On the steady-state error covariance matrix of Kalman filtering with intermittent observations in the presence of correlated noises at the same time

Recent problems in state estimation focusing on estimating the state of a dynamical system using sensor measurements that are transmitted over unreliable communication link. The embedded ideas for analyzing such systems were proposed in[3] and called Kalman filtering with intermittent observations. Unfortunately, to date, the tools for analyzing such system are woefully lacking when dealing with real time applications, because the earlier system tools are restricted to independent noises or correlated noises at one time step apart. In this paper, we consider a discrete time linear system state estimation problem across a lossy network when the process and measurement noises were assume to be correlated to each other at the same time, and we find minimum packet arrival rate that grantees certain performance at the remote estimator. Kalman filtering algorithm were used as an optimal estimator to estimate the system state. The prediction and update cycles of standard Kalman filter algorithm were reformulated to be applicable in the new system that we consider. The prediction cycle were found to be not affected by the random loss of measurements but affected by the correlated noises. We also show that the filtering update cycle were depend on both loss of measurements and correlated noises at the same time. Minimum packet arrival rate were recorded and tabulated with respect to the estimation error covariance which used as the performance criterion. As a result, we show that when measurements are subject to random losses in the case of correlated noises at the same time, the covariance of the estimation error of a state estimator becomes a random variable. We then derive conditions on channel parameters that meet this metric in the case of scalar systems. Examples are provided to illustrate the theories and algorithms developed and numerical simulations show that the proposed method provides tighter results than the ones available in the literature.