Moving horizon least-squares input estimation for linear discrete-time

Abstract This paper presents a novel moving horizon least-squares input estimation method for linear discrete-time stochastic systems. For systems with completely unknown initial state and no unstable zeros, some existing work showed that asymptotic input reconstruction is possible in the absence of noises. However, under the same condition but with stochastic noises, most existing input estimators, which are designed to optimally deal with noises, fail to ensure asymptotic unbiasedness. In order to address this limitation for linear discrete-time stochastic systems, we characterize necessary and sufficient conditions for input observability and detectability, and propose a moving horizon least-squares input estimator. Based on the conditions for input observability and detectability, it is proved that our proposed input estimator gives an asymptotically unbiased estimate and has minimal estimation error variance over all linear asymptotically unbiased input estimators. Its effectiveness is illustrated by simulation examples involving aircraft sensor and actuator faults.