1 / 55
GPSGlobal Positioning System
Dr. Volkan NalbantoğluAE 484 Inertial Navigation Systems
May 2008
2 / 55
Contents
Radio Navigation GPS History Parts of GPS GPS Signals How Does GPS Work? GPS Error Sources
3 / 55
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)
4 / 55
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.
5 / 55
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.
6 / 55
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.
7 / 55
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
8 / 55
GPS History 1978-1985
Total of 11 block I Satellites sent
1989 first block II Satellite sent
9 / 55
Current Configuration
Nominally there are 24 satellites (4 on 6 orbital planes)
Currently there are 29 operational Block II/IIA/IIR/IIR-M satellites
10 / 55
GPS Segments
There are 3 segments Space Control User
11 / 55
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
12 / 55
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
13 / 55
GPS Control Segment
Monitors and Controls the GPS satellites.
One Master Control Station (MCS),Five Monitor Stations (MS)
14 / 55
GPS Control Segment
15 / 55
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
16 / 55
GPS User Segment
Consists of receivers that can decode the satellite signals
GPS receivers transform the satellite signals into position, velocity and time information.
17 / 55
GPS Services
GPS has two levels of information Precise Positioning Service - PPS
Standard Positioning Service - SPS
18 / 55
GPS Services – PPS
Precise Positioning Service (PPS) Can be used by authorized users only Planned for military purposes
19 / 55
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
20 / 55
GPS Services – PPS
16 m SEP (3D - %50) Position accuracy 100 ns (1 σ) timing accuracy
21 / 55
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
22 / 55
GPS Services – SPS
SA has been removed on May 2000 SPS users have accuracies close to PPS
23 / 55
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
24 / 55
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
25 / 55
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
26 / 55
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)
27 / 55
GPS Signals
28 / 55
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)
29 / 55
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
30 / 55
GPS Signals
50 Hz 6 s for one subframe 30 s for one frame 12,5 min for the whole set
31 / 55
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 ”
32 / 55
How Does GPS Work?
If the distance to one object is known: Then I am on a sphere with the object at the center
33 / 55
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
34 / 55
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
35 / 55
How Does GPS Work?
To find the distance to a satellite “Signal Time of Transmission” is used
How is Signal Time of Transmission calculated?
36 / 55
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.
37 / 55
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
38 / 55
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)
39 / 55
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
40 / 55
How Does GPS Work?
41 / 55
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
42 / 55
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
43 / 55
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)
44 / 55
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
45 / 55
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
46 / 55
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
47 / 55
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)
48 / 55
GPS Error Sources Satellites close to each other have larger uncertainty
49 / 55
GPS Error Sources Satellites far away from each other have less uncertainty
50 / 55
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
51 / 55
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
52 / 55
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.
53 / 55
Differential GPS - DGPS
DGPS Correction Signals
GPS Referance
Station
DGPS Transmitter GPS &DGPS Receiver
54 / 55
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.
55 / 55
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