Stochastic Stability Condition for the Extended Kalman Filter with Intermittent Observations

In order to tackle the intermittent observations, this brief addresses the stochastic stability problem of the extended Kalman filter by means of analyzing the prediction error covariance matrix (PECM) and the estimation error performance of the estimator. With the transmitted measurement output of the filter modeled as a Bernoulli process, the existence of a crucial arrival rate is proved such that the PECM is mean bounded when the arrival rate exceeds a threshold value. Moreover, offline sufficient conditions for the stochastic stability of the estimation error are also derived. A numerical example is given to demonstrate the feasibility of the proposed method.