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Factor graph optimization-based multi-GNSS real-time kinematic system for robust and precise positioning in urban canyons

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Abstract

Recently, the factor graph-based global navigation satellite systems (GNSS) positioning methods have attracted much attention for more robust positioning performance in urban canyons compared with the traditional filter-based method. In the existing factor graph optimization (FGO)-based GNSS positioning methods, the pseudorange and Doppler measurements are mainly utilized to construct factors among consecutive GNSS epochs for outlier resisting and robust localization. However, the potential of high-precision positioning by using carrier phase observations is not fully explored. A factor graph optimization-based multi-GNSS real-time kinematic (FGO-RTK) framework is proposed to fill this gap, aiming to realize robust and precise positioning in urban canyons. In our method, a sliding window-based FGO estimator is designed, in which the continuously tracked double difference ambiguities are used to establish the ambiguity constraints of position states that have common-view satellites within the window. A marginalization-based carrier phase ambiguity propagation (AP) method is developed to fully use the information of carrier phase observations for achieving more reliable and continuous ambiguity resolution. Experiments in both medium urban and deep urban environments verified the effectiveness of the proposed method. Results show that FGO-RTK (with or without the AP) can achieve centimeter-level positioning accuracy in medium urban situations, showing comparable performance with the traditional extended Kalman filter (EKF)-based RTK. With the GNSS observation conditions deteriorating in deep urban environments, FGO-RTK without AP cannot outperform EKF-RTK. By contrast, the proposed FGO-RTK, considering the AP, achieves significant improvements in centimeter- to decimeter-level positioning availability, and the 3D positioning accuracy is improved by 69.6%, compared with the EKF-RTK. Furthermore, by analyzing the impact of the window size against the performance of FGO-RTK, we found that in comparison to the FGO-RTK only using the carrier phase observations inside a fixed-size window, the proposed AP method can significantly reduce the dependence on window size, and the optimal window size can be reduced from 10 to 4 epochs with more than 50% optimization time decreasing.

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Data availability

The data that support the results of this study are available from the corresponding author for academic purposes on reasonable request.

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Acknowledgements

Our algorithm implementation is based on the GREAT (GNSS+REsearch, Application, and Teaching) software developed by the GREAT Group, School of Geodesy and Geomatics, Wuhan University. The numerical calculations (e.g., base station coordinates) in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.

Funding

This work was supported in part by the National Key Research and Development Program of China (2021YFB2501102), the National Natural Science Foundation of China (Grant 41974027), and the Sino-German mobility program (Grant No. M-0054).

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Authors and Affiliations

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

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

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  1. Xuanbin Wang
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  2. Xingxing Li
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  3. Zhiheng Shen
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  4. Xin Li
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  5. Yuxuan Zhou
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  6. Hanyu Chang
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Contributions

Xuanbin Wang and Xingxing Li contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Zhiheng Shen, Xin Li, Yuxuan Zhou, and Hanyu Chang. Xuanbin Wang wrote the first draft of the manuscript, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xingxing Li.

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Wang, X., Li, X., Shen, Z. et al. Factor graph optimization-based multi-GNSS real-time kinematic system for robust and precise positioning in urban canyons. GPS Solut 27, 200 (2023). https://doi.org/10.1007/s10291-023-01538-x

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