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

摘要

We consider discrete linear stochastic processes in which the control variables take unknown jumps at unknown times and remain constant between jumps. A GLR algorithm is presented for detecting the jump time. The advent of the tri-filter technique together with the reinitialization procedure makes it unnecessary to augment the state x with the control u and to use augmented state filters in the estimation of state and piecewise constant controls. The new GLR algorithm avoids, therefore, computational problems that may be associated with processing large matrices in augmented state filters. It uses only unaugmented state filters and, consequently, it has particular application to problems involving a large number of state and/or jump variables.