Bounding the Heavy-Tailed Pseudorange Error by Leveraging Membership Weights Analysis of Gaussian Mixture Model

Penggao Yan, Yihan Zhong, and Li-Ta Hsu

Peer Reviewed

Abstract:	In integrity monitoring applications, a sharp yet conservative overbound for heavy-tailed error distribution is essential to meet the strict availability and continuity requirements. This paper proposes the Principal Gaussian overbound for heavy-tailed error distributions by leveraging the membership weights analysis of the Gaussian Mixture model. We prove that the overbounding property of the Principal Gaussian overbound is preserved through convolution, enabling the derivation of pseudorange-level requirements from position domain integrity requirements. On both the worldwide simulated dataset and the real-world urban dataset, the Principal Gaussian overbound provides a sharp bound in both the core and tail parts of the error distribution. In addition, the proposed method can lead to a significantly smaller vertical protection level (VPL) than the two-step Gaussian overbounding method on both datasets. Notably, the mean VPL is reduced by more than 53 % when compared to the two-step Gaussian overbounding method in the urban dataset. We further employ the fast Fourier transforms to reduce the computation time of protection levels, where the mean computation time of VPL is only 0.03 s with nine measurements in the urban dataset, suggesting the substantial potential of the Principal Gaussian overbound in meeting the stringent integrity and real-time requirements of global navigation satellite system (GNSS) applications.
Published in:	Proceedings of the ION 2024 Pacific PNT Meeting April 15 - 18, 2024 Hilton Waikiki Beach Honolulu, Hawaii
Pages:	541 - 555
Cite this article:	Yan, Penggao, Zhong, Yihan, Hsu, Li-Ta, "Bounding the Heavy-Tailed Pseudorange Error by Leveraging Membership Weights Analysis of Gaussian Mixture Model," Proceedings of the ION 2024 Pacific PNT Meeting, Honolulu, Hawaii, April 2024, pp. 541-555. https://doi.org/10.33012/2024.19604
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