1. Global Navigation Satellite Systems
Lecture 4.
Global Navigation Satellite Systems

2. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Accuracies / Error sources

3. Latitude and Longitude
History of Navigation
Navigation on the Ocean (must be independent from the continents)
Latitude and Longitude
j – Latitude
l – Longitude

4. History of Navigation Navigation on the Ocean
Speed and Bearing measurements to keep the course.
Sextant and Chronometer to determine the Latitude and Longitude and update the position

5. How do we determine the latitude?
History of Navigation
How do we determine the latitude? 90
j = 90 – a - b a j a b

6. How to determine the Longitude?
History of Navigation
How to determine the Longitude?
24h = 360o
We set the Chronometer on the Greenwich Meridian at noon to 0h.
We read the time at the local noon on the sea.
l = DZeit x 15o

7. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Accuracies / Error sources

8. History of GPS
After the 2nd World War it became important to create the global Navigation solution.
In the Space era the satellites could be used as „control points”.
Surveyors used various satellites equiped with reflectors as signals to link control networks (e.g. islands)
After 1960 the „US Navy Navigation Satellite System“ (NNSS) was created, after renamed to TRANSIT

9. History of GPS
TRANSIT contained 6 satellites in polar orbits with the elevation of ca km (period ca 107 Min).
The satellites were tracked from ground stations in US, and the orbital parameters were updated twice a day.
The satellites broadcasted the orbital parameters. The position could be computed from the observation of Doppler shifts with the accuracy of 1m.
Disadvantages
Good satellite constellation in every two hours only
Accurate position could be measured by long observations only.

10. History of GPS GPS (Global Positioning System) was developed to
determine 3D positions in real time.
determine accurate time
Speed
Bearing
NAVSTAR GPS (Navigation Satellite Time And Range) from 1973 as prototype
First GPS satellite was started on June 27, Orbit elevation ca km.
Today the term GNSS (Global Navigation Satellite System) is also used. Under this term, the NAVSTAR GPS, GLONASS and GALILEO is also meant.

11. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Accuracies / Error sources

12. GPS satellite concept
A minimum of 4 satellites must be tracked at the same time to determine position.
Basically 3 satellite could be enough, but we have to face some errors.
1 Satellite
2 Satellites

13. GPS satellite concept 3 Satellites Error-free solution

14. GPS satellite concept 24 Satellites planned
12-hour circular orbit in the elevation of km
55o inclination
4 satellites on each orbital plane (6 Orbital planes – rect ascebsion difference 60°)
At least 3 (now 8) reserve satellites

15. GPS satellite concept

16. GPS satellite concept GPS Carrier phases
L1 = 1575,42 Mhz (C/A Code, P-Code)
L2 = 1227,6 Mhz (P-Code)
C/A Kode – „coarse acquisiton code“ (low accuracy)
P Kode – „precision code“ (high accuracy)

17. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Accuracies / Error sources

18. GPS System Segments Three segments: space segment control segment
user segment

19. GPS System segments Space segment: 24+8 GPS Satellites
Orbits (20183 km, Inclination 55o and 60o between the orbital planes)
At least 4 Satellites on each orbital plane, where the angular difference is 120o
Period 12 hours
Each satellite has its own ID, which is boradcasted to the user.
The satellites are equiped with atomic clocks.

20. GPS System segments
Ground segment

21. GPS System segments Tasks of the ground segment:
Controlling and managing the telemetry and control stations.
Computation of ephemerids (orbit parameters) for each satellite.
Ordering satellite maneuvres.
Computing the data for the almanach
Determine the GPS time (Atomuhr)
Communication link to the satellites

22. GPS System segments User segment: GPS receivers
track L1 and/or L2 frequencies
track C/A code for at least 4 satellites, and demodulation
Time synchronization (Quartz clocks in the receivers)
Decrypt satellite data from the code observations (orbit, etc.)
receive P(Y) code (US Army)
Compute the pseudo-range to each satellite
Compute the time offset (receiver clock error)
Compute the position.

23. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Accuracies / Error sources

24. Principle of Positioning
Coordinate system (WGS-84)
The coordinates of satellites are given in this system.

25. Principle of Positioning
Equal time circles
2 Satellites
3 Satellites
p = cT

26. Principle of Positioning
Accuracies
Depends on the accuracy of distance measurements
Distance measurements – Travel time measurement
1ms (=) 300m (only atomic clocks could measure with this accuracy)
clock offset – a fourth satellite is also necessary for the determination of positions. (Receiver clock error)

27. Observation equations:
Principle of Positioning
Observation equations:
p1..p4 Pseudoranges
xp, yp, zp Coordinates of the receiver
xi, yi, zi Coordinates of the satellite i, i=1..4
Dp Offset due to the clock error
DT Receiver clock correction
ei additional error

28. Principle of Positioning
The navigation solution provides us a worlwide accurate time system.
By determining the receiver clock error, one can restore the GPS time using cheap quartz clocks.
Since the GPS time is an atomic time, we can substitute an atomic clock using a GPS receiver.

29. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Accuracies / Error sources
Differential GPS (DGPS)
Applications in Surveying

30. GPS codes and their travel time
Two frequencies: L1=1575,42 Mhz and L2=1227,60 Mhz
Both of them are a multiple of the ground freqency: L0=10,23 Mhz
The carrier phases are with PRN-codes („pseudo random noise“) modulated (L1 – C/A u. P, L2 – P).
All codes are biploar codes:
Positive Amplitude=0
Neg. Alplitude=1

31. GPS codes and their travel time
What is a PRN code?
It is a statistical distribution of impulses, which are similar to noise.
In reality the sequence of the impulses follow a complicated rule, which is necessary for the decryption. The receiver knows this algorithm.
If one can determine the time delay with the accuracy of 1%:
C/A Code accuracy of 3 m chiprate 1ms=300m
P Code accuracy of 0,3 m chiprate 0,1ms = 30m

32. GPS codes and their travel time
GPS Signal modulation:
The C/A code contains 1023 positive and negative Impulses (bits) with the span of 1 ms each. The whole sequence has the length of 300km (corresponds to 1ms).
A navigation message is also modulated to the carrier freqency with the frequency of 50bit/sec. The length of the message is 1500 bits (30 sec)
These 1500 Bits are split into 5 sub-frames with 10 words of 30 bits in each subframe. Each subframe is started with two special words:
„Telemetry Word“ (TLM) = Orbit corrections
„Hand Over Word“ (HOW) = GPS time

33. GPS codes and their travel time
Clock corrections are present in the first subframe.
In the second and third the orbit parameters and iono corrections are broadcasted.

34. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Phase observations
Accuracies / Error sources

35. Phase observations
It could be seen that the code observation is too inaccurate for the applications in surveying;
A more accurate method is needed for the determination of the satellite-receiver distance.
Instead of using the codes, the carrier phases are measured;
Since the wavelength of the L1 carrier signal is approx. 19cm, a more accurate distance observation can be achieved (in the order of a few mm)

36. Phase observations

37. Contents Navigation History of GPS GPS Satellite Concept
GPS System Segments
Principle of Positioning
GPS codes and the determination of travel time
Phase observations
Accuracies / Error sources

38. Error sources

39. Accuracy and error sources
Error sources – signal propagation
The atmosphere has an impact on the signal propagation path.
Troposphere and Ionosphere
Ionosphere
The Ionosphere ( km elevation) contain electrons and ions, which have an effect on the propagation of electromagnetic signals.
the delays depend on the frequency, intensity of the radiation of the sun (day-night variation, seasonal variation, effect of the solar activity - sunspots);

40. Accuracy and error sources
Troposphere
Up to km (tropospheric refraction)
Meteorological factors (weather, air pressure, temperature, etc.)
Empirical models
overall effect is ca. 2.3m in the vertical direction
Multipath
GPS signals are reflected, and direct and indirect signals are also received.
Indirect
Direct

41. Accuracy and error sources
Cycle slips
The continuous signal reception is broken;
Thus the counting of the number of full cycles is erroneous (nl)
Solution: avoid nearby objects that could obscure the satellites

42. Accuracy and error sources
Error sources – receiver error
Thermal noise
receiver clock corrections
antenna phase center offsets and variations

43. Accuracy and error sources
Error sources – satellite geometry
Not all of the satellite constellation enables the optimal positioning.
DOP – „Dilution of Precision“
dr accuracy of the pseudorange observation
dPOS accuracy of the positioning
PDOP is the reciprocal value of the volume V of a tetraeder of 4 satellites + 1 ground station.

44. Accuracy and error sources
Good
Bad