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GPSGlobal Positioning System

Dr. Volkan NalbantoğluAE 484 Inertial Navigation Systems

May 2008

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Contents

Radio Navigation GPS History Parts of GPS GPS Signals How Does GPS Work? GPS Error Sources

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Radio Navigation Systems

Radio navigation consists of finding position and heading by using electromagnetic wave propogation.

Examples: Radar VHF Omnidirectional Range (VOR,

VOR/DME) Long Range Navigation (LORAN-C) Global Positioning System (GPS)

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What is GPS ?

GPS is a satellite based navigation system.

It is developed and financed by the U.S. Department of Defense.

It provides position velocity and timing information anywhere in the world under any weather condition.

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Initially it was developed as a military system (1970s)

In 1980s it became available for civilian use.

Today it is being used in land, air and marine applications by millions of people.

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GPS History

First radio navigation research started in 1920s

During the 2nd World War LORAN became operational and it was possible to find latitude and longitude by using the time of arrival information of the radio signals sent from ground stations.

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GPS History

During 1959-1964: USA developed the TRANSIT satellite system to determine the location of nuclear submarines. 7 low orbit sattelites Latitude-Longitude information Long measurement time Only for slow dynamic vehicles

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GPS History 1978-1985

Total of 11 block I Satellites sent

1989 first block II Satellite sent

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Current Configuration

Nominally there are 24 satellites (4 on 6 orbital planes)

Currently there are 29 operational Block II/IIA/IIR/IIR-M satellites

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GPS Segments

There are 3 segments Space Control User

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GPS Space Segment Consitsts of the space

vehicles (satellites) and the radio signals sent by these satellites.

GPS satellites Height ~20200 km 6 orbits with at least 4

satellites on each orbit Period ~ 1 revolution / 12

hour Weight ~950 kg Size 1,6 x 6 m

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GPS Space Segment

At least 5 satellites are visible from anywhere on the earth

There are solar panels and 12 navigation antennas on each satellite.

Block II/IIA

Block IIR ve IIR-M

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GPS Control Segment

Monitors and Controls the GPS satellites.

One Master Control Station (MCS),Five Monitor Stations (MS)

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GPS Control Segment

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GPS Control Segment

Functions of the Control Segment Detection and determination of Satellite orbits Correction of satellite clocks Updating the satellite messages Monitoring the status of each satellite and

performing the maintanence tasks

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GPS User Segment

Consists of receivers that can decode the satellite signals

GPS receivers transform the satellite signals into position, velocity and time information.

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GPS Services

GPS has two levels of information Precise Positioning Service - PPS

Standard Positioning Service - SPS

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GPS Services – PPS

Precise Positioning Service (PPS) Can be used by authorized users only Planned for military purposes

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GPS Services – PPS

Access to PPS is controlled by two methods SA (Selective Availability), GPS accuracy is

degraded intentionally by adding pseudo-random errors on the signals.

A-S (Anti-Spoofing), Encrypted code

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GPS Services – PPS

16 m SEP (3D - %50) Position accuracy 100 ns (1 σ) timing accuracy

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GPS Services – SPS

Standard Positioning Service (SPS) Open to all users but less accurate With Selective Availability

100 m SEP (3D - %50) position accuracy 337 ns (1 σ) time accuracy

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GPS Services – SPS

SA has been removed on May 2000 SPS users have accuracies close to PPS

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GPS Signals

GPS satellites send very weak radio signals on two L – band frequencies (L1 and L2)

L1 and L2 are carrier frequencies.

These are sinusoidal signals

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GPS Signals

All GPS satellites use the same frequency carriers (L1 and L2)

But each satellite has its own identification code

These are two types of codes modulating the L1 and L2 carriers. C/A – Code P – Code

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L2

P(Y)P(Y)

L1C/AC/A

P(Y)P(Y)

GPS Signals L1: 1575.42 MHz

Modulated byC/A-code & P-code Signal Power: -160 dBW

L2: 1227.6 MHz Modulated by P-code only Signal Power : -166 dBW

1227 MHz

1575 MHz

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GPS Signals

Carriers (L1/L2)

Bipolar Phase Shift Keying (BPSK) Modulation

C/A - Code (L1)

P - Code (L1/L2)

Phase Quadrature O

SA Degredation

Nav Data (L1/L2)

A-S Encryption P – P(Y)

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GPS Signals

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GPS Signals

GPS receivers generate the equivalent of these codes internally and compares with the ones coming from the satellites.

GPS receiver shifts the internally generated code until it matches with the received one (cross-correlation)

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GPS Signals Another Message on the L1 ve L2 carrier

frequency is the “Navigation Message” Navigation Message

50 Hz Clock rate Has information specific for each satellite Has the satellite position and time delay information

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GPS Signals

50 Hz 6 s for one subframe 30 s for one frame 12,5 min for the whole set

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How Does GPS Work?

Based on a geometric principle“Position of a point can be calculated if the distances between this point and three objects with known positions can be measured ”

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How Does GPS Work?

If the distance to one object is known: Then I am on a sphere with the object at the center

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How Does GPS Work?

