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Factor graph-based PPP-RTK for accurate and robust positioning in urban environments

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Abstract

The PPP-RTK system, which is capable of providing a centimeter-level real-time positioning service for an unlimited number of users, is becoming a promising tool in mass-market applications such as smartphones, the Internet of Things (IoT), and the automotive industry. The extended Kalman filter (EKF) is the conventional method for parameter estimation in the existing PPP-RTK system. Recently, an alternative method known as factor graph optimization (FGO), which fully leverages the time correlation among current and historical measurements, has the potential to further improve the accuracy and robustness of PPP-RTK solutions. In this contribution, a factor graph optimization-based PPP-RTK framework is developed, where raw pseudorange, phase measurements, precise atmospheric corrections, and time-differenced carrier-phase (TDCP) measurements serve as factors in FGO estimators. The continuously tracked phase ambiguities are estimated as the time-invariant state node and propagated by marginalization while ambiguity resolution is conducted independently between epochs. A second optimization process with the utilization of ambiguity-resolved solutions and time-differenced carrier-phase (TDCP) measurements is conducted to further improve the reliability of positioning results. The effectiveness of the proposed method is evaluated by vehicular tests in urban environments. Results indicate that the FGO method could improve the performance of ambiguity resolution by reducing the ambiguity search space and increasing the ratio values, leading to a significant accuracy improvement of 55% in an open-sky environment compared to the traditional EKF-based method. Furthermore, in GNSS signal partly block scenes, the FGO-based PPP-RTK is capable of obtaining more robust and accurate positioning solutions with fewer outliers compared to the EKF method.

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Availability of Data and materials

Datasets collected in the road vehicular test campaign as well as the observation data of reference stations are available on the website of the international GNSS Monitoring and Assessment System (iGMAS) Innovation Center (http://igmas.users.sgg.whu.edu.cn/group/tool/19).

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China (No. 42204017), the special fund of Hubei Luojia Laboratory (220100006), the National Postdoctoral Program for Innovative Talents, China (No. BX20220239). The algorithm implementation is based on the GNSS+ REsearch, Application and Teaching (GREAT) software developed by the GREAT Group, School of Geodesy and Geomatics, Wuhan University. The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.

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Authors and Affiliations

  1. School of Geodesy and Geomatics, Hubei Luojia Laboratory, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Xin Li, Xingxing Li, Xuanbin Wang, Hanyu Chang, Yuxuan Tan & Zhiheng Shen

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  1. Xin Li
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  2. Xingxing Li
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  3. Xuanbin Wang
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  4. Hanyu Chang
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Contributions

X.L. and XX.L. provided the initial idea and designed the experiments for this study; X.L., XX.L., X.W., and H.C. analyzed the data and wrote the manuscript; Y.T. and Z.S. helped with the writing. All authors reviewed the manuscript.

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Correspondence to Xingxing Li.

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Li, X., Li, X., Wang, X. et al. Factor graph-based PPP-RTK for accurate and robust positioning in urban environments. J Geod 98, 21 (2024). https://doi.org/10.1007/s00190-024-01828-3

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