Once the particles spread out all over the
place and only a certain amount of particles are meaningful, effN will become small. This is the
right time to spend extra computational expense to discard low weight particles. A good estimate
4.4.1 Simplified resampling mechanism
69
of the effective sample size can be achieved with the quantity
1
2eff
1
[ ( )]N
it
i
N w
x . The
resampling step is performed when the number of meaningful particles is less than a
predetermined threshold, thresholdN . This enables the particle filter algorithm to simply do
resampling at appropriate times. The numerical approximation of adaptive resampling for m
targets is given as follows, if m is known.
The procedure is described below:
(i) Set up thresholdN , which represents the number of the meaningful particles, to be within [0,1] .
(ii) Derive 1,...,{max( ) | , 1,..., }inew k k mw i N w .
(iii) Calculate
1
1 2eff
1
1 [ 1] , 1,...,
Nik
i
N N k m
N w .
(iv) If eff 1 eff thresholdmin{ ( ), , ( )}mN w N w N , then take N samples with replacement from the current
particle set using neww .
Figure 4-20: Resampling mechanism for multiple targets.
70
4.4.2 Supplementary particle filter algorithm
As the ADS-B radar measurement is available once per second and the PF can be
completed in the order of one-tenth of a second, most of the time the system is idling and waiting
for the new measurement. To improve the estimation performance, some sort of upsampling
process is desirable and can be realized through piecewise constant interpolation between
successive measurements. We name the algorithm using interpolated measurement on PF as the
supplementary particle filter (SPF). Before the new measurement arrives, SPF performs
iteratively using the current observation as if the target were static. Standard PF is vulnerable to
sample impoverishment because a finite number of particles are used to approximate a continuous
distribution. The benefit of SPF over standard PF is that SPF minimizes the estimation error when
the sample size is not sufficiently large. SPF provides improved estimation accuracy because
particles will be redistributed to high likelihood areas over iterations although the same
measurement information is reused. The sample resolution is essentially enhanced during SPF
iterations, thereby improving the estimation performance.
SPF not only improves the estimation accuracy between successive measurements, but
also benefits further the estimation result when new measurement arrives because more particles
are already allocated to local mode of the posterior density. Through extensive simulation
analysis, it has been noticed that PF takes many iterations to converge. While the ADS-B
message is available only once a second, a few dozen seconds may be needed to obtain accurate
estimated target locations. However, for the pilots to react on imminent collisions, it is critical to
improve the convergence rate and estimation accuracy in spite of the low measurement update
rate. Overall, the convergence rate of SPF is about 2-3 times faster than PF and the estimation
error of SPF is about one half of the estimation error using standard PF. The gain is significant
especially during the very first few measurements.
71
4.4.3 Performance Comparisons
In order to ascertain the effectiveness of the algorithm for the ADS-B radar system, the
transmitted signal is simulated according to the ADS-B radar message format, which follows the
requirements of the ADS-B signal specification. The ADS-B radar waveform, as shown in Figure
4-21, is generated by adding random bi-phase modulation into each bit of the ADS-B signal. The
signals received by multiple sensors are essentially the attenuated and delayed replica of the
transmitted signal with measurement noise, n . The sensor locations are not restricted, and in the
simulation setup, the sensors are circularly positioned and 30 meters apart, using the maximum
available distance on an airplane. The transmitted ADS-B radar signal and the returned signals
received by the four sensors are shown in Figure 4-22. The time differences between the
transmitted and received signals are used to calculate the ranges from the target to each of the
sensors. Since the ADS-B radar signal is broadcast every second, a new measurement will also
arrive approximately once per second.
Figure 4-21: Transmitted ADS-B radar signal waveform.
72
Figure 4-22: Transmitted ADS-B radar signal and received signals from four sensors.
Without prior estimation of motion model, additional positional uncertainty is incorporated
in the state transition equation to allow the particles to have the potential to move around and to
compensate the unknown maneuver while searching for the best solution. As long as one or a few
particles are able to “follow” the target, the calculated weights will be high, and subsequently, in
the next resampling step a large amount of particles will be drawn to the neighboring regions of
the particles that have high weights. In the simulation, the positional uncertainty is set to 300 m
after considering the relative aircraft speed and the finite amount of particles. By taking into
account the detection range of 10 km and the computational load for multi-target tracking, the
number of particles is chosen to be 10,000 and threshold 5%N for the following three simulation
scenarios: (1) constant velocity with random acceleration and direction noise, (2) basic flight
maneuvers, and (3) multiple targets.
