Kalman filtering with state‐dependent packet losses

This study addresses the problem of state estimation for discrete‐time, linear time invariant systems subject to packet losses, which occur in specific regions of the state space. Most practical estimation problems are characterised by occurrences of loss of observation packets, which makes the packet arrival process a non‐stationary statistic, making the analysis and design of such an estimator challenging. This estimation problem subject to state‐dependent packet losses is formulated using a state‐dependent hybrid measurement model and solved using the projection theorem‐based approach to obtain minimum mean square error state estimates. By systematically utilising the a priori information of the regions where the packet loss is likely to occur, the proposed estimator takes the Kalman filter structure with the modified algebraic Riccati iteration for the error covariance matrix being stochastic due to the probabilistic packet arrival process. Finally, the proposed estimator is demonstrated using an illustrative two‐dimensional aircraft tracking example with state‐dependent packet loss and is shown to have improved performance over the baseline packet loss algorithm.