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Posterior Linearization Filter: Principles and Implementation Using Sigma Points

A. F. Garcia-Fernandez ; Lennart Svensson (Institutionen för signaler och system, Signalbehandling) ; M. R. Morelande ; S. Sarkka
IEEE Transactions on Signal Processing (1053-587X). Vol. 63 (2015), 20, p. 5561-5573.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Bayes' rule, Kalman filter, nonlinear filtering, sigma-points, statistical linear regression



Denna post skapades 2015-10-21. Senast ändrad 2016-07-21.
CPL Pubid: 224518

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Signalbehandling

Ämnesområden

Signalbehandling

Chalmers infrastruktur