A Friedland-Like Filtering Technique for Estimating Piecewise Constant Controls in Discrete Linear Stochastic Systems

We address discrete linear stochastic proposes in which the control variable takes unknown jumps at unknown times and remains constant between jumps. We present a three-stage Friedland-like filtering technique for obtaining the optimum estimates of the state and the control. A search procedure is presented which greatly reduces the number of times that the log likelihood ratio needs to be evaluated in locating its maximum. A generalized likelihood ratio (GLR) technique is outlined for detecting the jump time. It uses a decomposition of the maneuver signature matrix to greatly reduce the computational burden.