On the Implementation of Reduced Sub-Optimal Kalman Filters, for Discrete, Linear, Stochastic Processes with Time-Invariant Dynamics

摘要

Three different approaches to the problem of implementing a reduced-order, sub-optimal Kalman filter for a discrete, linear stochastic process, with time-invariant dynamics, are presented. A first method, A, is based upon the partitioning of the system dynamics. A second method, B, is implemented using matrix pseudo-inversion and a third method, C, is based upon reduction of the original process to one of lower order using the dominant roots of the system. An expression for the performance degradation in method A is derived. In method B, expression for the sub-optimal estimation error, and sub-optimal variance of estimation error are derived. The several methods are applied to a fourth-order process for illustration. (Author)