1

Prof. Shirish S. Gedam

CSRE, IIT Bombay

GNR 630: Introduction To GeoSpatial Technologies

GPS : Technology and Applications

2

Session 1 14/03/2012

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3

• Slot 6

• Wednesday (1105-1230)

• Friday (1105-1230)

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• To introduce operating principles of GPS systems and their applications

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5

• Global space positioning and navigation systems • Segments of GPS : Concepts and principles of space intersection

• GNSS signal Characteristics• Single and Dual frequency Receivers concept; • Sources of error; Dilution of precision and its treatment

• GPS Signal Travel Delays and corrections • Static, Differential and Kinematic modes of GPS operations

• GPS data Post Processing and Applications

6

• No specific text books are recommended

• Books given below covers the geodetic and engineering aspects of GPS

• Global Positioning System: theory and Applications VolI and II, Ed. Bradford W. Parkinson, James J. Spiker, American Institute of Aeronautics and Astronautics, Inc., Washington D.C., 1996

• Understanding GPS :Principles and Applications Ed. lliottD. Kaplan and Christopher J. Hegarty; ARTEC House, Bosyon

• Global Positioning System: theory and practice, Hofman-Wellenhof. B., Wein Springer 2001

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7

• On track …. Let’s Begin

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• Global Positioning System

• A GNSS (global navigational satellite system) developed by the US military

• Provides reasonably accurate positional coordinates to determine a user’s location on the globe

• Primarily a military system find civilian applications in Global navigation, Transportation, agriculture, police science, marketing, construction, Mining, ……

• Timekeeping …….

5

� Trilateration

� Measures (Computes) Time

for signal to travel from

satellite to the receiver

� The distance from 4 or more

satellites is calculated from

signal travel time.

� Receiver calculates its

position on earth based on

these 4 distances and known

(Estimated) position of GPS

satellites in their respective

orbits

6

45°N, changes with time.

This is a file from the Wikimedia Commons

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13

• 1950’s Need established–navigational/location systems inaccurate

• 1960’s GNSS concept designed

• 1970’s engineered and built

• 1980’s first satellites in orbit (1978)

• 1990’s positioning available

• 1995 Full Operational Capacity (FOC)

• Other systems (GLONASS, Galileo, Compass, IRNSS)

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• Current Constellation

http://tycho.usno.navy.mil/gpscurr.htmlhttp://tycho.usno.navy.mil/gpscurr.html

http://www.usno.navy.mil/USNO/time/gps/current-gps-constellation

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15

The Global Navigation Satellite System (GLONASS) is based on a

constellation of active satellites which continuously transmit coded

signals in two frequency bands, which can be received by users

anywhere on the Earth's surface to identify their position and velocity

in real time based on ranging measurements. The system is a

counterpart to the United States Global Positioning System (GPS)

and both systems share the same principles in the data transmission

and positioning methods. GLONASS is managed for the Russian

Federation Government by the Russian Space Forces and the system

is operated by the Coordination Scientific Information Center

(KNITs) of the Ministry of Defense of the Russian Federation

GLONASS SYSTEM OF GPS

16

GLONASS Global'naya Navigatsionnaya Sputnikovaya Sistema

Global Navigation Satellite System

CONSTELLATION DESCRIPTION

Number of Satellites

24 Active

Geometry 3 planes, 8 satellites each

OrbitMEO - 19,100 km (10,313 nmi) circular, 64.8° inclination

Orbit Period 11 hours 15 minutes

Coverage Global

Initial Operational Capability (IOC)

1993 September 24

Full Operational Capability (FOC)

Operated by:Coordination Scientific Information Center (KNITs)

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17

Galileo GPS

Galileo will be Europe’s own global navigation satellite system, providing a highly accurate, guaranteed global positioning service under civilian control. It will be inter-operable with GPS and GLONASS, the two other global satellite navigation systems.

• First experimental satellite, GIOVE-A, was launched on 28 December 2005• Fully deployed Galileo system consists of 30 satellites (27 operational + 3 active spares), positioned in three circular Medium Earth Orbit (MEO) planes at 23 222 km altitude above the Earth, and at an inclination of the orbital planes of 56 degrees with reference to the equatorial plane.

