NEW CLASSES OF FINITE DIMENSIONAL FILTERS WITH NONMAXIMAL RANK ESTIMATION ALGEBRA ON STATE DIMENSION n AND LINEAR RANK n-2

摘要

Ever since the Kalman filter technique was popularized, there has been an abundance of interest in finding new classes of finite dimensional recursive filters. In this paper, by applying Wong's theorem [W. S. Wong, Systems Control Lett, 9 (1987), pp. 79-83], we construct a new class of finite dimensional filters with arbitrary state space dimension n and linear rank n - 2. Importantly, we show that in the new class of nonlinear filtering systems, the entries of Wong's Omega-matrix need not be constants or polynomials and can be C-infinity functions.