Asymptotic efficiency and probabilistic error bound for maximum likelihood‐based identification of finite impulse response systems with binary‐valued observations and unreliable communications

Abstract

SummaryThis article addresses the identification of finite impulse response systems with binary‐valued observations under packet losses and transmission errors. First, the maximum likelihood function of the available data sequence is derived, based on which the estimation algorithm for the unknown parameter vector is given. Then, by making full use of the statistical properties of communication uncertainty and system noise, the algorithm performance is established, including the strong convergence, the mean‐square convergence rate, and the asymptotic efficiency in terms of Cramér‐Rao low bound. Also the probabilistic upper bound and lower bound of the estimation error are presented. Finally, the validity and rationality of the results are verified by numerical simulation.