An Adaptive Linear Approach to Nonlinear Filtering
Giovanni B. Di Masi, Wolfgang J. Runggaldier · 1989
A nonlinear filtering problem is considered for a dynamic model with piecewise linear coefficient and with initial condition and disturbances distributed according to finite mixtures of normal distributions. It is shown that, for vanishing variances of the normal distributions relative to the signal process, the infinite-dimensional optimal filter coincides with the finite dimensional filter for a suitably defined adaptive linear model. The results obtained illustrate, in the particular situation considered here, the relevance of adaptive linear techniques for the approximation of optimal nonlinear filters.