Kalman Filtering over the Random Delay and Packet Drop Channel

This paper studies the steady-state Kalman filtering over the random delay and packet drop channel, motivated by the state estimation in wireless sensor networks and networked control systems. Such systems induce both packet drops and time-varying delays. Assuming the Bernoulli processes for random delays and packet drops and enforcing nonrepetitive observations, we show that the channel states associated with random delays and packet drops form a finite Markov chain, and can thus be modeled as a finite state discrete Markov process. Furthermore, the composite system consisting of the process model and output communication channels results in a special type of the Markov jump linear systems. Design results for the steady-state Kalman filter over the channel of random delays and packet drops are presented, including the stabilizability and detectability conditions in the mean-square sense. The steady-state Kalman filtering results over the random delay and packet drop channel are illustrated by a numerical example.