Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model

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 e...

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Main Authors: Pasha, S., Tuan, H., Vo, Ba-Ngu
Format: Journal Article
Published: I E E E 2010
Subjects:
Online Access:http://hdl.handle.net/20.500.11937/29881
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author Pasha, S.
Tuan, H.
Vo, Ba-Ngu
author_facet Pasha, S.
Tuan, H.
Vo, Ba-Ngu
author_sort Pasha, S.
building Curtin Institutional Repository
collection Online Access
description 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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institution Curtin University Malaysia
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publishDate 2010
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spelling curtin-20.500.11937-298812017-09-13T15:28:02Z Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model Pasha, S. Tuan, H. Vo, Ba-Ngu nonlinear model linear fractional transformation Bayesian filtering 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. 2010 Journal Article http://hdl.handle.net/20.500.11937/29881 10.1109/TSP.2009.2028950 I E E E restricted
spellingShingle nonlinear model
linear fractional transformation
Bayesian filtering
Pasha, S.
Tuan, H.
Vo, Ba-Ngu
Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model
title Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model
title_full Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model
title_fullStr Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model
title_full_unstemmed Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model
title_short Nonlinear Bayesian Filtering Using the Unscented Linear Fractional Transformation Model
title_sort nonlinear bayesian filtering using the unscented linear fractional transformation model
topic nonlinear model
linear fractional transformation
Bayesian filtering
url http://hdl.handle.net/20.500.11937/29881