Search

Abstract: This paper is concerned with persistent system identification for plants that are equipped with binary sensors whose unknown parameter is a random process represented by a Markov chain. We treat two classes of problems. In the first class, the parameter is a stochastic process modeled by an irreducible and aperiodic Markov chain with transition rates sufficiently faster than adaptation rates of identification algorithms. In this case, an averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and can be estimated with empirical measures. Upper and lower error bounds are established that explicitly show impact of unmodeled dynamics. In the second class of problems, the state switches values infrequently. A moving-window maximum a posterior (MAP) algorithm is introduced for tracking the time-varying parameters. Numerical results are presented to illustrate the tracking performance of the MAP algorithm and compare it with the widely used Viterbi algorithm. [Copyright &y& Elsevier]

Abstract: This work is concerned with tracking and system identification for time-varying parameters. The parameters are Markov chains and the observations are binary valued with noise corruption. To overcome the difficulties due to the limited measurement information, Wonham-type filters are developed first. Then, based on the filters, two popular estimators, namely, mean squares estimator (MSQ) and maximum posterior (MAP) estimator are constructed. For the mean squares estimator, we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation. The asymptotic normality is then used to derive error bounds. When the Markov chain is infrequently switching, we derive error bounds for MAP estimators. When the Markovian parameters are fast varying, we show that the averaged behavior of the parameter process can be derived from the stationary measure of the Markov chain and that can be estimated using empirical measures. Upper and lower error bounds on estimation errors are also established. [Copyright &y& Elsevier]