Galileo – Status (2011)

First experimental satellite, GIOVE-A, was launched in 2005 and was followed by a second test satellite, GIOVE-B, launched in 2008. The first four operational satellites for navigation will be launched in 2011 and once this In-Orbit Validation (IOV) phase has been completed, additional satellites will be launched. On 30 November 2007 the 27 EU transportation ministers involved reached an agreement that it should be operational by 2013,[4]but later press releases suggest it was delayed to 2014.[5]

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• European Union project.

• Galileo had plans to put 30 satellites in orbit 23,000km above the Earth by 2007, but has been delayed.

• The whole project would cost upwards of 3bn Euros.

• If the scheme does get off the ground, it would cost about 220m Euros a year to run.

• Aimed at new transport infrastructure and offering positioning and timing services.

• For commercial, safety, security and government applications.

• Current Status http://www.galileo-pgm.org/

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Indian GPS ( IRNSS)India will put a constellation of seven satellites into a geo-synchronous orbit in the next six years to create a comprehensive navigational system for the South Asian region, ISRO chairman G Madhavan Nair said today. The system, to be called the Indian Regional Navigational Satellite System (IRNSS), will provide invaluable positioning and timing data to aircraft and ships operating in the region. The constellation is being designed on the lines of the US Global Positioning System (GPS).

Amitabh Sinha Tags : Posted: Friday , Sep 28, 2007 at 0057 hrs HYDERABAD, SEPT 27:

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Latest News

July 20, 2009Share via: Technorati TwitterThe Indian Space Research Organization (ISRO) has awarded a new $82 million contract to Raytheon Company to modernize the Indian air navigation system. Raytheon will build the ground stations for the GPS-Aided Geosynchronous Augmented Navigation System (GAGAN), and the Indian Space Research Organization will provide the space segment and additional ground equipment. GAGAN will provide satellite-based navigation for civil aviation over Indian airspace and adjoining areas in south and east Asia. The Indian satellite-based augmentation system (SBAS) is expected to bridge the gap between the European EGNOS (European Geostationary Navigation Overlay Service) and the Japanese MSAS (MTSAT Satellite-Based Augmentation System) to provide seamless navigation of aircraft across a wide portion of the Earth. Raytheon will continue the work it began several years ago and expects to have the GAGAN system fully functional by 2013.

GAGAN System

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•Satellite The Signals ( space segment).

•Satellite Control ( control segment).

•Receiver and Data Processing ( user segment)

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Space Segment

Segments of GPS

http://upload.wikimedia.org

www.PDHonline.org

(P. H. Dana, 1995)

www.maic.jmu.edu

1.Space segment

2.Control segment

3.User segment

14

Signal Transmission

L5CARRIER 1176.45 MHz

L5 SIGNALModified form (P. H. Dana, 1998)

CSRE, IIT Bombay

L1(1575.42 MHz)

C/A code (1.023MHz) P-code10.23MHz

L2(1227.60 MHz)

No C/A code P-code10.23MHz

Fundamental Freq. 10.23 MHz

X 120

X 154

/10

Navigation message@ 50 bps

L5(1176.45 MHz)

l5 Q5X 115

Positioning by Pseudorange measurements

dtcRt +∆+= )(ρ

The pseudo-range(R) is given by;

2222)()()( WZVYUX

t −+−+−=ρ

The True range is given by;

2

1

2

1

2

1

2

11 )()()()( WZVYUXdtcR −+−+−=−∆−

2

2

2

2

2

2

2

22 )()()()( WZVYUXdtcR −+−+−=−∆−2

3

2

3

2

3

2

33 )()()()( WZVYUXdtcR −+−+−=−∆−2

4

2

4

2

4

2

44 )()()()( WZVYUXdtcR −+−+−=−∆−

•Total delay due to atmosphere is the contribution of Ionosphere and troposphere.

•After calculating the position the delays due to the atmospheric effects can be

measured by inverse process

CSRE, IIT Bombay

15

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• 2 Solar panels for power

• main body is size of small car

• 2- 4 atomic clocks (cesium/rubidium)

( space segment).

• Each satellite has a unique SV number

• 49 Navstar (number changes as more are launched or phased out)

• Types of Satellites SV (space vehicle)– Block I

– Block II

– Block IIA

– Block IIF

– Block IIRM

– Block III (Future)

( space segment).

