Overbounding Sequential Estimation Errors Due to Non-Gaussian Correlated Noise

Steven Langel, Omar García Crespillo, Mathieu Joerger

Abstract:	In this paper, we develop, analyze, and implement a new recursive method to conservatively account for non-Gaussian measurement errors with an uncertain correlation structure in Kalman filters (KFs). Under the assumptions of symmetric overbounding, the method guarantees a CDF overbound on the entire KF estimation error distribution. First, we leverage previous work on symmetric overbounding and frequency-domain overbounding to show how to transform a measurement domain CDF overbound into a position domain overbound. The second part of the paper evaluates the proposed method through Monte Carlo simulation for a GPS-based position estimation problem. Specifically, we show that while frequency domain overbounding produces a position domain overbound for Gaussian noise with an uncertain correlation structure, combination with symmetric overbounding is required to ensure position domain overbounding for non-Gaussian correlated noise.
Published in:	Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020) September 21 - 25, 2020
Pages:	1054 - 1067
Cite this article:	Langel, Steven, Crespillo, Omar García, Joerger, Mathieu, "Overbounding Sequential Estimation Errors Due to Non-Gaussian Correlated Noise," Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020), September 2020, pp. 1054-1067. https://doi.org/10.33012/2020.17576
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