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Solution separation-based integrity monitoring for RTK positioning with faulty ambiguity detection and protection level

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Abstract

Due to the multipath and signal shading effects, there exist biases in the carrier phase measurements, which degrades the reliability of ambiguity resolution in real-time kinematic (RTK) positioning and, subsequently, the positioning accuracy. Integrity monitoring is an effective way to measure, improve, and guarantee the correctness of the RTK positioning solutions, but most integrity monitoring has focused only on the pseudorange faults and further the traditional ambiguity validation methods cannot monitor faulty ambiguity resolution separately. To provide high accuracy and high reliability for safety–critical applications, this study proposes a solution separation (SS)-based method for integrity monitoring of RTK precise positioning, in which the SS failure mode and test statistics are used to monitor the reliability of fixed ambiguity solutions by detecting faulty ambiguity fixes and bound positioning errors in the position domain using protection level (PL). The vehicular test with a low-cost receiver shows that the SS method can effectively detect and exclude fault ambiguity resolutions by 98.35%, and the double-difference residuals of SS are reduced from 6.89 cm to 2.56 cm. The positioning accuracy with the SS method has gained an 83.64% improvement compared with the traditional methods. The horizontal PL and the vertical PL can also effectively bound the positioning errors, with average values of 4.49 cm and 12.25 cm, respectively. The SS PL can achieve 99.17% and 96.14% in the horizontal and vertical directions to provide normal integrity service, respectively.

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Data availability

The GNSS dataset associated with this study is publicly accessible in the GitHub repository (https://github.com/Yuting1117/SS-IM-RTK-low-cost).

References

  • Ahmad KAB (2015) Reliability monitoring of GNSS aided positioning for Land vehicle applications in urban environments. Doctoral dissertation, Université de Toulouse.

  • Amiri-Simkooei AR, Jazaeri S, Zangeneh-Nejad F, Asgari J (2016) Role of stochastic model on GPS integer ambiguity resolution success rate. GPS Solutions 20(1):51–61

    Article  Google Scholar 

  • Baarda W (1967) Statistical concepts in geodesy. Netherlands Geodetic Commission, Publ. on geodesy, New series 2(4).

  • Blanch J, Walter T (2020) Fast Protection Levels for Fault Detection with an Application to Advanced RAIM. IEEE Trans Aerosp Electron Syst 57(1):55–65

    Article  Google Scholar 

  • Blanch J, Walter T, Enge P (2013) Optimal positioning for advanced RAIM. J Inst Navig 60(4):279–289

    Article  Google Scholar 

  • Blanch J et al (2015) Baseline advanced RAIM user algorithm and possible improvements. IEEE Trans Aerosp Electron Syst 51(1):713–732

    Article  Google Scholar 

  • El-Mowafy A (2019) On detection of observation faults in the observation and position domains for positioning of intelligent transport systems. J Geodesy 93(10):2109–2122

    Article  Google Scholar 

  • Euler H-J, Schaffrin B (1991) On a measure for the discernibility between different ambiguity solutions in the static-kinematic GPS-mode Kinematic Systems in Geodesy, Surveying, and Remote Sensing. Springer, New York, pp 285–295

    Google Scholar 

  • Feng S, Ochieng W, Moore T, Hill C, Hide C (2009) Carrier phase-based integrity monitoring for high-accuracy positioning. GPS Solutions 13(1):13–22

    Article  Google Scholar 

  • Gao Y (1991) A new algorithm of receiver autonomous integrity monitoring (RAIM) for GPS navigation, Proceeding ION GPS-91, Albuquerque, NM, September 11–13, 887–896.

  • Gao Y, Gao Y, Liu B, Jiang Y (2021a) Enhanced fault detection and exclusion based on Kalman filter with colored measurement noise and application to RTK. GPS Solutions 25(3):1–13

    Article  Google Scholar 

  • Gao Y, Jiang Y, Gao Y, Huang G (2021b) A linear Kalman filter-based integrity monitoring considering colored measurement noise. GPS Solutions 25(2):1–13

    Article  Google Scholar 

  • Gunning K, Blanch J, Walter T, de Groot L, Norman L (2018) Design and evaluation of integrity algorithms for PPP in kinematic applications. Proceeding ION GNSS+ 2018, Institute of Navigation, Miami, Florida, September 24–28, 1910–1939.

  • Han S (1997) Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning. J Geodesy 71(6):351–361

    Article  Google Scholar 

  • Hatch R (1982) The Synergism of GPS Code and Carrier Measurements. Proceedings of the Third International Symposium on Satellite Doppler Positioning at Physical Sciences Laboratory of New Mexico State University 2:1213–1231

    Google Scholar 

  • Henkel P, Günther C (2012) Reliable integer ambiguity resolution: multi-frequency code carrier linear combinations and statistical a priori knowledge of attitude. Navigation 59(1):61–75

    Article  Google Scholar 

  • Ji S, Chen W, Ding X, Chen Y, Zhao C, Hu C (2010) Ambiguity validation with combined ratio test and ellipsoidal integer aperture estimator. J Geodesy 84(10):597–604

    Article  Google Scholar 

  • Jiang Y, Wang J (2016) A new approach to calculate the horizontal protection level. J Navig 69(1):57–74

    Article  Google Scholar 

  • Joerger M, Chan FC, Pervan B (2014) Solution separation versus residual-based RAIM. Navigation 61(4):273–291

    Article  Google Scholar 

  • Khanafseh S, Pervan B (2010) New approach for calculating position domain integrity risk for cycle resolution in carrier phase navigation systems. IEEE Trans Aerosp Electron Syst 46(1):296–307

    Article  Google Scholar 

  • Langley RB (1998) RTK GPS. GPS World, University of New Brunswick 9(9):70–76

    Google Scholar 

  • Lawrence DG (2009) A new method for partial ambiguity resolution. Proc. ION ITM 2009, Institute of Navigation, Anaheim, CA, January 26–28, 652–663.

