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**Harvard**

Garcia-Fernandez, A., Svensson, L., Morelande, M. och Sarkka, S. (2015) *Posterior Linearization Filter: Principles and Implementation Using Sigma Points*.

** BibTeX **

@article{

Garcia-Fernandez2015,

author={Garcia-Fernandez, A. F. and Svensson, Lennart and Morelande, M. R. and Sarkka, S.},

title={Posterior Linearization Filter: Principles and Implementation Using Sigma Points},

journal={IEEE Transactions on Signal Processing},

issn={1053-587X},

volume={63},

issue={20},

pages={5561-5573},

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.},

year={2015},

keywords={Bayes' rule, Kalman filter, nonlinear filtering, sigma-points, statistical linear regression},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 224518

A1 Garcia-Fernandez, A. F.

A1 Svensson, Lennart

A1 Morelande, M. R.

A1 Sarkka, S.

T1 Posterior Linearization Filter: Principles and Implementation Using Sigma Points

YR 2015

JF IEEE Transactions on Signal Processing

SN 1053-587X

VO 63

IS 20

SP 5561

OP 5573

AB 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.

LA eng

DO 10.1109/tsp.2015.2454485

LK http://dx.doi.org/10.1109/tsp.2015.2454485

LK http://publications.lib.chalmers.se/records/fulltext/224518/local_224518.pdf

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