Combined Filtering and Parameter Estimation for Discrete-time Systems Driven by Approximately White Gaussian Noise Disturbances

Runggaldier W & Visentin C (1988). Combined Filtering and Parameter Estimation for Discrete-time Systems Driven by Approximately White Gaussian Noise Disturbances. IFAC Proceedings Volumes 21 (9): 869-872. DOI:10.1016/S1474-6670(17)54838-7.

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Abstract

We consider a partially observable, discrete-time process{xt, θt, yt} over a finite horizon T, where the unobservable components are {xt, θt}. Conditionally on {θt}, the pair {xt}, {yt} satisfies a linear model of the form (1) below; {θt} itself evolves according to a given joint a-priori distribution p(θ0,…, θT), The purpose of the paper is to determine recursively the joint conditional distribution p(xt, θt|yt), (yt: = {y0,…,yt}), or, more specifically, E{f(xt, θt)|yt}, namely the (mean squre)optimal filter for a given When θtis constant our problem becomes that of the combined filtering and parameter estimation.

The optimal filter is computed for the ideal situation of white Gaussian noises and it is shown that, when this filter is applied to a more realistic situation where the noises are only approximately (in the sense of weak convergence of measures) white Gaussian and also {θt} has only approximately the given distribution p(θ0,…,θT), then it remains almost (mean-square) optimal with respect to all alternative filters that are continuous and bounded functions of the past observations.

Item Type: Article
Uncontrolled Keywords: Adaptive systems; Bayes methods; Discrete time systems; Nonlinear filtering; Parameter estimation; Robust procedures
Depositing User: Luke Kirwan
Date Deposited: 04 Jul 2017 12:53
Last Modified: 04 Jul 2017 12:53
URI: http://pure.iiasa.ac.at/14725

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