ee 495 modern navigation systems the global positioning system (gps) friday, april 03 ee 495 modern...

EE 495 Modern Navigation Systems

The Global Positioning System (GPS)

Friday, April 03 EE 495 Modern Navigation Systems Slide 1 of 24

http://www.erau.edu/

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

Friday, April 03 EE 495 Modern Navigation Systems

• Navigation can be accomplished via “position fixing” or “dead reckoning” Dead Reckoning - Measures changes in position and/or

attitudeo Inertial sensors provide relative position (and attitude)

Position Fixing - Directly measuring locationo 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 24


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 19892. 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 (GNSS) exist GLONASS – Russian COMPASS/BeiDou – China Galileo - European Union (EU)

wikipedia

Slide 3 of 24


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

inclinationo Each satellite’s orbital

period is ~12 hourso >6 satellites visible in each

hemisphere

Courtesy of MATLAB

GEO is 35,786 km (22,236 mi)

Slide 4 of 24


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


• The Control segment Tracking stations around

the worldo 1 Master control station

– Command & Controlo 1 Alternate control station

– Backupo 16 Monitor stations

– Orbit monitoringo 4 dedicated ground antenna

– Communication

gps.gov

Slide 5 of 24


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 24

http://www.u-blox.com/

http://www.vectornav.com/


The Global Positioning System (GPS)Multilateration - Intersection of Spheres - 2D Case


R 1




1 satellite – A sphere2 s

atell

ites –

A ci

rcle

3 satellites – Two points

Slide 8 of 24




• Only one of the two points will be feasible E.g. on the surface of the Earth

3 satellites – Two points

Slide 9 of 24


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 baseso Receiver clock bias

Slide 10 of 24


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 11 of 24




• 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 2 = 24 cm

• Two main PRN codes C/A: Course acquisition

o 10-bit 1 MHz P: Precise

o 40 bit 10 MHzo Encrypted P(Y) code

Slide 12 of 24




• Quadrature BPSK modulation

Ref: JNC 2010 GPS 101 Short Course by Jacob Campbell

Slide 13 of 24


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

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

Slide 14 of 24


The Global Positioning System (GPS)Pseudorange


1 23

n

Sat 1

(x 1,y 1,z 1

)

Sat2(x

2 ,y2 ,z2 )

Sat3

(x3,y3,z3)

Sat n

(x n,y n,z n)

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 21 1 1 1

1 1 12 2 2 2 22 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

..

.

- pseudorangere - Earth’s radius

Slide 15 of 24


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 16 of 24


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 almostlinearly dependent

Slide 17 of 24


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 18 of 24


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 19 of 24


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 20 of 24


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


• Provide corrections based on user position• Assumes

atmosphericerror is locally correlated

Slide 21 of 24


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

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

Slide 22 of 24


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*


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*


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*


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*


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 23 of 24


The Global Positioning System (GPS)The Future of GPS



ee 495 modern navigation systems the global positioning system (gps) friday, april 03 ee 495 modern...

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