Robust Kalman filters based on the sub-Gaussian a-stable distribution

Hao, Pengcheng, Karakus, Oktay ORCID: https://orcid.org/0000-0001-8009-9319 and Achim, Alin 2024. Robust Kalman filters based on the sub-Gaussian a-stable distribution. Signal Processing 224 , 109574. 10.1016/j.sigpro.2024.109574 Item availability restricted.

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Abstract

Motivated by filtering tasks under a linear system with non-Gaussian heavy-tailed noise, various robust Kalman filters (RKFs) based on different heavy-tailed distributions have been proposed. Although the sub-Gaussian -stable (SG S) distribution captures heavy tails well and is applicable in various scenarios, its potential has not yet been explored for RKFs. The main hindrance is that there is no closed-form expression of its mixing density. This paper proposes a novel RKF framework, RKF-SG S, where the process noise is assumed to be Gaussian and the heavy-tailed measurement noise is modelled by the SG S distribution. The corresponding joint posterior distribution of the state vector and auxiliary random variables is approximated by the Variational Bayesian approach. Also, four different minimum mean square error (MMSE) estimators of the scale function are presented. The first two methods are based on the Importance Sampling (IS) and Gauss–Laguerre quadrature (GLQ), respectively. In contrast, the last two estimators combine a proposed Gamma series (GS) based method with the IS and GLQ estimators and hence are called GSIS and GSGL. Besides, the RKF-SG S is compared with the state-of-the-art RKFs under three kinds of heavy-tailed measurement noises, and the simulation results demonstrate its estimation accuracy and efficiency.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Publisher:	Elsevier
ISSN:	0165-1684
Funders:	N/A
Date of First Compliant Deposit:	6 August 2024
Date of Acceptance:	7 June 2024
Last Modified:	08 Nov 2024 16:15
URI:	https://orca.cardiff.ac.uk/id/eprint/171220

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