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    Posterior Linearization Filter: Principles and Implementation Using Sigma Points

    Access Status
    Open access via publisher
    Authors
    Garcia-Fernandez, Angel
    Svensson, Lennart
    Morelande, M.
    Sarkka, S.
    Date
    2015
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Garcia-Fernandez, A. and Svensson, L. and Morelande, M. and Sarkka, S. 2015. Posterior Linearization Filter: Principles and Implementation Using Sigma Points. IEEE Transactions on Signal Processing. 63 (20): pp. 5561-5573.
    Source Title
    IEEE TRANSACTIONS ON SIGNAL PROCESSING
    DOI
    10.1109/TSP.2015.2454485
    Additional URLs
    https://research.chalmers.se/publication/224518
    ISSN
    1053-587X
    School
    Department of Electrical and Computer Engineering
    Funding and Sponsorship
    http://purl.org/au-research/grants/arc/DP130104404
    URI
    http://hdl.handle.net/20.500.11937/5634
    Collection
    • Curtin Research Publications
    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.

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