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GPS developers in the US are currently piecing together the next generation of global positioning satellites, which will bring the accuracy of GPS receivers down from ten feet to three feet.

More than 30 of the new satellites are being put together and will be known as the Block III satellites, according to the Congressional Budget Office. Col. Harold "Stormy" Martin of the Air Force Space Command, said that the new machines - which are due to start being launched in 2014 - will tremendously enhance the results of the existing satellite constellation and, eventually, completely replace them.

"It's a really big jump," said Col. Martin. "With [the] additional signals, the additional power it's going to bring, it's quite a leap from the other systems."

The new, additional signals that the satellites will relay will be provided for enhanced civilian use, offering greater precision and making more satellites available for use by non-military receivers.

In terms of military uses, the Block III satellites will increase the availability of two new, encrypted military-only signals that are currently only being transmitted from a select few satellites. The US Air Force has said they will be more powerful than previous signals, making them less susceptible to jamming from enemies and capable of penetrating deeper into urban canyons formed by skyscrapers

http://www.surveyequipment.com/news/article/us-nextgeneration-gps-block-iii-satellites-unveiled-180299.htmlUS next-generation GPS 'Block III' satellites unveiled

20/12/2011Jim Warner

NAVSTAR GPS/Block III Satellites

PAYLOAD CAPABILITIES

Types of Services Navigation

Downlink frequencies1572.42 MHz and 1227.6 MHz (L-Band)2227.5 MHz (S-Band

Technical Specifications

The GPS III architecture study, the first of a three-phase program, will conclude in late 2001. Boeing and Lockheed Martin were each awarded US$16 million contracts for the first phase. The U.S. Air Force plans to award two 26-month program definition and risk reduction contracts to begin hardware development, in 2002. One contractor will be selected in 2004 to complete development and build the satellites. The first of the new satellites is to be launched in 2009, with the entire constellation expected to remain operational through at least 2030. The USAF wants GPS III to deliver better anti-jam capability, by providing two new high-power spot beams for the military-code (M-code) signals to the L-1 and L-2 channels that service military users. Furthermore, it will have two other channels that provide navigation signals for civilian use in local, regional and national safety-of-life applications for improved position, navigation and timing knowledge. One of the new civil signals is expected to transmit higher power than the other two signals for improved reception worldwide.

http://www.spaceandtech.com/spacedata/constellations/navstar-gps-block3_conspecs.shtml

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• Orbit of satellites

– 6 different planes with a

minimum of 4 satellites in each

– 12 hr orbit

• height of orbit 20000 km

( space segment).

• Signals are in L-band (390 – 1550)MHz

• L1 carrier - 1575.42 MHz– Military - P code

– Civilian - CA code

– Navigation Message

• L2 carrier - 1227.6 MHz– Military only - P code

– Civilian - CA code (L2C)

• L5 carrier – (2009)– Additional civilian with SOL for aircraft

( space segment).

18

Signal Transmission

L5CARRIER 1176.45 MHz

L5 SIGNAL

Modified form (P. H. Dana, 1998)

CSRE, IIT Bombay

L1(1575.42 MHz)

C/A code (1.023MHz)

P-code10.23MHz

L2(1227.60 MHz)

No C/A code P-code10.23MHz

Fundamental Freq. 10.23 MHz

X 120

X 154

/10

Navigation message@ 50 bps

L5(1176.45 MHz)

l5 Q5X 115

36

• GPS transmits at two frequencies

– L1 1575.42 MHz (2x77x10.23 MHz)

– L2 1227.60 MHz (2x60x10.23MHz)

– Wavelengths L1 ~190 mm; L2 ~244 mm

• Codes:

– Course acquisition code (C/A) Chip rate (rate at which phase might change) 1.023 MHz

– Precise positioning code (P code) 10.23 MHz

– Y-code (Antispoofing code) also 10.23 MHz derived by multiplying P-code by ~20KHz code (highly classified)

( space segment).

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• Code lengths:

– C/A code is 1023 bits long

– P-code is 37 weeks long (2x1014 bits in code)

– Only one P-code, satellites use different weeks from same code (P-code repeats each week)

– As far as we know Y-code never repeats (again classified)

• Data message: Implemented by changing sign of code at rate of 50 bits/second (low data rate)

( space segment).

