Optimal reduced-order filtering

Abstract

An optimal reduced-order filter is developed which can provide a full vector of state estimates for the case where the dimension of the measurement vector is smaller than that of the state vector and no measurements are noise-free. The reduced-order filter consists of an observer type subfilter and a complementary subfilter, each of which provides a subset of the optimal estimate. A two-step L-K transformation is employed to minimize the estimate error covariance of each subfilter. A target tracking problem is studied as an example.<>