An approximate minimum mean-square error estimator for linear discrete time-varying systems: Handling Try-Once-Discard protocol

Abstract

This paper is concerned with the remote state estimation problem for a class of linear discrete time-varying stochastic systems under communication constraints. In order to mitigate the undesired phenomena of data collisions, a Try-Once-Discard (TOD) protocol is utilized to regulate the signal transmissions over the sensor-to-estimator communication channel, where the TOD protocol is based on the scheduling rule described by a specific switching function. Under the introduced TOD protocol, the approximate minimum mean-square error (MMSE) state estimation problem is investigated and a recursive algorithm is developed for the MMSE estimator design whose computational complexity is comparable to that of the conventional Kalman filter. Furthermore, some conditions are established for the boundedness of the estimation error covariance. A numerical example is presented to illustrate the effectiveness of the proposed MMSE estimator.