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• 10.23 MHz is fundamental frequency in GPS

• All radiofrequencies and codes generated from the same 10.23 MHz crystal whose long term stability is controlled by Cesium or Rubidium clock (older satellites)

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GPS signals

• The SVs transmit two microwave carrier signals.

• The L1 frequency (1575.42 MHz) carries the navigation message and the SPS code signals.

• The navigation message is a 50 Hz signal consisting of data bits that describe the GPS satellite orbits, clock corrections, and other system parameters.

• The L2 frequency (1227.60 MHz) is used to measure the ionospheric delay by suitably equipped receivers.

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GPS Signals

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GPS Satellite Constellation

� 6 orbits, each satellites takes 12 hours to go around the Earth once.

� At least 4 satellites in each orbit

� Orbits evenly spread and positioned around the Earth, so that we can receive signals from six of them nearly 100 percent of the time at any point on Earth

41contd

Space Segment

• Minimum of 24 satellites (some additional standby 7-8)

• Altitude of about 20,000km.

• Satellites transmit GPS message needed for positioning

• We need many signals to get the best position information.

• Satellites have clocks and batteries on board

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Control Segment

Control Segment

• Four monitor stations located around the world; 1) Hawaii and Kwajalein in the Pacific Ocean; 2) Diego Garcia in the Indian Ocean, 3) Ascension Island in the Atlantic Ocean, 4) Colorado Springs in Colorado

� The master control station at Schriever (Falcon) Air Force Base in Colorado Springs, Colorado..

� Four large ground antenna stations that broadcast signals to the satellites.

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Operational Control Segments (OCS)

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Ground stations send

orbital info to master station

Master sends corrected

orbital parameters to

GPS satellites

Corrected and exact position

(ephemeris data)

GPS Master Control and Monitoring Network

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International Terrestrial Reference Frame (ITRF)

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International Terrestrial Reference Frame (ITRF)

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16/03/2012

User/Receiver Segment

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Positioning by Pseudorange measurements

dtcRt +∆+= )(ρ

The pseudo-range(R) is given by;

2222)()()( WZVYUX

t −+−+−=ρ

The True range is given by;

2

1

2

1

2

1

2

11 )()()()( WZVYUXdtcR −+−+−=−∆−

2

2

2

2

2

2

2

22 )()()()( WZVYUXdtcR −+−+−=−∆−2

3

2

3

2

3

2

33 )()()()( WZVYUXdtcR −+−+−=−∆−2

4

2

4

2

4

2

44 )()()()( WZVYUXdtcR −+−+−=−∆−

•Total delay due to atmosphere is the contribution of Ionosphere and troposphere.

•After calculating the position the delays due to the atmospheric effects can be

measured by inverse process

CSRE, IIT Bombay

GPS Receivers

GPS receivers can be hand carried out or installed on aircraft, ships, tanks, submarines, cars and trucks.

27

GPS signals• The SVs transmit two microwave carrier signals.

• The L1 frequency (1575.42 MHz) carries the navigation message and the SPS (Standard Positioning Services) code signals.

• The navigation message is a 50 Hz signal consisting of data bits that describe the GPS satellite orbits, clock corrections, and other system parameters.

• The L2 frequency (1227.60 MHz) is used to measure the ionospheric delay by PPS (Precise Positioning Services) equipped receivers.

• The L5 frequency (1176.45 MHz) carries the navigation message and the SPS (Standard Positioning Services) code signals.

•53

L5, Safety of LifeCivilian, safety of life signal available with first GPS IIF launch (2010)

• Two PRN ranging codes are transmitted on L5: • the in-phase code (denoted as the I5-code); and the quadrature-

phase code (denoted as the Q5-code). • Both codes are 10,230 bits long and transmitted at 10.23 MHz (1ms

repetition). In addition, the I5 stream is modulated with a 10-bit Neuman-Hofman code that is clocked at 1 kHz and the Q5-code is modulated with a 20-bit Neuman-Hofman code that is also clocked at 1 kHz.

