Tracking and identification of regime-switching systems using binary sensors

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.

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