What is GPS
The Global Positioning System (GPS) is a
Constellation of Earth-Orbiting Satellites
Maintained by the United States Government for
the Purpose of Defining Geographic Positions On
and Above the Surface of the Earth.
Slide 1
Instantaneous positioning with GPS
Accuracy of
+/- 10 m error (horizontal)
+/- 15 m error (vertical)
Your location is:
37o 23.323’ N
122o 02.162’ W
Range = Distance between the satlllite and the rceiver
Xll
Vl
Range
Xll
Vl
Range
Xll
Vl
Range = Time Taken x Speed of Light
Point position
Cartesian Coordinates (x,y,z)
Z
Greenwich
Meridian
y • x
z
O Y
X
Equator
Prof. Adel El-shazly
Surveying Introduction
CVE125 – Fall 2007
Position
R1
We are somewhere on a sphere of
radius, R1
Position
R1
R2
2 Spheres intersect as a circle
Position
R1
R3
R2
3 Spheres intersect at a point
3 Ranges to resolve for ground point coordinates
X, Y ,Z
Position
• The satellites are like “Orbiting Control Stations”
• Ranges (distances) are measured to each satellite using time
dependent codes
• Typically GPS receivers use inexpensive clocks. They are much
less accurate than the clocks on board the satellites
• A radio wave travels at the speed of light
• (Distance = Velocity x Time)
– Consider an error in the receiver clock
• 1/10 second error = 30,000 Km error
• 1/1,000,000 second error = 300 m error
• To eliminate the receiver clock error a forth satellite is used
Point Positioning
4 Ranges to resolve for (X, Y ,Z) & Time
It is similar in principle to a resection problem
Three Segments of the GPS
Space Segment
User Segment
Control Segment
Ground
Antennas
Master Station Monitor Stations
Space Segment
• 24 satellites
– 6 planes with 55° Inclination • Very high orbit
– Each plane has 4 or 5 satellites – 20,200 km
– Constellation has Spares – 1 revolution in
approximately 12 hrs
– Coverage (at least four
satellites are available
worldwide
Slide 13
Control Segment
Monitor and Control
Colorado
Springs
Ascension Kwajalein
Hawaii
Islands
Diego
Master Control Station Garcia
Monitor Station
Ground Upload station
Control Segment
Satellite
• Observe
Satellites • Create new
Satellite message
Upload Stations
Monitor Stations Master control station
User Segment
Receivers are used in civil and military
applications.
Receivers types:
Hand held receivers:
- Code measurements
- accuracy 2 - 10m
Geodetic receivers
- Carrier phase measurements
- accuracy 2 - 10mm
How the system works
Space Segment
24+ Satellites
The Current
Ephemeris is
Transmitted to
Monitor Stations Users
• Diego Garcia
• Ascension Island
• Kwajalein
• Hawaii
• Colorado Springs
End
GPS Control User
Colorado Springs
.
GPS Signal Structure
• Each GPS satellite transmits a number of signals
• The signal comprises two carrier waves (L1 and L2) and two codes (C/A
on L1 and P or Y on both L1 and L2) as well as a satellite orbit message
Fundamental
Frequency
10.23 MHz ÷ 10
L1 C/A Code P (Y)-Code
x 154 1575.42 MHz 1.023 MHz 10.23 MHz
x 120
L2 P (Y)-Code
1227.60 MHz 10.23 MHz
50 BPS Satellite Message (Almanac & Ephemeris)
GPS Signal structure
• Carrier waves: (to carry codes and satellite message)
– L 1 : f=1575.43 MHz, ( =19 cm )
– L 2 : f=1227.60 MHz, ( =24 cm)
• Codes: (to measure the waves travelling time (T) )
– C/A-code (Clear Access / Coarse Acquisition): 1.023 MHz ( =300 m)
– P-code (Protected / Precise): 10.23 MHz ( = 30 m )
• Satellite Message: (to determine satellite position )
– ( satellite coordinates X, Y, Z )
Signal Structure
L1 , L2 Carrier Waves
C/A Code
Satellite Message
P - Code
.
Range Determination from Code Observations
• Pseudoranges (Code)
– Each satellite sends a unique Received Code
signal which repeats itself approx. from Satellite
1 msec
– Receiver compares self generated
signal with received signal Generated
Code from
– From the time difference (T) a Receiver
range observation can be
determined
– Receiver clock needs to be T
synchronized with the satellite
clock
ACCURACY = (1/100) (λ)
P = C (T)
Observations Equations
Using Code measurements:
– Pseudorange measurements by measured time
difference (Trs) of the received satellite and receiver
replica codes
Prs = C (Trs) = Rrs + C (∆tr)
Where: C is the speed of light; Prs is the receiver to
satellite measured distance; R is the true distance,
is the wavelength , ∆ tr is the receiver clock error .
Pseudoranges to Four Satellites
Positioning
• Solution of range equations for 4 unknowns,
receiver x, y, z, Δt
P1 = ( (x1 - x)2 + (y1 - y)2 + (z1 - z)2 )1/2 + c Δt
P2 = ( (x2 - x)2 + (y2 - y)2 + (z2 - z)2 )1/2 + c Δt
P3 = ( (x3 - x)2 + (y3 - y)2 + (z3 - z)2 )1/2 + c Δt
P4 = ( (x4 - x)2 + (y4 - y)2 + (z4 - z)2 )1/2 + c Δt
Linearize problem by using a reference, or a
priori, position for the receiver
