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GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

Ambiguity Resolution of Phase Measurements in Precise Point Positioning working on initial frequencies. Andrey Podkorytov , graduate student at Moscow Aviation Institute (National Research University), Russia currently at York University, Canada.

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GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

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  1. Ambiguity Resolution of Phase Measurements in Precise Point Positioning working on initial frequencies AndreyPodkorytov, graduate student at Moscow Aviation Institute (National Research University), Russia currently at York University, Canada Alexander Povalyaev, Ph.D., Prof. at Moscow Aviation Institute (National Research University), Russia GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  2. Initial point for research: P3L3A4 observation system (1) Ionosphere-free satellite decoupled clocks (NRCan) *Decoupled clock model presented by Paul Collins (NRCan) GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  3. PPP results for P3L3A4 observation system GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  4. Why ionosphere-free combinations? Alternative approaches Standard ionosphere-free approach 1. Working on initial frequencies (2) 2. Re-parameterized Extended Decoupled clock model* Re-parameterization (3) *by Paul Collins (NRCan) GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  5. Approach 1. Working on initial frequencies P1P2L1L2 Observation system with measurements on initial GPS frequencies: (4) Two problems: 1. There is no direct way to transit from available ionosphere-free decoupled clocks to decoupled clocks for initial frequencies (coloured with blue) 2. Ionosphere delays in P1P2L1L2 observation system GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  6. Approach 1. Working on initial frequencies. 1st problem. Problem 1, solution: Direct transition to initial frequencies is impossible but pseudo-observations can be used as kind of constraints Supplemented\extended P1P2L1L2 system: Estimated parameters: (5) (6) GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  7. Approach 1. Working on initial frequencies. 2nd problem. Problem 2, solution: Considering ionosphere delays as nuisance parameters according to the following elimination technique*: (7) useful estimated parameters nuisance estimated parameters weight matrix of observation vector (8) where modified weight matrix (singular matrix) *Geoffrey Blewitt. 6.3 Equivalence of stochastic and functional models, pp.246, P.J.G. Teunissen, A. Kleusberg (Eds.). GPS for Geodesy. 2-nd edition. Springer-Verlag Berlin Heidelberg 1998.) GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  8. Approach 1. Working on initial frequencies. Rank issue. Supplemented/extended P1P2L1L2 observation system contains rank deficiency which equals 1 Non-physical estimates of satellite decoupled clocks, but correct estimates for all other parameters: GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  9. Approach 1. Working on initial frequencies, results. Supplemented\extended P1P2L1L2 observation, 3D-position accuracy (float and fixed solution): GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  10. Approach 2. Re-parameterizing Extended Decoupled clock model Transition from Extended Decoupled clock model to uncombined-like 4-observations model: (9) (10) (11) (12) *Extended Decoupled clock model presented by Paul Collins (NRCan) GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  11. Approach 2. Re-parameterizing Extended Decoupled clock model, results. GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  12. Convergence time for two described approaches with comparison to initial solution. Float solutions. GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  13. Convergence time for two described approaches with comparison to initial solution. Fixed solutions. GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  14. Convergence time for two described approaches with comparison to initial solution. Fixed solutions. GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  15. Validation. Ratio test values for described approaches with comparison to initial solution GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  16. Conclusions. Future work. Conclusions: Integer PPP can be realized with raw uncombined measurements on initial GPS frequencies providing better (at least the same) results in terms of accuracy and convergence time. Instead of satellite decoupled clocks for measurements on initial frequencies, ionosphere-free satellite decoupled clocks can be used to realize full uncombined solution (First approach) or at least estimating of initial N1 and N2 ambiguities (Second approach). Having decoupled satellite clocks for measurement on initial frequencies, we can rigorously calculate ionosphere-free decoupled clocks, but reverse rigorous transition is impossible. Future work: Rigorous analysis of integer search space in Integer PPP with use of satellite decoupled clocks for measurements on initial frequencies. Calculating decoupled satellite clocks for measurements on initial GPS frequencies in network solution. Statistical analysis of the approach. GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

  17. Thanks for your attention. Any questions? Feel free to contact us: Andrey Podkorytov: thepompous@gmail.com Alexander Povalyaev: povalyaev_aa@rniikp.ru Moscow Aviation Institute (National Research University): www.mai.ru GNSS Precise Point Positioning Workshop: Reaching Full Potential 12-14 June 2013, Ottawa, Canada

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