73
To test the tracking capability, we first assume a non-cooperative aircraft with of RCS of 20
dBsm at a range of 10 km. According to the link budget analysis, as discussed in Sec. 3.B, the
SNR is 11.1 dB. The target is moving at a constant velocity of 150 m/s with a Gaussian
distributed acceleration and heading direction. Figure 4-23 depicts the tracking performance
comparison of PF and SPF against the true target. In addition, the range errors of one trial and the
root-mean-square error (RMSE) of twenty Monte Carlo (MC) trials are plotted in Figure 4-24 and
Figure 4-25. The plots indicate that SPF estimated location converge to the true target location
much faster, especially during the first few seconds. The range RMSEs of SPF and PF estimates
at the 5th, 10
th, and 15
th seconds are listed in Table 4-3. Note the difference of the two tracking
methods increases during the first few measurement because each SPF estimation results benefit
from previous estimates that are closer to the true target location. After convergence, SPF also
performs better than PF in terms of RMSE.
Figure 4-23: Tracking trajectories of PF and SPF methods against true target (20 MC trials).
74
Figure 4-24: Range errors during each iteration (one trial).
Figure 4-25: RMSE for a target with constant velocity, as well as Gaussian distributed
acceleration and heading direction (20 MC trials).
Table 4-3: Estimation error comparison.
75
after 5 seconds after 10 seconds after 15 seconds
PF 885.2 m 488.7 m 289.6 m
SPF 212.9 m 146.5 m 45.33 m
In the following simulation, the benefit of the additive positional uncertainty will be shown
through tracking a maneuvering target even though the motion model is unknown. For a non-
cooperative and maneuvering target 5 km away, Figure 4-26 shows that both PF and SPF are
capable to track the target with decent accuracy. Again, 20 MC trials are performed, and the
range error for each iteration and the RMSE results are depicted in Figure 4-27 and Figure 4-28,
respectively. Compared to the target at 10 km away in the first example, the error in the position
estimate rolls off much faster when the target is closer to the sensors. Nevertheless, the
improvement of SPF over PF is still noticeable in terms of convergence rate and estimation
accuracy.
Figure 4-26: Tracking performance for a maneuvering target (20 MC trials).
76
Figure 4-27: Range errors during each iteration (one trial).
Figure 4-28: RMSE for a maneuvering target (20 MC trials).
77
A multi-target scenario is simulated as well to test the capability to track multiple
surrounding targets simultaneously. Since this dissertation focuses on the non-cooperative targets,
we assume two non-cooperative targets located relative to own aircraft at (−4000 m, −3000 m)
and (−5000 m, −5000 m), respectively. The relative speeds are 100 m/s and 150 m/s, and the
trajectories are drawn in Figure 4-29. Even though the two target trajectories cross over, the
proposed method is still able to provide satisfactory estimated trajectories. However, similar to
PSR, the target identification is not included in the radar report and trajectory for each aircraft
needs to be constructed using data association methods, which is another discrete problem.
Figure 4-29: Tracking performance for multiple targets (20 MC trials).
78
Chapter 5
Conclusions and Future Work
5.1 Conclusions
In the very near future, the air surveillance system paradigm will move away from a
conventional ground-based ATC to a decentralized ADS-B system to be ready for high capacity
of air traffic with improved aviation safety. In order to overcome the setbacks of the ADS-B
system, such as vulnerability to spoofing and incapability to avoid non-cooperative targets, the
ADS-B radar system is proposed and developed. The ADS-B radar system is an innovative add-
on implementation that exploits the constantly broadcast signals from the standard ADS-B
systems with only a few additional integrated devices for detection and estimation of non-
cooperative targets as well. Besides, the radar report can be used wisely to compare the incoming
ADS-B messages to reject any potential spoofed information. It is important to point out the
independence of the communication and radar capability because the radar performance will not
be deteriorated in the event of an incorrect ADS-B message. The communication message is
encoded using PPM while the radar signature is embedded in the sequence of the random phase
modulation.
