Optimal Stationary State Estimation Over Multiple Markovian Packet Drop Channels

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

Remote State Estimation with Smart Sensors over Markov Fading Channels

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 $\rho^2(\mathbf{A})\rho(\mathbf{DM})<1$, where $\rho(\cdot)$ denotes the spectral radius, $\mathbf{A}$ is the state transition matrix of the LTI system, $\mathbf{D}$ is a diagonal matrix containing the packet drop probabilities in different channel states, and $\mathbf{M}$ 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 $\mathbf{M}$. 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