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    Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model

    Access Status
    Fulltext not available
    Authors
    Pasha, S.
    Tuan, H.
    Vo, Ba-Ngu
    Date
    2010
    Type
    Journal Article
    
    Metadata
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    Citation
    Pasha, S. and Tuan, H. and Vo, B. 2010. Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model. IEEE Transactions on Signal Processing. 58 (2): pp. 477-489.
    Source Title
    IEEE Transactions on Signal Processing
    DOI
    10.1109/TSP.2009.2028950
    ISSN
    1053-587X
    URI
    http://hdl.handle.net/20.500.11937/29881
    Collection
    • Curtin Research Publications
    Abstract

    For nonlinear state space model involving random variables with arbitrary probability distributions, the state estimation given a sequence of observations is based on an appropriate criterion such as the minimum mean square error (MMSE). This leads to linear approximation in the state space of the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), which work reasonably well only for mildly nonlinear systems. We propose a Bayesian filtering technique based on the MMSE criterion in the framework of the virtual linear fractional transformation (LFT) model, which is characterized by a linear part and a simple nonlinear structure in the feedback loop. LFT is an exact representation for any differentiable nonlinear mapping, so the virtual LFT model is amenable to a wide range of nonlinear systems. Simulation results demonstrate that the proposed filtering technique gives better approximation and tracking performance than standard methods like the UKF. Furthermore, for highly nonlinear systems where UKF diverges, the LFT model estimates the conditional mean with reasonable accuracy.

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