ee 570: location and navigation: theory & practiceelosery/spring_2013/ee570/lectures/gps.pdf ·...

EE 570: Location and Navigation: Theory & Practice

The Global Positioning System (GPS)

Thursday 11 April 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 1 of 23

The Global Positioning System (GPS) Dead Reckoning vs Position Fixing

Thursday 11 April 2013 NMT EE 570: Location and Navigation: Theory & Practice

• Navigation can be accomplished via “position fixing” or “dead reckoning”

Dead Reckoning - Measures changes in position and/or attitude

o Inertial sensors provide relative position (and attitude)

Position Fixing - Directly measuring location

o GPS provides absolute position (and velocity)

• How does GPS work?

Effectively via Multilateration

o If I can measure my distance to three (or more) satellites at known locations, then, own location can be resolved

– Measure distance via “time-of-flight” (speed of light)

Slide 2 of 23

The Global Positioning System (GPS) An Overview


• The GPS is a Space-Based Global Navigation Satellite System (GNSS)

1. Space segment (satellites)

o First satellites launched in 1989

2. Control segment (ground station(s))

o Master control segment, alternate, and monitors

3. User segment (receivers)

o Both military and civilian

• Other GPS-like systems exist

GLONASS – Russian

COMPASS/BeiDou – China

Galileo - European Union (EU)

wikipedia

Slide 3 of 23

The Global Positioning System (GPS) Overview – The Space Segment


• The Space Segment

A constellation of 24 satellites in 6 orbital planes

Four satellites in each plane

20,200 km altitude at 55 inclination

o Each satellite’s orbital period is ~12 hours

o >6 satellites visible in each hemisphere

Courtesy of MATLAB Slide 4 of 23

The Global Positioning System (GPS) Overview – The Control segment


• The Control segment

Tracking stations around the world

o 1 Master control station

– Command & Control

o 1 Alternate control station

– Backup

o 16 Monitor stations

– Orbit monitoring

o 4 dedicated ground antenna

– Communication

gps.gov

Slide 5 of 23

The Global Positioning System (GPS) Overview – The User Segment


• The User Segment

Military receivers can receive encrypted GPS signals to realize higher performance

– E.g. Selectively Available Anti-Spoofing Module (SAASM ) and Precise Positioning System (PPS) encrypted key based systems

Civilian receivers

o Commercial handheld

– e.g. Gamrin Montana 650

o OEM chipsets

– ublox

» Multi-GNSS engine for GPS, GLONASS, Galileo and QZSS

– Vectornav

» VN-200 OEM GPS-Aided Inertial Navigation System

NavAssure® 100

Slide 6 of 23

The Global Positioning System (GPS) Multilateration - Intersection of Spheres


1 satellite – A sphere 3 satellites – Two points

Slide 7 of 23

The Global Positioning System (GPS) Multilateration - Intersection of Spheres


• Only one of the two points will be feasible

E.g. on the surface of the Earth

Slide 8 of 23

The Global Positioning System (GPS) Multilateration – Basic Idea


• Multilateration – The Basic Idea

Determine range to a given satellite via time-of-flight of an RF signal (i.e. speed of light)

Requires very precise time bases

o Receiver clock bias

Slide 9 of 23

The Global Positioning System (GPS) Modulation Scheme


• Position is determined by the travel time of a signal from four or more satellites to the receiving antenna

Three satellites for X, Y, Z position, one satellite to solve for clock biases in the receiver

Image Source: NASA

Transmission Time

Receiver

Time delay

Satellite

Slide 10 of 23



• The GPS employs quadrature Binary Phase Shift Keying (BPSK) modulation at two frequencies (CDMA)

L1 = 1,575.42 MHz

o 1 = 19 cm

L2 = 1,227.6 MHz

o 1 = 24 cm

• Two main PRN codes

C/A: Course acquisition

o 10-bit 1 MHz

P: Precise

o 40 bit 10 MHz

o Encrypted P(Y) code

Slide 11 of 23



• Quadrature BPSK modulation

Ref: JNC 2010 GPS 101 Short Course by Jacob Campbell

Slide 12 of 23

The Global Positioning System (GPS) Signal Processing


• Code and Carrier Phase Processing

Code used to determine user’s gross position

Carrier phase difference can be used to gain more accurate position

o Timing of signals must be known to within one carrier cycle

Slide 13 of 23

The Global Positioning System (GPS) Pseudorange


Sat3

(x3,y3,z3)

GPS receiver

(x,y,z)

All measurements in ECEF coordinates

2 2 2

i i i ix x y y z z

2 2 2 2 2

2 2

2

2 2

i i i i

i i i

x x x x y y

y y z z z z

2 2 2 2 2 2 2 2 2 2i i i i i i ix y z x y z x x y y z z

2 2 2 2

1 1 1 11 1 1

2 2 2 2

2 2 2 2 2 2 2

2 2 2 2

2 2 2

2 2 2

2 2 2

e

e

n n nn n n n e

x y z r x y zx

x y z r x y zy

zx y zx y z r

- pseudorange re - Earth’s radius

Slide 14 of 23

The Global Positioning System (GPS) Pseudorange


• A more realistic model is

• Can perturb this model to form

• This can be solved via least-squares or Kalman filter

2 2 2

i i i i ix x y y z z c T n

1

2

1

1

1n

x

yn

z

c t

Slide 15 of 23

The Global Positioning System (GPS) Sources Of Error - GDOP


• Geometry of satellite constellation wrt to receiver

• Good GDOP occurs when Satellites just above the horizon

spaced and one satellite directly overhead

• Bad GDOP when pseodurange vectors are almost linearly dependent

Slide 16 of 23

The Global Positioning System (GPS) Other Sources Of Error


• Selective Availability Intentional errors in PRN Discontinued in 5/1/2000

• Atmospheric Effects Ionospheric Tropospheric

• Multipath • Ephemeris Error (satellite position data) • Satellite Clock Error • Receiver Clock Error

