Search

This paper studies identification of linear systems with binary-valued observations generated via fixed thresholds. In addition to stochastic measurement noises, the systems are also subject to structural uncertainties, including deterministic unmodelled dynamics, nonlinear model mismatch, and sensor observation bias. Since binary-valued observations can supply only limited information on the signals, truncated empirical measures are introduced to extract further information for system identification. An effective identification algorithm is constructed based on the proposed empirical measures. Optimal identification errors, time complexity, optimal input design, and impact of disturbances, unmodelled dynamics, observation bias, and nonlinear model mismatch are thoroughly investigated in a stochastic information framework. Asymptotic upper and lower bounds are established on identification errors. Numerical experiments are presented to demonstrate the effectiveness of the algorithms and the main results. [ABSTRACT FROM PUBLISHER]

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]