Paired Cauchy-Gaussian Overbound for not Symmetric Unimodal Heavy-Tailed Distributions

Zhengdao Li, Penggao Yan, Weisong Wen, and Li-Ta Hsu

Peer Reviewed

Abstract:	Overbounds of heavy-tailed measurement errors are essential to meet stringent navigation requirements in integrity monitoring applications. This paper proposes the paired Cauchy-Gaussian overbound to bound not symmetric unimodal (n.s.u.) heavy-tailed measurement errors, which combines the sharp bounding performance of the Cauchy distribution at the core region and the Gaussian distribution at the tail region. A systematic procedure is developed to determine the optimal parameters for the paired Cauchy-Gaussian overbound for empirical error distributions. Moreover, the overbounding properties of the paired Cauchy-Gaussian overbound is proven to be preservable through convolution, making it possible to rigorously derive the positioning error bound. The bounding performance of the proposed method is compared with the two-step Gaussian overbound through a simulated heavy-tailed n.s.u. error dataset and a real-world urban error dataset. For both datasets, the paired Cauchy-Gaussian overbound can generate sharper bounding at both core and tail regions. In the position domain, the average percentage of reduction in vertical protection level (VPL) given by the proposed method reaches over 20% for the simulated dataset and approximately 15% for the urban dataset. Index Terms—Overbounding techniques, Heavy-tailed distributions, Cauchy distribution, Global navigation satellite system.
Published in:	2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) April 28 - 1, 2025 Salt Lake Marriott Downtown at City Creek Salt Lake City, UT
Pages:	214 - 225
Cite this article:	Li, Zhengdao, Yan, Penggao, Wen, Weisong, Hsu, Li-Ta, "Paired Cauchy-Gaussian Overbound for not Symmetric Unimodal Heavy-Tailed Distributions," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 214-225.
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