1. Surveying with the Global Positioning System Phase Observable

2. Outline of Session 2 Phase Observable Differencing Ambiguity Resolution

3. Phase Observable

4. The GPS Baseline Y X Z GPS Surveying produces “baselines” between known and unknown positions expressed as  X,  Y and  Z

5. GPS Survey Measurement n Distance with a steel band; whole metres plus fractional part from leader A p GPS Similar - Whole wavelengths, “A” plus fractional part of last wavelength, “p” Phase “p” measured to 1/100 of wavelength ~ 2mm “A” is ambiguous and unknown Finding “Ambiguity” (“A”) is crux of GPS Surveying

6. The GPS Measurement in 3 Dimensions Y X Z Distance Squared = (X S - X R ) 2 +(Y S - Y R ) 2 +(Z S - Z R ) 2 A p

7. Computing a Baseline SV 6 i j Coordinates of Satellite 6 are known Coordinates of Receiver i are known Phase is measured at both receivers Unknowns are the Ambiguities (though one can be calculated) and the Coordinates of j Single Difference satellite errors removed

8. Computing a Baseline SV 6 i j SIngleSIngle SV 9 SIngleSIngle Double Difference receiver errors minimized DoubleDouble

9. Differencing and Ambiguity Resolution

10. Single difference between satellite Receiver clocks have large errors Eliminate this error

11. Single difference between receiver Satellite clocks are extremely accurate but still have errors too large to ignore Eliminates satellite bias and drift

12. The Double Difference From two single differences Basic GPS observable Ambiguity still to be estimated

13. The Triple Difference From two double differences Eliminates ambiguity term Very “noisy” Useful for approximating “robust” baseline solutions

14. Solving Ambiguities With more satellites -various combinations of equations are possible If signal is continuous ambiguities do not change for next measurement some time later (e.g. 15 seconds) Can give triple difference Gives approximate baseline and even more redundancy ~ making it possible to solve for the ambiguities

15. Solving Ambiguities “Double Difference” is the most effective Once “ambiguities” are known they can be held “fixed” to Integer values Thus the term “double difference fixed solution” Ambiguity is held fixed and substituted back into equations to solve for only the remote receivers coordinates

16. Further Explanation Required?

17. Conclusion to Session 2 Phase Observable Differencing Ambiguity Resolution

18. Questions?