Comparison of Ionosphere-free, Uofc and Uncombined PPP Observation Models

doi:10.11947/j.AGCS.2015.20140161

Abstract

Abstract:

GNSS precise point positioning (PPP) has become the research hotspot in the most recent years due to its capability of obtaining precise position with single receiver. Usually, three models are used in PPP, that is,uncombined model, Uofc model and ionosphere-free combination model. The relationships between the these models are described in detail in this paper. On the one hand, it is clarified that the uncombined model is equivalent to the Uofc model and both of them are better than the ionosphere-free model in the sense of ambiguity resolution. On the other hand, in comparison with the Uofc model that eliminates the ionosphere delay by using the equivalence principle, the uncombined model that takes the ionosphere delay as the parameter has its advantage that it can provide the users with the prior constrained conditions for the ionosphere. As a result, the model can be converted to the ionosphere-weighted model easily. In the circumstance of fixing the wide-lane, when comparing with the ionosphere-free model by using ambiguity dilution of precision (ADOP) from the aspect of fixing ambiguity, Uofc model has many advantages such as small noise, origin information preserving etc.,while the ionosphere-weighted model can improve the ambiguity resolution significantly when the high precise prior ionosphere information is available.

Key words: precise point positioning(PPP), position model, equivalence principle, ambiguity fixing, ADOP

CLC Number:

P228

LI Bofeng, GE Haibo, SHEN Yunzhong. Comparison of Ionosphere-free, Uofc and Uncombined PPP Observation Models[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(7): 734-740.

References

[1] COLOMBO O L, SUTTER A W, EVANS A G. Evaluation of Precise, Kinematic GPS Point Positioning[C]// Proceedings of ION GNSS. Long Beach, California: [s.n.], 2004: 21-24.
[2] KOUBA J, HÉROUS P. Precise Point Positioning Using IGS Orbit and Clock Products[J]. GPS Solutions, 2001, 5(2): 12-28.
[3] GE M, GENDT G, ROTHACHER M, et al. Resolution of GPS Carrier-phase Ambiguities in Precise Point Positioning(PPP) with Daily Observations[J]. Journal of Geodesy, 2008, 82(7): 389-399.
[4] HAO Ming, WANG Qingliang, CUI Duxin. Study on Fast Convergence Method in Precise Point Positioning[J]. Journal of Geodesy and Geodynamics, 2009, 29(2): 88-91. (郝明, 王庆良, 崔笃信. GPS精密单点定位快速收敛方法研究[J]. 大地测量与地球动力学, 2009, 29(2): 88-91.)
[5] GAO Y, SHEN X. Improving Ambiguity Convergence in Carrier Phase-based Precise Point Positioning[C]//Proceedings of ION GPS. Salt Lake City: [s.n.], 2001: 1532-1539.
[6] ABDEL-SALAM M, GAO Y. Precise GPS Atmosphere Sensing Based on Un-differenced Observations[C] // Proceedings of ION GNSS. Long Beach: [s.n.], 2004: 933-940.
[7] CHEN K, GAO Y. Real-time Precise Point Positioning Using Single Frequency Data[C]//Proceedings of ION GNSS. Long Beach: [s.n.], 2004: 1514-1523.
[8] SHI C, GU S F, LOU Y D, et al. An Improved Approach to Model Ionospheric Delays for Single-frequency Precise Point Positioning[J]. Advances in Space Research, 2012, 49(12): 1698-1708.
[9] ZHANG Baocheng, OU Jikun, YUAN Yunbin, et al. Precise Point Positioning Algorithm Based on Original Dual-frequency GPS Code and Carrier-phase Observations and Its Application[J]. Acta Geodaetica et Cartographica Sinica,2010, 39(5): 478-482. (张宝成, 欧吉坤, 袁运斌, 等. 基于GPS双频原始观测值的精密单点定位算法及应用[J]. 测绘学报, 2010, 39(5): 478-482.)
[10] LI X X, GE M R, ZHANG H P, et al. A Method for Improving Uncalibrated Phase Delay Estimation and Ambiguity-fixing in Real-time Precise Point Positioning[J]. Journal of Geodesy, 2013, 87(5): 405-416.
[11] SUN Xiaogong. Equal Observation and GPS Differencial Positioning[J]. Acta Geodaetica et Cartographica Sinica, 1992, 21(1): 50-56. (孙效功. 等价观测与GPS差分法定位[J]. 测绘学报, 1992, 21(1): 50-56.)
[12] SHEN Y Z, XU G C. Simplified Equivalent Represtation of GPS Observation Equations[J]. GPS Solutions, 2007, 12(2): 99-108.
[13] SHEN Y Z, LI B F, XU G C. Simplified Equivalent Multiple Baseline Solutions with Elevation-dependent Weights[J]. GPS Solutions, 2008, 13(3): 165-171.
[14] LI B F, TEUNISSEN PJG. GNSS Antenna Array-aided CORS Ambiguity Resolution[J]. Journal of Geodesy, 2014, 88(4): 363-376.
[15] WEI Ziqing, GE Maorong. Mathmatical Model of GPS Relative Positioning[M]. Beijing: Publishing House of Surveying and Mapping, 1998: 56-82. (魏子卿, 葛茂荣. GPS相对定位的数学模型[M]. 北京: 测绘出版社, 1998: 56-82.)
[16] SCHAFFRIN B, GRAFAREND E. Generating Classes of Equivalent Linear Models by Nuisance Parameter Elimination[J]. Manuscripta Geodaetica, 1986, 11: 262-271.
[17] XU G C. GPS Data Processing with Equivalent Observation Equations[J]. GPS Solutions, 2002, 6(1-2): 28-33.
[18] LI B F, VERHAGEN S, TEUNISSEN PJG. Robustness of GNSS Integer Ambiguity Resolution in the Presence of Atmospheric Biases[J]. GPS Solutions, 2014, 18(2): 283-296.
[19] LI B F, SHEN Y Z,FENG Y M, et al. GNSS Ambiguity Resolution with Controllable Failure Rate for Long Baseline Network RTK[J]. Journal of Geodesy, 2014, 88(2): 99-112.
[20] LI B F, VERHAGEN S, TEUNISSEN PJG. GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA [C]//China Satellite Navigation Conference (CSNC) 2013 Proceedings. Wuhan: Springer, 2013: 291-301.
[21] ODIJK D, Teunissen P J G. ADOP in Closed Form for a Hierarchy of Multi-frequency Single-baseline GNSS Models [J]. Journal of Geodesy, 2008, 82(8): 473-492.
[22] VERHAGEN S, TEUNISSEN PJG,VAN DER MAREL H, et al. GNSS Ambiguity Resolution: Which Subset to Fix?[C]// Proceedings of IGNSS Symposium. Sydney, Australia: [s.n.], 2011.
[23] TEUNISSEN PJG, JOOSTEN P,TIBERIUS C. Geometry-free Ambiguity Success Rates in Case of Partial Fixing[C]//Proceedings of ION-NTM. San Diego: [s.n.], 1999: 25-27.