Stability of Kalman Filtering with Multiple Sensors Involving Lossy Communications

We study a networked state estimation problem for a linear system with multiple sensors, each of which transmits its measurements to a central estimator via a lossy communication network for computing the minimum mean-square-error (MMSE) state estimate. Under a general Markov packet loss process, we establish necessary and sufficient conditions for the stability of the estimator for any diagonalizable system in the sense that the mean of the state estimation error covariance matrix is uniformly bounded. For the second-order systems under an i.i.d. packet loss model, the stability condition is expressed as a simple inequality in terms of open-loop poles and the packet loss rate.