  • Li T, Wang J (2014) Analysis of the upper bounds for the integer ambiguity validation statistics. GPS Solutions 18(1):85–94

    Article  Google Scholar 

  • Li L, Li Z, Yuan H, Wang L, Hou Y (2016) Integrity monitoring-based ratio test for GNSS integer ambiguity validation. GPS Solutions 20(3):573–585

    Article  Google Scholar 

  • Li L, Shi H, Jia C, Cheng J, Li H, Zhao L (2018) Position-domain integrity risk-based ambiguity validation for the integer bootstrap estimator. GPS Solutions 22(2):1–11

    Article  Google Scholar 

  • Liu B, (2019) Integrity monitoring of GNSS/MEMS integration system, Ph.D. thesis, Shanghai Jiao Tong University.

  • Milner CD, Ochieng WY (2011) Weighted RAIM for APV: The ideal protection level The. J Navig 64(1):61–73

    Article  Google Scholar 

  • Odijk D, Teunissen P (2008) ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models. J Geodesy 82(8):473–492

    Article  Google Scholar 

  • Oehler V, Luongo F, Trautenberg HL, Boyero JP, Krueger J, Rang T (2005) The Galileo integrity concept and performance. In: Proceedings of ION GNSS 2005, Institute of Navigation, Fort Worth, 604–615

  • Parkins A (2011) Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm. GPS Solutions 15(4):391–402

    Article  Google Scholar 

  • Peters M, Gates R, Chertoff M (2008) Federal radionavigation plan. Department of Transportation, USA

    Google Scholar 

  • Shi J, Huang Y, Ouyang C (2019) A GPS relative positioning quality control algorithm considering both code and phase observation errors. J Geodesy 93:1419–1433

    Article  Google Scholar 

  • Takasu T, Yasuda A (2008) Evaluation of RTK-GPS performance with low-cost single-frequency GPS receiver. In: Proceedings of international symposium on GPS/GNSS 2008, Odaiba, Tokyo, November 11–14, 852–861. https://gpspp.sakura.ne.jp/paper2005/isgps2008_paper_ttaka.pdf

  • Takasu T, Yasuda A (2009) Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB. International Symposium on GPS/GNSS, International Convention Center Jeju Korea 4(1):1–6

    Google Scholar 

  • Teunissen P (1998) Success probability of integer GPS ambiguity rounding and bootstrapping. J Geodesy 72(1):606–612

    Article  Google Scholar 

  • Teunissen PJG, Joosten P, Tiberius CCJM (1999). Geometry-free ambiguity success rates in case of partial fixing. In Proceedings of the 1999 national technical meeting of the institute of navigation (pp. 201-207)

  • Tiberius C, De Jonge P (1995) Fast positioning using the LAMBDA method. Proceedings DSNS-95, paper 30

  • Verhagen S (2004) Integer ambiguity validation: an open problem? GPS Solut 8(1):36–43

    Article  Google Scholar 

  • Verhagen S, Teunissen PJ (2006) New global navigation satellite system ambiguity resolution method compared to existing approaches. J Guid Control Dyn 29(4):981–991

    Article  Google Scholar 

  • Wang J, Stewart M, Tsakiri M (1998) A discrimination test procedure for ambiguity resolution on-the-fly. J Geodesy 72(11):644–653

    Article  Google Scholar 

  • Wang J, Stewart MP, Tsakiri M (2000) A comparative study of the integer ambiguity validation procedures. Earth Planets Sp 52(10):813–817

    Article  Google Scholar 

  • Yun H, Kee C (2014) Multiple-hypothesis RAIM algorithm with an RRAIM concept. J Adv Navig Technol 16(4):593–601

    Article  Google Scholar 

  • Zhao L, Zhang J, Li L, Yang F, Liu X (2020) Position-Domain Non-Gaussian Error Overbounding for ARAIM. Remote Sens 12(12):1992

    Article  Google Scholar 

Download references

Acknowledgements

The financial support was provided by the National Natural Science Foundation of China (42204034, 42127802), the Natural Sciences and Engineering Research Council of Canada (NSERC), the Key Project of Science and Technology Research provided by the Henan Province under Grant 212102210085, and in part by the Fundamental Research Funds for the Universities of Henan Province under Grant NSFRF210309.

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Gao, Y., Jiang, Y., Gao, Y. et al. Solution separation-based integrity monitoring for RTK positioning with faulty ambiguity detection and protection level. GPS Solut 27, 140 (2023). https://doi.org/10.1007/s10291-023-01472-y

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