  In this paper, we investigate the state estimation problem over multiple
Markovian packet drop channels. In this problem setup, a remote estimator
receives measurement data transmitted from multiple sensors over individual
channels. By the method of Markovian jump linear systems, an optimal stationary
estimator that minimizes the error variance in the steady state is obtained,
based on the mean-square (MS) stabilizing solution to the coupled algebraic
Riccati equations. An explicit necessary and sufficient condition is derived
for the existence of the MS stabilizing solution, which coincides with that of
the standard Kalman filter. More importantly, we provide a sufficient condition
under which the MS detectability with multiple Markovian packet drop channels
can be decoupled, and propose a locally optimal stationary estimator but
computationally more tractable. Analytic sufficient and necessary MS
detectability conditions are presented for the decoupled subsystems
subsequently. Finally, numerical simulations are conducted to illustrate the
results on the MS stabilizing solution, the MS detectability, and the
performance of the optimal and locally optimal stationary estimators.
