Recursive state estimation for nonlinear systems with missing measurements and filter‐and‐forward relays

Abstract This paper studies the state estimation problem for nonlinear systems with missing measurements and filter‐and‐forward relays. By introducing stochastic variables obeying the Bernoulli distribution, the phenomenon of randomly occurring missing measurements is taken into consideration. The filter‐and‐forward relay is implemented in the channel from the sensor to the remote estimator, enhancing the quality of signal transmission. A matrix‐inequality‐based approach is proposed to design the filter in the filter‐and‐forward relay under which the filtering error in the relay is ensured to be ultimately bounded. Subsequently, a recursive estimator is built by employing the extended Kalman filter method. An upper bound on the estimation error covariance is derived by solving Riccati‐like difference equations and is then minimized by choosing an appropriate estimator gain. Finally, the validity of the estimation method is verified through two examples.