• Improves signal structure for enhanced performance• Higher transmitted power than L1/L2 signal (~3 db, or twice as powerful)• Wider bandwidth provides a 10× processing gain• Longer spreading codes (10× longer than C/A)• Uses the Aeronautical Radionavigation Services band• GPS IIR-M7 satellite transmits a demonstration of this signal

28

L5 Navigation messageThe L5 CNAV data includes SV ephemerides, system time, SV clock behavior data, status messages and time information, etc. The 50 bit/s data is coded in a rate 1/2 convolution coder. The resulting 100 symbols per second (sps) symbol stream is modulo-2 added to the I5-code only; the resultant bit-train is used to modulate the L5 in-phase (I5) carrier. This combined signal will be called the L5 Data signal. The L5 quadrature-phase (Q5) carrier has no data and will be called the L5 Pilot signal.

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GPS Signals

58

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GPS Receiver Block Diagram

59

GPS Unit is like a radio, receiving radio waves from GPS satellites

• GPS receivers can be – Land; handhelds, cars, tractors, Ocean; boats, bouys

– Spaced based; space shuttle, space station, Aircrafts, Guided Missiles, Unmanned Vehicles

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61

• SPS - Standard Positioning System

– for civilian use

– relies on C/A code on L1 signal

– Selective Availability can be used to degrade signal (off as of 5/1/2000)

• PPS - Precise Positioning System

– for military use

– relies on P code on L1 & L2 signals

– difference between P code on two frequencies increases accuracy

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• Basics:

– Signal, tagged with time from satellite clock, transmitted.

– About 60 msec (20,000 km) later the signal arrives at GPS receiver. Satellite has moved about 66 m during the time it takes signal to propagate to receiver.

– Time the signal is received is given by clock in receiver. Difference between transmit time and receive time is pseudorange.

– During the propagation, signal passes through the ionosphere (10-100 m of delay, phase advance), and neutral atmosphere (2.3-30 m depending on elevation angle).

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• To determine an accurate position from range data, we need to account for offsets caused by propagation effects.– (Will study ionospheric, atmospheric delays, and multipath effects near antenna)

• Basic clock treatment in GPS– True time of reception of signal needed– True time of transmission needed (af0, af1 from broadcast ephemeris data can be used for initial estimates)

– WGS84 referred position of satellite when signal was transmitted

• Components

–Antenna

–Receiver

–Display

–Firmware

– Input Graphic from

http://www.trimble.com/geoexplorer3.html

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65

• Components include antenna, receiver, input, datalogger, software & display

• antenna collects GPS radio signals• receiver trilaterates a position (4 sats = 3D) typically in latitude/longitude/altitude

• display shows info - sat position, data and current position

• Firmware - software that controls commands, setup, and menu structure

• Input – buttons to enter commands• memory stores position and possibly attribute data

Receivers

� How do they calculate a position?

� Signal from NAVSTAR satellites include:

� Binary timed code

� Almanac with position of satellite

� Accurate time

� With this information the receiver can

calculate the time the coded signals

takes to get from the satellite to receiver.

34

Positioning by Pseudorange measurements

dtcRt +∆+= )(ρ

The pseudo-range(R) is given by;

2222)()()( WZVYUX

t −+−+−=ρ

The True range is given by;

2

1

2

1

2

1

2

11 )()()()( WZVYUXdtcR −+−+−=−∆−

2

2

2

2

2

2

2

22 )()()()( WZVYUXdtcR −+−+−=−∆−2

3

2

3

2

3

2

33 )()()()( WZVYUXdtcR −+−+−=−∆−2

4

2

4

2

4

2

44 )()()()( WZVYUXdtcR −+−+−=−∆−

•Total delay due to atmosphere is the contribution of Ionosphere and troposphere.

•After calculating the position the delays due to the atmospheric effects can be

measured by inverse process

CSRE, IIT Bombay

35

TIME ESTIMATION

Knowing theTime

• Almanac tells the receiver exactly where each satellite is located in its orbit.

• Receiver acquires & locks into signal from each visible satellite

• From the Pseudo random Coded signal – receiver knows when signal left the satellite

• Difference in coded signal between time it left satellite and reached the unit is calculated precisely

• Exact time for signal to reach receiver can be calculated for each satellite in view

0.028376185 sec

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• Distance calculation depends on accurate timing

• Error of 1/1000 of a second = a positional error of about 300,000 m

• SVs contain atomic clocks, which are extremely accurate

• However, receivers do not contain clocks as accurate as SVs

• Receivers “calculate” correct time based on multiple signals . . .