If I know the distance to a second object: Then I am on a circle which is the intersection of two

spheres

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How Does GPS Work?

If I know the distance to a thrid object: Then I am on one of the two points which are at the

intersection of three spheres

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How Does GPS Work?

To find the distance to a satellite “Signal Time of Transmission” is used

How is Signal Time of Transmission calculated?

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How Does GPS Work?

Satellite

Receiver

GPS receiver generates the same signal that is coming from the satellite (C/A - Code) starting at the same time.

But the code coming from the satellite is delayed because it travels the distance between the satellite and the receiver.

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How Does GPS Work?

GPS receiver shifts the internally generated code until it matches with the received one and finds ΔT, Signal Time of Transmission

Code generatede by the receiver

T

Code generatede by the sattelite

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How Does GPS Work?

Signal Time of Transmission is actually an indication of the distance between the receiver and the satellite

Signal travels with the speed of light and in Δt time travels a distance of

Pr= C. ΔT (C = Speed of light)

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How Does GPS Work?

Pr is the “Pseudo-Range” It is called Pseudo-Range because it is not

the real range between the receiver and the satellite due to uncertainties such as: Synchronisation error between the receiver

and satellite clocks Change in the medium in which the signal

travels

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How Does GPS Work?

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How Does GPS Work?

The dominant source of error in Pseudo-Range calculation is the synchronisation between the receiver and the satellite

Satellites have very accurate and very expensive atomic clocks

It is not practical to use atomic clocks in the receivers. Standard crystal oscillators are used instead

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How Does GPS Work?

This syncrhronisation error is called Clock Bias

To eliminate clock bias a forth satellite is used 4 unknowns (3 dimensional position + Clock

Bias) 4 equations

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How Does GPS Work?

bZZYYXXP

bZZYYXXP

bZZYYXXP

bZZYYXXP

24

24

244

23

23

233

22

22

222

21

21

211

)()()(

)()()(

)()()(

)()()(

Pi = Pseudo-Range to satellites

Xi , Yi , Zi = 3 Dimensional satellite cartesian coordinates

X , Y , Z = 3 Dimensional satellite cartesian coordinates

b = Receiver clock bias (in terms of distance)

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How Does GPS Work?

These 4 non-linear equations are solved and receiver coordinates and clock bisa are obtained

These equations are in ECEF (Cartesian) Coordinates

Latitiude, Longitude and hight values can be obtained by a transformation

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How Does GPS Work?

ECEF and Latitude / Longitude

X

Y

Px

Py

Pz

R

h

Z

GREENWICH Meridian

Px: ECEF Pos x (M) Py: ECEF Pos y (M) Pz: ECEF Pos z (M)

O

Equator

LOCAL Meridian User position

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GPS Error Sources

SA (Selective Availability) Satellite clock errors Satellite orbit errors Atmospheric effects Receiver noise Multipath Number of satellites in range Satellite geometric

configuration

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GPS Error Sources

DOP (Dilution of Precision) GDOP - Geometric DOP It is a metric to define the effect of the satellite

geometry on the accuracy of the solution: PDOP – Position DOP (3 D Position) HDOP – Horizontal DOP (Horizontal position) TDOP – Time DOP (Time)

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GPS Error Sources Satellites close to each other have larger uncertainty

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GPS Error Sources Satellites far away from each other have less uncertainty

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GPS Error Sources

1 signifies the ideal situation

Satellites grouped on the same side cause larger DOP – Bad accuracy

Well distributed, smaller DOP – better accuracy

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GPS Error SourcesGPS Pseudo-Range Error Budget

Segment Error SourceError contribution (m, %95)

P-Code C/A-Code

Space

Frequency stability 6.5 6.5

D-Band Delay 1.0 1.0

Satellite acceleration uncertainty 2.0 2.0

Other 1.0 1.0

ControlEphemeris Estimation 8.2 8.2

Other 1.8 1.8

User

Ionospheric Delay compensation 4.5 9.8 – 19.6

Troposphere Delay compensation 3.9 3.9

Receiver noise 2.9 2.9

Multipath 2.4 2.4

Other 1.0 1.0

Total System Error (m, %95) 13.0 15.7 - 23.1

Reference: Navstar GPS User Equipment Introduction

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Differential GPS - DGPS

Used for applications where GPS accuracy is not enough

In a typical DGPS application There is a reference receiver (base receiver) at an

exactly known location And there are other receivers (rover receivers) that

can receive the correction signals sent by the base receiver.

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Differential GPS - DGPS

DGPS Correction Signals

GPS Referance

Station

DGPS Transmitter GPS &DGPS Receiver

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Differential GPS - DGPS Since the exact location of the reference station

is known it can calculate the distances to satellites accurately

It compares these distances with its own solutions as a GPS

Calculates corrections from these measurements

Sends these corrections to the rover receivers from a different frequency than the GPS frequencies.

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Differential GPS - DGPS

Transmission is usually over a FM channel The rover receivers are able to receive

these corrections and they use them to correct their solutions

Corrections are valid within a certain range Referance and rover receivers must have

the same satellites in view