Linear filtering in the presence of time-varying bias

Abstract

The problem of estimating the state of a linear system subjected to a time-varying bias with sample paths generated from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\dot{b} = F^{\astr}b</tex> is considered, and an optimal filtering algorithm is derived. It is shown that the structure of the optimal estimator is the same as that determined earlier by Friedland for constant bias disturbances, and that the algorithm possesses the same computational advantages over the augmented Kalman-Bucy filter.