Posterior Linearization Filter: Principles and Implementation Using Sigma Points

Garcia-Fernandez, Angel F ORCID: 0000-0002-6471-8455, Svensson, Lennart, Morelande, Mark R and Sarkka, Simo (2015) Posterior Linearization Filter: Principles and Implementation Using Sigma Points. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 63 (20). pp. 5561-5573.

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Abstract

This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples.

Item Type:	Article
Uncontrolled Keywords:	Bayes' rule, Kalman filter, nonlinear filtering, sigma-points, statistical linear regression
Depositing User:	Symplectic Admin
Date Deposited:	03 Jan 2018 11:46
Last Modified:	15 Mar 2024 13:55
DOI:	10.1109/TSP.2015.2454485
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3015335