Moscow Aviation Institute (State University of Aerospace Technologies) 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 GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada Alexander Povalyaev, Ph.D., Prof. at Moscow Aviation Institute (National Research University), Russia

Moscow Aviation Institute (State University of Aerospace Technologies) Initial point for research: P3L3A4 observation system GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 2 *Decoupled clock model presented by Paul Collins (NRCan) Ionosphere-free satellite decoupled clocks (NRCan) (1)

Moscow Aviation Institute (State University of Aerospace Technologies) PPP results for P3L3A4 observation system GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 3

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

Moscow Aviation Institute (State University of Aerospace Technologies) Approach 1. Working on initial frequencies GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 5 P1P2L1L2 Observation system with measurements on initial GPS frequencies: 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 (4)

Moscow Aviation Institute (State University of Aerospace Technologies) Approach 1. Working on initial frequencies. 1 st problem. GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 6 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)

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 7 Approach 1. Working on initial frequencies. 2 nd problem. Problem 2, solution: Considering ionosphere delays as nuisance parameters according to the following elimination technique*: *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.) useful estimated parameters nuisance estimated parameters weight matrix of observation vector wheremodified weight matrix (singular matrix) (7) (8)

Moscow Aviation Institute (State University of Aerospace Technologies) Approach 1. Working on initial frequencies. Rank issue. GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 8 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 :

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 9 Approach 1. Working on initial frequencies, results. Supplemented\extended P1P2L1L2 observation, 3D-position accuracy (float and fixed solution):

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential 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: *Extended Decoupled clock model presented by Paul Collins (NRCan) (9) (10) (11) (12)

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 11 Approach 2. Re-parameterizing Extended Decoupled clock model, results.

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 12 Convergence time for two described approaches with comparison to initial solution. Float solutions.

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 13 Convergence time for two described approaches with comparison to initial solution. Fixed solutions.

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 14 Convergence time for two described approaches with comparison to initial solution. Fixed solutions.

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 15 Validation. Ratio test values for described approaches with comparison to initial solution

Moscow Aviation Institute (State University of Aerospace Technologies) GNSS Precise Point Positioning Workshop: Reaching Full Potential 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.

Moscow Aviation Institute (State University of Aerospace Technologies) Thanks for your attention. Any questions? Feel free to contact us: Andrey Podkorytov: Alexander Povalyaev: Moscow Aviation Institute (National Research University): GNSS Precise Point Positioning Workshop: Reaching Full Potential June 2013, Ottawa, Canada 17