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

2. 2 Overview 1. Introduction 2. Theoretical approach 3. Results of the simulations 4. Conclusions

3. 3 In the near future there will be a modernization of GNSS Additional 3 rd frequency on GPS Galileo will become operational Hybrid solutions of GPS and Galileo 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) Introduction

4. 4 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. 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 2 nd best integer ambiguity set

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

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

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

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

10. 10 Theoretical approach Position de la station fixe P(  ) Latitude 45 o, longitude 0 o Elevation mask 15 o Combination of frequencies MonoDoubleTriple GPSL12 of 3L1 L2 L5 GALILEOE12 of 3E1 E5 E6 HYBRIDL1 E1All comb.L1 L2 L5 E1 E5 E6 Std. dev. of ionospheric delay  I 0 cm, 1cm, 2cm …. 1m Std. dev. of observations code30 cm Phase3 mm Confidence level 1 – a 99% Range of simulation parameters

11. 11 Results Number of satellites and PDOP

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

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

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

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

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

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

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

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

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

21. 21 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. Success rate (an other interesting indicator) Results

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

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

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

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

26. 26 FrequenciesSystems Max. ionospheric noise (cm) SR=100%SR=95%SR=90% TRIPLE HYBRIDE435560 GALILEO212425 GPS172122 DOUBLE HYBRIDE406065 GALILEO91723 GPS31921 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. 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. 28 Questions ?