Abstract
The Gauss-Newton algorithm has been widely used in GNSS positioning and indoor positioning applications, but it requires an initial guess. An unfavorable initial guess may cause the iteration divergence. This issue is particularly important in indoor positioning scenarios but has not attracted enough attention. The non-iterative closed-form algorithms are suitable to provide the initial guess since they are divergence-free but sub-optimal. This study systematically evaluated performance of four representative non-iterative closed-form algorithms, namely the differenced squared range (DSR) algorithm, the Bancroft algorithm, and constrained virtual parameter (CVP) algorithm in terms of positioning precision, robustness, and computation efficiency. The performance of these algorithms is evaluated with both simulative data and real data. The results indicate that the CVP algorithm achieves 0.2–0.6 m accuracy in the static scenarios and about 2 m accuracy in the kinematic scenario, which outperforms the Gauss-Newton algorithm and the other two non-iterative approaches. The Gauss-Newton approach also achieves promising results in the LOS scenario, but it is more vulnerable to the NLOS observations. The DSR algorithm and the Bancroft algorithms are sub-optimal, robust to NLOS biases, but their performance in real data test depends on the test scenario. The CVP algorithm is free of divergence issue, robust to NLOS bias, and computationally efficient and achieves the best positioning accuracy in all four algorithms, thus should be recommended in highly non-linear localization estimation scenarios, such as the indoor positioning applications.
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Acknowledgements
The authors thank Dr. Shenghong Li from the Commonwealth Scientific and Industrial Research Organisation (CSIRO), Australia, for the data collection.
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This research is supported by the NSFC (Grant No. 41704002 and 42074036) and the Fundamental Research Funds for the Central Universities.
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Responsible Editor: Biswajeet Pradhan
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Wang, L., Wu, Z., Yang, J. et al. Performance of the non-iterative ToA-based positioning algorithms in complex indoor environments. Arab J Geosci 14, 700 (2021). https://doi.org/10.1007/s12517-021-06996-6
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DOI: https://doi.org/10.1007/s12517-021-06996-6