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BDS/GPS Stochastic Model Refinement and Assessment Using Satellite Elevation Angle and SNR

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China Satellite Navigation Conference (CSNC) 2015 Proceedings: Volume I

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 340))

Abstract

Satellite elevation angle and Signal-to-Noise Ratio (SNR) are usually used as measurement quality indicators for global navigation satellite system (GNSS) measurements. The relationship of quality indicators and accuracies of measurements can be expressed as stochastic models. To model the relationship for Beidou navigation satellite system (BDS) and global position system (GPS), five basic stochastic models are presented from satellite elevation angle and SNR. Also, coefficients of these models are refined. It’s found that SNR stochastic models with same coefficients can’t treat all measurements from BDS and GPS. Moreover, stochastic models with an additive constant could model the relationship better. The performance of the five models are tested, independent and combined, in BDS/GPS precise positioning. The results show that refined stochastic models could improve the success rate of integer ambiguity single-epoch solution 8 % comparing to empirical models. Models with an additive constant could improve the success rate 10 % comparing to models without additive constants. SNR model with an additive constant performs better in performance for integer ambiguity resolution, especially for low elevation satellite or combined system. Using stochastic models with an additive constant, ratios of posteriori and prior variances are closer to 1 in precise positioning. Therefore, for the used receivers, we suggest to choose refined stochastic models with an additive constant, and give priority to SNR model. Here, a refinement and assessment method is proposed to derive proper stochastic models for GNSS data processing, taking into account the differences between navigation satellite systems (e.g. BDS and GPS) and stochastic models.

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References

  1. Brown N, Kealy A et al (2002) Stochastic modelling of GPS phase observations for improved quality estimation. Cartography 31(2):143–151

    Article  Google Scholar 

  2. Brunner FK, Hartinger H et al (1999) GPS signal diffraction modelling: the stochastic SIGMA-Δ model. J Geodesy 73(5):259–267

    Article  Google Scholar 

  3. Collins JP, Langley RB (1999) Possible weighting schemes for GPS carrier phase observations in the presence of multipath. Final contract report for the US Army Corps of Engineers Topographic Engineering Center, no. DAAH04-96-C-0086/TCN 98151

    Google Scholar 

  4. Deng C, Tang W et al (2013) Reliable single-epoch ambiguity resolution for short baselines using combined GPS/BeiDou system. GPS Solutions 18(3):375–386

    Article  MathSciNet  Google Scholar 

  5. Hartinger H, Brunner FK (1999) Variances of GPS phase observations: the SIGMA-ɛ model. GPS Solutions 2(4):35–43

    Article  Google Scholar 

  6. Jin S, Wang J et al (2005) An improvement of GPS height estimations-stochastic modeling. Earth Planets Space 57(4):253–259

    Article  Google Scholar 

  7. Langley RB (1997) GPS receiver system noise. GPS World 8(6):40–45

    Google Scholar 

  8. Li B, Shen Y et al (2008) Assessment of stochastic models for GPS measurements with different types of receivers. Chin Sci Bull 53(20):3219–3225

    Article  Google Scholar 

  9. Luo X (2013) GPS stochastic modelling. Springer, Berlin

    Book  MATH  Google Scholar 

  10. Luo X, Mayer M et al (2011) Verification of ARMA identification for modelling temporal correlations of GNSS observations using the ARMASA toolbox. Stud Geophys Geod 55(3):537–556

    Article  Google Scholar 

  11. Odolinski R, Teunissen PJ et al (2013) Quality analysis of a combined COMPASS/BeiDou-2 and GPS RTK positioning model. Methodology 5(1176.45):25.48

    Google Scholar 

  12. Odolinski R, Odijk D et al (2014) Combined GPS and BeiDou instantaneous RTK positioning. Navigation 61(2):135–148

    Article  Google Scholar 

  13. Odolinski R, Teunissen PJG et al (2014) First combined COMPASS/BeiDou-2 and GPS positioning results in Australia. Part II: single- and multiple-frequency single-baseline RTK positioning. J Spat Sci 59(1):25–46

    Article  Google Scholar 

  14. Ozludemir MT (2004) The stochastic modeling of GPS observations. Turk J Eng Environ Sci 28:223–231

    Google Scholar 

  15. Satirapod C (2006) Stochastic models used in static GPS relative positioning. Surv Rev 38(299):379–386

    Article  Google Scholar 

  16. Satirapod C, Wang J (2000) Comparing the quality indicators of GPS carrier phase observations. Geom Res Australasia 73:75–92

    Google Scholar 

  17. Satirapod C, Wang J et al (2003) Comparing different global positioning system data processing techniques for modeling residual systematic errors. J Survey Eng 4(129):129–135

    Article  Google Scholar 

  18. Tang W, Deng C et al (2013) Triple-frequency carrier ambiguity resolution for Beidou navigation satellite system. GPS Solutions 18(3):335–344

    Article  MathSciNet  Google Scholar 

  19. Teunissen PJG, Odolinski R et al (2013) Instantaneous BeiDou+GPS RTK positioning with high cut-off elevation angles. J Geodesy 88(4):335–350

    Article  Google Scholar 

  20. Tiberius CCJM, Kenselaar F (2000) Estimation of the stochastic model for GPS code and phase observables. Surv Rev 35(277):441–454

    Article  Google Scholar 

  21. Tiberius C, Jonkman N et al (1999) The stochastics of GPS observables. GPS World 10(2):49–54

    Google Scholar 

  22. Wang J (2001) Modelling and quality control for precise GPS and GLONASS satellite positioning. Curtin University of Technology, Perth

    Google Scholar 

  23. Wang J, Stewart MP et al (1998) Stochastic modeling for static GPS baseline data processing. J Surv Eng 124(4):171–181

    Article  Google Scholar 

  24. Wieser A, Brunner FK (2000) An extended weight model for GPS phase observations. Earth Planets Space 52(10):777–782

    Article  Google Scholar 

  25. Xin Xiang Jin CDDJ (1996) Relationship between satellite elevation and precision of GPS code observations. J Navig 49(2):253–265

    Google Scholar 

Download references

Acknowledgments

This study is supported by 2013 doctoral innovation fund in Southwest Jiao Tong University and the fundamental research funds in Central Universities.

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Correspondence to Yan Li .

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Li, Y., Dingfa, H., Meng, L., Dongwei, Z. (2015). BDS/GPS Stochastic Model Refinement and Assessment Using Satellite Elevation Angle and SNR. In: Sun, J., Liu, J., Fan, S., Lu, X. (eds) China Satellite Navigation Conference (CSNC) 2015 Proceedings: Volume I. Lecture Notes in Electrical Engineering, vol 340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46638-4_48

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  • DOI: https://doi.org/10.1007/978-3-662-46638-4_48

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  • Publisher Name: Springer, Berlin, Heidelberg

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  • Online ISBN: 978-3-662-46638-4

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