Generalized pseudo-Bayes estimation and detection for abruptly changing systems

The problem of state estimation and system-structure detection for linear discrete-time systems with unknown parameters which may switch among a finite set of values is considered. The switching parameters are modeled by a Markov chain with known transition probabilities. Since the optimal solutions require exponentially growing storage and computations with time, a new method of generalized pseudo-Bayes algorithm (GPBA) is proposed to circumvent this problem by using a multi-stage measurement update technique. A minor modification is also presented to correct a defect of the Jaffer and Gupta method. Some simulation comparisons are included to illustrate the effectiveness of the proposed algorithms. It is then shown that, as compared with other GPBAs, a feature of the present GPBA is that it noticeably decreases the size of the required memory when the number of states in the Markov chain is large. The cost to be paid is a slight increase in the computing time.