"On the- Filtering of Linear Stochastic Systems with Jumping Coefficients"

Abstract

The problem under consideration is the filtering of Markovian processes with jumping parameters. These systems are described by a linear Ito-equation with state /spl Xscr/ in which the coefficients are fed by a finite Markov chain process /spl theta/ describing the mode jumps. The state and /spl theta/-process are observed separatly in independent white noises. Under the reasonable assumption that the mode estimation is done quickly through an image-based sensor measurement, we first show the linear dependence between the state estimate and the initial condition; then we demonstrate that the mathematical expectation of /spl Xscr//sub 0/ can be obtained by minimizing a certain quadratic criterion. The resulting filter is finally applied to a simple example to show its efficiency in presence of dynamic model changes.