An Alternative Look at the Constant-Gain Kalman Filter for State Estimation Over Erasure Channels

This technical note studies state estimation problems subject to data loss. We consider a class of switched estimators, where missing data is replaced by optimal estimates. The considered class of estimators encompasses a number of estimation schemes proposed in the literature. We show that the estimator that minimizes the steady-state estimation error covariance within that class, is given by a constant-gain Kalman filter which was previously proposed as an alternative to the Kalman filter with intermittent observations. As a by-product of our results, we derive expressions that allow one to compare, analytically, popular suboptimal data-dropout compensation mechanisms.