PPP Workshop: Reaching Full Potential June 12-14, 2013, Ottawa, Canada

1. Single-Station Ionosphere Modelling for Precise Point PositioningPaul Collins, Reza Ghoddousi-Fard, Simon Banville François LahayeGeodetic Survey Division, Natural Resources Canada, Ottawa, Ontario, Canada PPP Workshop: Reaching Full Potential June 12-14, 2013, Ottawa, Canada

2. A clearer understanding of the role of the ionosphere in high-precision GNSS permits: rapid PPP-AR (under some circumstances), those ‘circumstances’ look suspiciously like RTK… One goal of this presentation is to retain: a distinction between PPP & RTK techniques. Motivation: What was the point of GPS in the first place? Why the desire for dense reference networks? Introduction

3. Two kinds of RTK: Observation Space Representation (OSR-RTK) State Space Representation (SSR-RTK) Preferably not PPP-RTK, because… Differentiator between RTK and PPP: Network Size: RTK: local/regional. PPP: (wide-area)/global. Network Dependence: RTK User: No network, no solution. PPP User: What network? PPP/RTK Review

4. Ionosphere/Ambiguity Relationship Ionosphere-free model • code s = 10cm; phase s = 1mm • L1 iono bias = 2cm/0.12TECU Ionosphere-fixed model

5. Four-observable PPP model • Original three-observable decoupled clock model: • Split widelane-phase/narrowlane-code observable: • Result: phase ionosphere. • Biased by datum ambiguities and hardware delays.

6. Slant ionosphere estimates float sigma fixed sigma

7. Applying the Constraints • Ionospheric Slant delays contain: • Integer-biased satellite phase equipment delay. • Common to all stations. • Integer-biased station phase equipment delay. • Unique to all stations, can change on solution reset. • Use single-differences to eliminate station bias: • Add as pseudo-observations: ,

8. float solution LAMBDA AR AR fixed solutions AR AR AR AR ion ion float/fixed solutions LAMBDA AV constrained solutions ion AR AR ion AR ion AR ion PPP-ICAR Methodology

9. NRC1 S1 JO2P 8.5km S2b S2a S2c 0019 0015 PPP-ICAR Testing • Local stations around Ottawa. • JO2P (30sec); NRC1 (1sec). • Two receivers driven on the Rideau Canal (frozen). • 0015, 0019 (1sec). • frozen surface should be ‘level’.

10. 67% ~1cm 95% ~2cm Solution 1 JO2P → NRC1 (2D-Horiz.)

11. 67% ~3cm 95% ~7cm Solution 1 JO2P → NRC1 (3D)

12. Solution 2: Height Estimates • PPP(SMD) HGT = 30.34 ± 0.10 • PPP(ICAR) HGT = 30.26 ± 0.05 • RTK(NRC1) HGT = 30.25 ± 0.02

13. NRC1 JO2P 0019 0015 Solution 2: JO2P→0019→NRC1→0015 0019 (kinematic) NRC1 (stationary) Ion 0015 (kinematic) Ion

14. Master Ref. User RTK Network

15. “Ref.” User PPP Local ‘Network’

16. PPP Local Augmentation

17. STD PPP PPP−AR PPP−ICAR Point Positioning Scalability • Broadcast Orbits & Clocks • pseudoranges • Precise Orbits & Clocks • carrier phases • Decoupled Clock Model • equipment delays • Ionosphere Constraints • ambiguity constraints

18. Key Points: Know the Ionosphere, Know the Ambiguities. Constrain ambiguity resolution, not the observation model. Using external ionosphere constraints for AR pushes PPP as close to RTK as possible, without being RTK. An RTK solution is still (a little) better! In principle, Permits a generalised local augmentation concept: Peer-to-Peer in nature, no centralised solution or coordination required; state space representation of information. Regular PPP-AR solution possible at all times and all locations. Conclusions

19. Future Work • Analyse Ionosphere Spatial Gradients

20. Acknowledgements • Pierre Hérouxand Christian Prévost • Rideau Canal dataset • Thank You