Slide 17 of 23

The Global Positioning System (GPS) Error Mitigation Techniques


• Carriers at L1 = 1,575.42 MHz & L2 = 1,227.6 MHz Ionospheric error is frequency dependent so using two

frequencies helps to limit error

• Differential GPS Post-Process user measurements using measured error

values

• Space Based Augmentation Systems(SBAS) Examples are U.S. Wide Area Augmentation System (WAAS),

European Geostationary Navigational Overlay Service (EGNOS)

SBAS provides atmospheric, ephemeris and satellite clock error correction values in real time

Slide 18 of 23

The Global Positioning System (GPS) Error Mitigation Techniques – Differential GPS


• Uses a GPS receiver at a fixed, surveyed location to measure error in pseudorange signals from satellites

Pseudorange error for each satellite is subtracted from mobile receiver before calculating position (typically post processed)

Slide 19 of 23

The Global Positioning System (GPS) Error Mitigation Techniques - WAAS/EGNOS


• Provide corrections based on user position

• Assumes atmospheric error is locally correlated

Slide 20 of 23

The Global Positioning System (GPS) Summary of the Sources of Error


• Single satellite pseudorange measurement

• GPS error summary

SPS: L1 C/A with S/A off

PPS: Dual frequency P/Y code

Ref: Navigation System Design by Eduardo Nebot, Centre of Excellence for Autonomous Systems, The University of Sydney

Slide 21 of 23

measured true ionospheric tropospheric ephemeris satelite clock receiver clock multipath

Table 1. GPS Error sources: SPS vs PPS

ERROR

SOURCE

DETERMINISTIC RANDOM TOTAL (RMSE) DGPS

SPS PPS SPS PPS SPS PPS SPS PPS

Ephemeris 2.1 2.1 0.0 0.0 2.1 2.1 0.0 0.0

Satellite Clock 2.0 2.0 0.7 0.7 2.1 2.1 0.0 0.0

Ionosphere 4.0 1.0 0.5 0.5 4.0 1.2 0.4 0.1

Troposphere 0.5 1.0 0.5 1.0 0.7 1.4 0.2 1.4

Multipath 1.0 1.0 1.0 1.0 1.4 1.4 1.4 1.4

UERE 5.1 3.3 1.4 1.5 5.3 3.6 1.6 1.5

Vertical 1 12.8 8.6 3.9 3.7

Horizontal 1 10.2 6.6 3.1 3.0

II/IIA IIR IIR‐M IIF III (A,B,C)

Number SV’s 28 13 8 12 30*

First Launch 1989 1997 2005 2010* 2014*

Satellite Weight

(Kg)

900 1,100 1,100 844 TBD

Power (W) 1,100 1,700 1,700 NA TBD

Design Life

(Years)

7.5 10 10 15* TBD

Unit Cost ($M) 43 30 30 39* TBD

In Use (2010) 11 12 7 0 0


Number SV’s 28 13 8 12 30*

First Launch 1989 1997 2005 2010* 2014*

Satellite Weight

(Kg)

900 1,100 1,100 844 TBD

Power (W) 1,100 1,700 1,700 NA TBD

Design Life

(Years)

7.5 10 10 15* TBD

Unit Cost ($M) 43 30 30 39* TBD

In Use (2010) 11 12 7 0 0


Number SV’s 28 13 8 12 30*

First Launch 1989 1997 2005 2010* 2014*

Satellite Weight

(Kg)

900 1,100 1,100 844 TBD

Power (W) 1,100 1,700 1,700 NA TBD

Design Life

(Years)

7.5 10 10 15* TBD

Unit Cost ($M) 43 30 30 39* TBD

In Use (2010) 11 12 7 0 0


Number SV’s 28 13 8 12 30*

First Launch 1989 1997 2005 2010* 2014*

Satellite Weight

(Kg)

900 1,100 1,100 844 TBD

Power (W) 1,100 1,700 1,700 NA TBD

Design Life

(Years)

7.5 10 10 15* TBD

Unit Cost ($M) 43 30 30 39* TBD

In Use (2010) 11 12 7 0 0

The Global Positioning System (GPS) The Future of GPS


• The Future of GPS


Number SV’s 28 13 8 12 30*

First Launch 1989 1997 2005 2010* 2014*

Satellite Weight

(Kg)

900 1,100 1,100 844 TBD

Power (W) 1,100 1,700 1,700 NA TBD

Design Life

(Years)

7.5 10 10 15* TBD

Unit Cost ($M) 43 30 30 39* TBD

In Use (2010) 11 12 7 0 0

Slide 22 of 23

The Global Positioning System (GPS) The Future of GPS

Thursday 11 April 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 23 of 23

ee 570: location and navigation: theory & practiceelosery/spring_2013/ee570/lectures/gps.pdf ·...

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