72

• After the correct position is determined, the receiver’s clock is adjusted

• Adding or subtracting time will make the location more or less precise

• If the receiver’s clock is ahead, the position will be over-estimated for each signal

37

73

• If the receiver’s clock is behind, the position will be under-estimated for each signal

74

• If the receiver’s clock is correct, the position will be properly estimated for each signal

38

75

• The receiver adds and subtracts time from simultaneous equations until the only possible (correct) position is located.

• The receiver’s clock becomes virtually as accurate as the atomic clocks onboard the SVs

Trilateration of Pseudo Ranges

39

40

• If the distance from three satellites is known,

• the point of intersection between the three distances is the receiver’s location

79

80

R1= 20000 Km

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81

R1 = 20000 Km

With knowledge of ONE range distance: GPS receiver could be any where on the surface of Sphere with Satellite position as Centre and radius of range Distance

R1 = 20000 Km

82

With knowledge of TWO range distance: GPS receiver could be on the Circle of Intersection of Two range spheres

R1 = 20000 Km R2 = 20100 Km

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83

With knowledge of THIRD range distance: GPS receiver could be on the Intersection of this third Sphere with that of Circular intersection with TWO ranges, which will have Two probable points

R1 = 20000 Km R2 = 19900 Km

R3 = 20100 Km

GPS –Sources of Errors20/03/2012

• Satellite constellation Geometry at User Location ( Dilution of Precision)• Atmospheric effects

• Ionospheric• Tropospheric

• Operator Controlled Errors ( Selective Availability Pre 2000 period)• Multi-path• Receiver Hardware malfunction• User Blunders

•

43

Dilution of Precision

S1S2

Most Preferred : Two ( Four) Pseudo Ranges intersect at Right Angle

Error Zone

44

S1

Error Zone

Less Preferred : Two ( Four) Pseudo Ranges intersect at High Oblique Angle

User position in three dimensions (xu, yu, zu) and the offset tu,

where j ranges from 1 to 4 Satellites

45

These nonlinear equations can be solved for the unknowns by employing either

(1) closed-form solutions(2) iterative techniques based on linearization, or(3) Kalman filtering. (Kalman filtering provides a means for improving

Position Velocity and Time estimates based on optimal processing of time sequence measurements)

If we know approximately where the receiver is, then we can denote the offset of the true position (xu, yu, zu) from the approximate position (xu’, yu’, zu’)by a displacement (∆xu ∆yu ∆zu). By expanding the Pseudo range equation in a Taylor seriesabout the approximate position, we can obtain the position offset (∆xu, ∆yu, ∆zu) aslinear functions of the known coordinates and pseudorange measurements.

46

The DOP parameters are defined as geometry factors thatrelate parameters of the user position and time bias errors to those of the pseudorange errors

The offset ∆x in the user’s position and time bias relative to the linearization point is related to the offset in the error-free pseudorange values by the relation

The vector ∆x has four components.The first three are the position offset of the userfrom the linearization point; the fourth is the offset of the user time bias from the bias assumed in the linearization point.

is the vector offset of the error-free pseudorange values corresponding to the user’s actual position and the pseudorange values that correspond to the linearization point. H is the n × 4 matrix

47

ai = (axi, ayi, azi) are the unit vectors pointing from the linearization point tothe location of the ith satellite

If n = 4 and data from just four satellites are being used, and if the linearization point is close to the user’s location, the user’s location and time offset are obtained by solving

For ∆x as

(i.e., if the linearization point is close enough to the user position, iteration is not required).

where xT is the error-free position and time, xL is the position and time defined as the linearization point, and dx is the error in the position and time estimate

The matrix K is sometimes called the least-squares solution matrix,

48

The usual assumption is that the components of are identically distributed and independent and have a variance equal to the square of the satellite UERE.

User-equivalent range error (UERE),

Dilution of precision parameters in GPS are defined in terms of the ratio of combinations of the components of cov(dx) and σUERE.

