LAVAL UNIVERSITY DEPARTMENT OF GEOMATICS

1. LAVAL UNIVERSITYDEPARTMENT OF GEOMATICS Instantaneous ambiguity resolution for future GNSSa simulation study Mohammed Boukhecha (Laval University) Marc Cocard (Laval University) René Landry (École technique supérieure Montréal)

2. Overview Introduction Theoretical approach Results of the simulations Conclusions

3. Introduction • Situation nowadays with GPS only: • (Quasi-) Instantaneous ambiguity resolution works under certain conditions : • Differential mode • Dual frequency receivers • Negligible ionospheric noise --» short baselines (up to 10 km) • In the near future there will be a modernization of GNSS • Additional 3rd frequency on GPS • Galileo will become operational • Hybrid solutions of GPS and Galileo

4. Introduction Main question of our research : What will be the impact of modernized GNSS on instantaneous ambiguity resolution ? In order to elucidate this question lets do some simulations

5. Theoretical approach • Review of basic search strategy in ambiguity resolution : • Define the search space containing all possible candidates of integer sets • Look for the best set (characterized by the smallest variance factor) and the second best set (characterized by the second smallest variance factor) • Apply a statistical test in order to discard the second best set as highly improbable. If the test is successful, only one set remains (the best one) which is accepted as the correct one. Discrimination factor : where, : estimated variance factor for the best integer ambiguity set : estimated variance factor for the 2nd best integer ambiguity set

6. Theoretical approach In the absence of real observations this discrimination factor has to be adapted to the a priori case. best solution 2nd best solution where, : a priori variance factor can be obtained a priori : difference between 2nd best and best integer ambiguity set : cofactor matrix of the float ambiguities : degree of freedom

7. Theoretical approach Simplified structure of the simulator Observation equations forcode and phase measurements Satellite orbits simulated by a Keplerian representation Choice of several parameters(will be presented in details later on) Normal Equation Matrix A priori Discrimination factor

8. Theoretical approach Observation equations and unkown parameters Coordinates (X Y Z) Clocks Integer ambiguity Code measurement Phase measurement Receiver phase bias Ionosphere biases

9. Theoretical approach Ionospheric modeling and constrains The ionospheric delay Iis related to the unknown vertical ionospheric delay Iz by the following relationship: Iz is regarded as a pseudo-observation having expectation value of 0 with a known a priori variance sI sI = 0 sI > 0 Ionospheric layer Ionospheric layer Large baseline Short baseline

10. Theoretical approach Range of simulation parameters

11. Results Number of satellites and PDOP

12. Results The normalized discrimination factor : discrimination factor : Fisher distribution with 99% confidence level : degree of freedom Statistical validation of integer ambiguity resolution : success : failure

13. Results Normalized discrimination factor GNSS dual frequency Ionospheric Noise : sI = 0cm

14. Results Normalized discrimination factor GNSS mono frequency Ionospheric Noise : sI = 0cm

15. Results Normalized discrimination factor GNSS dual frequency Ionospheric Noise : sI = 0cm

16. Results Normalized discrimination factor GNSS triple frequency Ionospheric Noise : sI = 0cm

17. Results Normalized discrimination factor Ionospheric Noise : sI = 0cm

18. Results Normalized discrimination factor Ionospheric Noise : sI = 10cm

19. Results Normalized discrimination factor Ionospheric Noise : sI = 20cm

20. Results Normalized discrimination factor Ionospheric Noise : sI = 30cm

21. Results Success rate (an other interesting indicator) Submitting the instantaneous discrimination factor to a statistical test leads to a binary results : Ambiguity resolution theoretically possible (YES) or not (NO) Based on this test a success rate is calculated over a period of 3 days with a sampling rate of 1 minute.

22. Results Impact of ionospheric noise on the success rate GNSS mono frequency

23. Results Impact of ionospheric noise on the success rate GPS only and GALILEO only dual frequency

24. Results Impact of ionospheric noise on the success rate HYBRIDE dual frequency

25. Results Impact of ionospheric noise on the success rate GNSS triple frequency

26. Results Impact of ionospheric noise on the success rate Classifying GNSS solutions as a function of the maximum ionospheric noise allowed still leading to different success rate (SR) values

27. Conclusions • Approach • Simulation is an appropriate tool for analyzing the performance of future GNSS in the absence of real observations. • Results • Concerning instantaneous ambiguity resolution Galileo shows a similar or even slightly better performance compared to GPS. • HYBRID RTK solutions will allow instantaneous ambiguity resolution even with mono-frequency receivers (in the absence of ionosphere). • Especially the HYBRID dual and triple frequency will allow to absorb quite a high ionospheric noise still leading to an instantaneous ambiguity resolution. • Future work • Integration of GLONASS in the simulations.

28. Questions ?