1. 1 GPS processing. Sat05_82.ppt, 2005-12-05. 1.Directly from the observations 2.From differences (especially if vectors between points are to be determined) (1)Is flexible, no requirements about same satellites or sam epoch (2)Can only be used for shorter distances

2. 2 GPS Integer-ambguities, Sat05_82.ppt, 2005-12-05. One more frequency will help (is comming) Methods: Geometric Combination of measurements Search in integer space Combined (1) N fixed at beginning, and is kept fixed. Waves are counted. 1.-differences used to eliminate N (2) Regarded as integer: 2521.08 -> 2521.00 Closest integer used

3. 3 Search in integer space. Sat05_82.ppt, 2005-12-05..Software will tell how much better chosen solution is compared to next-best.

4. 4 Cycle-slips. Sat05_82.ppt, 2005-12-05. Due to: Obstructions Large ionospheric activity Multipath Low height angle Interference Sloping antenna Errors in processing

5. 5 Cycle-slips. Sat05_82.ppt, 2005-12-05. If station coordinates and orbits well known then one may follow how double differences change.

6. 6 GPS Accuracy, DOP. Sat05_82.ppt, 2005-12-05. Accuracy depends on instrument range error, σ r And on geometric configuration of satellites. Expressed using ”dillution of precision”, DOP...

7. 7 DOP. Sat05_82.ppt, 2005-12-05...

8. 8 DOP computation. Sat05_82.ppt, 2005-12-05..

9. 9 H and V DOP. Sat05_82.ppt, 2005-12-05. Rotation of coordinate system needed: Local East, North, Up.

10. 10 Error measures. Sat05_82.ppt, 2005-12-05. 2-D accuracy: Distance Root Mean Square Probability of being in a circle with this as radius between 63 % and 68 %. Sometimes multiplies with 2: Circular radial error: 95 % - 98 %. Circular probable error: 50 % 3-D accuracy: Mean radial Spherical error (MRSE):

11. 11 Earth Rotation. Sat05_82.ppt, 2005-12-05. We must know Earth rotation: The Earth moves while the signal is send:

12. 12 Relativistic effects on the clocks. Sat05_82.ppt, 2005-12-05. Special theory of relativity: velocity dependent General theory: Potential difference Earth - Satellite Main part the same for all GPS satelites (same distance from the Earth):

13. 13 Relativistic effect. Sat05_82.ppt, 2005-12-05. Potential difference in the Orbit is not constant with respect to the Earth. Generally corrected in Receivers. What is left disappears in relative obervations.

14. 14 Relativistic correction. Sat05_82.ppt, 2005-12-05.

15. 15 Ionospheric delay. Sat05_82.ppt, 2005-12-05. ….

16. 16 First order correction (Code). Sat05_82.ppt, 2005-12-05. Range on both frequencies must be the same: See Table 7.15 for magnitudes.

17. 17 1. Order correction, Phase. Sat05_82.ppt, 2005-12-05.

18. 18 1 Frequency receiver correction. Sat05_82.ppt, 2005-12-05. Klobuchar empirical model gives 50% at middle latitudes: Or obtain values from GSP-observatories like CODE, Analysis centers: IGS – IAAC. Or predicted values http://igscb.jpl.nasa.gov/components/dcnav/cddis _products_ionex.html

19. 19 Other effects:. Sat05_82.ppt, 2005-12-05. Antenna phase-center variations Oscillator instabilities Receiver noise Troposphere Militaty restrictions or noise (SA)

20. 20 GPS Advantages. Sat05_82.ppt, 2005-12-05. High 3-D precision for both position and velocity Independent of weather (- magnetic storms) Unlimited number of users Precise time-transfer Low costs (only receiver) for 1-frequency receivers Resistent ot Jamming But the system does not give physical heights ! Geoid model needed ! Users need coordinates in Local system. Datum- transformation.

21. 21 Datum-shift. Sat05_82.ppt, 2005-12-05. (a) If datum-shift known:

22. 22 Datum-shift. Sat05_82.ppt, 2005-12-05. (b) Datum-shift un-known: 1.Observed with GPS in a number of points where (X N, Y N, Z N ) is known 2.If only one point, Translation vector determined by taking difference 3.If two points also rotation, 3 or more points C (scale- factor) But often only latitude, longitude and height above mean- sea-level (orthometric height) known. We need ellipsoidal height. (Geoid height needed !)

23. 23 Datum-shift. Sat05_82.ppt, 2005-12-05. In Denmark: KMS has established points with kown coordinates in ED1950, WGS84 Main-station: Satellite station in Buddinge Determined in European GPS Campaigns. 7-parameter-shift not satisfactory, and does not agree if more than 2 points. Polynomials are used: