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Resilient GNSS real-time kinematic precise positioning with inequality and equality constraints

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Abstract

How to conduct the GNSS real-time kinematic precise positioning in challenging environments is not an easy problem. The challenging environment mainly refers to frequent signal reflection, refraction, diffraction, and occlusion, inevitably introducing large positioning errors. We propose a resilient positioning method considering the inequality and equality constraints. Specifically, first, we introduce the functional and stochastic models of real-time kinematic (RTK) positioning, considering the impacts of challenging environments. Second, specific iterative procedures of resilient GNSS precise positioning method with inequality and equality constraints are proposed. In addition, a general form of inequality constraints in terms of coordinate components is given that is suitable for real-time kinematic situations. Four 24-h real datasets in canyon environments were collected to verify the performance of the proposed method. The results show that compared with the traditional RTK positioning without inequality constraints, the proposed method can improve the success rates of ambiguity resolution by 42.2% on average. Also, the positioning accuracy of fixed solutions can be improved significantly after applying the proposed method, where the root mean square errors can be reduced by 77.2% on average. Therefore, the proposed method can significantly improve success rates of ambiguity resolution and positioning accuracy, which is especially promising in challenging environments.

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Data availability

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

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (42004014) and the Natural Science Foundation of Jiangsu Province (BK20200530).

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Authors and Affiliations

  1. School of Earth Sciences and Engineering, Hohai University, Nanjing, 211100, China

    Zhetao Zhang, Yuan Li & Xiufeng He

  2. Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China

    Lita Hsu

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  1. Zhetao Zhang
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  2. Yuan Li
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  3. Xiufeng He
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  4. Lita Hsu
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Contributions

ZZ derived the formulae, proposed the methods, developed the software, and wrote the paper. YL developed the software, worked out the technical details, and wrote the paper. XH and LH designed the experiments and modified the original manuscript. All authors approved of the manuscript.

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Correspondence to Xiufeng He.

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Zhang, Z., Li, Y., He, X. et al. Resilient GNSS real-time kinematic precise positioning with inequality and equality constraints. GPS Solut 27, 116 (2023). https://doi.org/10.1007/s10291-023-01454-0

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