Asymptotic Analysis for Piecewise Linear Filtering

Di Masi, G.B. & Runggaldier, W.J. (1987). Asymptotic Analysis for Piecewise Linear Filtering. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-87-053

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Abstract

A discrete-time nonlinear filtering problem with piecewise linear coefficients and not necessarily Gaussian disturbances is considered. It is shown that it possesses asymptotic properties that coincide with the analogous properties of a filtering problem for a suitably randomized linear model which admits a finite-dimensional solution. The asymptotic properties are connected to the behavior of the nonlinear filters when some parameters of the distribution of the initial condition and of the signal disturbances become small. These asymptotic properties allow to consider the finite-dimensional filter as an approximate solution to the original problem. It can in fact be shown that, asymptotically, the original and the approximate models have the same conditional moments and, in particular, the same conditional mean square errors.

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