We demonstrate the ADS-B radar system is able to detect both cooperative and non-
cooperative targets in the range of several kilometers, which will allow the pilot adequate amount
of reaction time. Trilateration-based localization algorithms are proposed for resource-limited
platform, such as UAVs. The trilateration problem is viewed in this research work as finding the
most possible RSFs according to the noise statistics that would allow scaled range circles to meet
at one point. The authors present the framework that can be used in determine the quality of
intersections, which is further used to provide a good trilateration estimate. In addition, it is
79
pointed out that the distance from a predicted location to the triangle edge is a better metric than
to vertex, as traditional thinking. The weight of an intersection is defined based on the geometric
relationship between the intersection and the range circle which does not pass through this
intersection. When intersections are used to find the target location, the associated weights need
to be considered. LP is shown to be the optimal among the deterministic trilateration estimate
approaches at nearly no additional computational load compared to traditionally used CL. WT
and RAWT are presented to deal with severe trilateration scenarios when not all trilateration
range circles meet each other. In addition, SPF is designed for the ADS-B radar system to deal
with the low measurement update rate. It allows the particles to redistribute to most possible
target locations and significantly improves the estimation accuracy and convergence rate,
especially during the first few iterations.
5.2 Future work
This research work opens a lot of opportunities for the ADS-B system to incorporate
airborne sense-and-avoid capability, which can be useful for the purpose of collision avoidance
for resource-limited UAVs. Moreover, the radar functionality of the ADS-B radar system has the
potential to serve as a backup surveillance in the event of loss of GNSS function and make the
communication system spoof-resistant to incorrect ADS-B reports. Possible future work for the
ADS-B radar system includes, but not limited to, the hardware implementation of the ADS-B
radar system, system-wide verification and evaluation, and flight testing. Safety is always the top
concern for a new onboard avionics. It is critical to understand the system performance under
various real-world challenges, such as weather hazards and unexpected interference. Before the
ADS-B radar system gains acceptance from the aerospace society, reliable design, development,
and flight testing are anticipated.
80
Although the current design of the ADS-B radar system is able to detect targets a few
kilometers away, it is much desired to extend the ADS-B radar system operational range to the
order of tens of kilometers, possibly through the design of the ADS-B radar signal waveform. The
limitation of trilateration approaches over distant targets may need further investigation. It will be
ideal if the signal specification considers the communication and radar functionality altogether.
By relaxing the constraints of the current ADS-B signal, e.g. signal modulation scheme, the radar
capability can be significantly improved.
While SPF improves the estimation accuracy by exploiting the waiting time for the new
measurement, the balance between the number of particles and the number of SPF iterations can
be further investigated for optimal performance. Furthermore, an automated mechanism to
determine whether additional SPF iteration is needed based on the distribution of the particles
may be an interesting direction to explore.
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VITA
Ming-Shih Huang
1000 Davit Lane #114, Redwood City, CA 94065 || Email: [email protected]
Education
Ph.D. in Electrical Engineering, Pennsylvania State University 2013
B.S. in Electrical and Control Engineering, National Chiao Tung University 2004
Certification
National Instruments Certified LabVIEW Associate Developers 2011
Engineer-In-Training, US-Pennsylvania Certification 2010
Federal Communications Commission Amateur Radio Service licenses 2009
Work Experience
Senior Systems Engineer, ASSIA Inc. Feb. 2012 – present
Instructor, The Pennsylvania State University Summer 2011
Technical Consultant, Siemens AG, Erlangen, Germany Summer 2010
Research Intern, Siemens AG, Munich, Germany Summer 2009
Research Intern, Intelligent Automation Inc., MD Summer 2008
Teaching Assistant, The Pennsylvania State University Aug. 2008 – Dec. 2011
Selected Publications
[1] M.-S. Huang and R. M. Narayanan, “Trilateration-based localization algorithm for
unmanned aerial vehicles,” International Journal of Robotics, 2013 (submitted).
[2] M.-S. Huang, R. M. Narayanan, Y. Zhang, A. Feinberg, “Tracking of non-cooperative
airborne targets using ADS-B signal and radar,” International Journal of Aerospace
Engineering, Vol. 2013, Article ID 521630, 12 pages.
[3] M.-S. Huang, R.M. Narayanan, “Non-cooperative collision avoidance concept for
unmanned aircraft system using satellite-based radar and radio communication,”
Proceedings of 30th Digital Avionics Systems Conference, Seattle, WA, October 2011,
pp. 5.C.2-1–5.C.2-9. [Best Student Paper, Best of Session, and Best of Track]
[4] M.-S. Huang, A. Feinberg, R.M. Narayanan, “Multiple targets tracking and
estimation for ADS-B radar system”, Proceedings of 27th Digital Avionics Systems
Conference, St. Paul, MN, October 2008, pp. 3.C.1-1–3.C.1-10. [Best Student Paper and
Best of Session]
