Stability analysis for Kalman filtering in a muti-hop network

In this paper, we consider the stability properties for Kalman filtering in a multi-hop network. A time-homogeneous Markov chain is used to characterize the packet loss phenomenon of each relay. Since, after several relays, the average expected estimation error covariance at the terminal is difficult to calculate, we derive lower and upper bounds for the average value. Using these bounds, it is found that the stability is related to one special entry in the channel´s transition probability matrix, from which we obtain a necessary and sufficient condition for the stability of the single-hop case and extend the result to the multi-hop one.