We consider a fundamental remote state estimation problem of discrete-time
linear time-invariant (LTI) systems. A smart sensor forwards its local state
estimate to a remote estimator over a time-correlated M-state Markov fading
channel, where the packet drop probability is time-varying and depends on the
current fading channel state. We establish a necessary and sufficient condition
for mean-square stability of the remote estimation error covariance as
ρ2(A)ρ(DM)<1, where ρ(⋅) denotes the
spectral radius, A is the state transition matrix of the LTI system,
D is a diagonal matrix containing the packet drop probabilities in
different channel states, and M is the transition probability matrix
of the Markov channel states. To derive this result, we propose a novel
estimation-cycle based approach, and provide new element-wise bounds of matrix
powers. The stability condition is verified by numerical results, and is shown
more effective than existing sufficient conditions in the literature. We
observe that the stability region in terms of the packet drop probabilities in
different channel states can either be convex or concave depending on the
transition probability matrix M. Our numerical results suggest that
the stability conditions for remote estimation may coincide for setups with a
smart sensor and with a conventional one (which sends raw measurements to the
remote estimator), though the smart sensor setup achieves a better estimation
performance.Comment: The paper has been accepted by IEEE Transactions on Automatic
Control. Copyright may be transferred without notice, after which this
version may no longer be accessibl