The most general parameter is termed the geometric dilution of precision (GDOP) and is defined by the formula

A relationship for GDOP is obtained in terms of the components of (HT H)−1 by expressing (HT H)−1 in component form

49

Several other DOP parameters in common use are useful to characterize the accuracy of various components of the position/time solution. These are termed - position dilution of precision (PDOP), - horizontal dilution of precision (HDOP), - vertical dilution of precision (VDOP), - time dilution of precision (TDOP).

- These DOP parameters are defined in terms of the satellite UERE and elements of the covariance matrix for the position/time solution as follows:

The DOP values can be expressed in terms of the components of (HT H)−1 as follows:

50

99

Uses measurements from 4+ satellites

distance = travel time x speed of light

100

• The best spread of satellites makes the best trilateration

• We want low DOP

• Satellites that are close to each other result in higher DOP:

– HDOP: horizontal DOP

– VDOP: vertical DOP

– PDOP: positional DOP (combination of HDOP & VDOP)

– TDOP: time DOP

– GDOP: geometric DOP (combination of PDOP & TDOP)

51

101

• Wider spread gives better precision

102

• Light travels at 299,792,458 m/s only in a vacuum

• Ionospheric effects: ionizing radiation

• Tropospheric effects: water vapor

• Light is “bent” or reflected/refracted

52

103

Sources of Error

1. Atmospheric Interference

signal slows as it passes through atmosphere

Use model to correct

troposphere

ionosphere

104

• Receiver clock errors, mostly corrected by software in receiver

• Satellite clock errors

– Satellite time stamp errors

– Time stamp errors are not correctable

– SV timing & clocks are constantly monitored and corrected

53

105

• Power interrupts

• On-board microprocessor / Hardware failure

• Firmware

• Software

• Blunders (user error)

106

• Clock timing error factor introduced by the DOD

• Standard operation on the satellites.

• S/A changes the time stamp of the outgoing signals

• Calculated positions are erroneous

• SA causes locations to be in error up to 100 m

• Each satellite encrypts its own data separately

• Encryption keys shift frequently

• In the event of warfare, enemy forces cannot use the same accuracy as the US armed forces

• Military-grade have the ability to decrypt the time dithering, which lowers error to about 15 m from ~100 m uncorrected

54

107

• Natural & artificial features can intercept signals

• Mountains, valleys, hills, buildings, tree canopies, etc.

108

• Natural & artificial features can reflect signals

• Multiple “ghost” signals can confound timing

55

109

4. Ephemeris Error (Orbital errors)

inaccuracies in reported position of satellite

110

5. Satellite Configuration

The configuration of the satellites in view to a

receiver at any given time can affect the accuracy

of position determination. For instance, if all of the

visible satellites happen to be bunched close

together, the triangulated position will be less

accurate than if those same satellites were evenly

distributed around the visible sky.

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6. Selected Availability

Scrambling of signal for military use

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GPS ERROR MITIGATION (Improvement of Accuracy)

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• Place a GPS receiver (reference or base station) at a

known location. This base station receiver will calculate

receiver errors by comparing its actual location to the

location computed from the GPS signals. This error

information is sent to the rover receiver, which uses it

to correct the position information it computes from the

signals. Accuracies of DGPS systems can range from

15 feet to 3 feet depending on system configuration.

Differential GPS (Real Time)

Real Time

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• Place a GPS receiver (reference or base station) at a

known location and keep recording the data at this

location.

• Another compatible GPS receiver GPS collects data at

user defined location in Static or Kinemetic Mode.

• In post processing software, errors for known Base

location are computed and used for correcting rover

GPS locations. ( Limited to within 100 Kms of base

station)

Differential GPS (Post Processing)

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RTK Differential GPS in Action

1. Compares field data to data

collected at the same time at

a nearby base station

2. Error at base station known

and subtracted from field data

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Known base station location Unknown field locationsData corrected in office

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GPS Error Budget

Typical Error in Meters (per satellite)

Standard GPS Differential GPSSatellite clocks 1.5 0.0Orbital errors 2.5 0.0Ionosphere 5.0 0.4Troposhpere 0.5 0.2Receiver noise 0.3 0.3Multipath 0.6 0.6Selective availability* 30 0.0

Typical Position Accuracy

Horizontal 50 1.3Vertical 78 2.03-D 93 2.8

* No longer used

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Next Class

GPS error mitigation through Augmentation( Sourced from GNSS user meet ISAC 2012)

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