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Register a new userOptimal Stationary State Estimation Over Multiple Markovian Packet Drop Channels
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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.
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We consider remote state estimation of multiple discrete-time linear time-invariant (LTI) systems over multiple wireless time-varying communication channels. Each system state is measured by a sensor, and the measurements from sensors are sent to a remote estimator over the shared wireless channels in a scheduled manner. We answer the following open problem: what is the fundamental requirement on the multi-sensor-multi-channel system to guarantee the existence of a sensor scheduling policy that can stabilize the remote estimation system? To tackle the problem, we propose a novel policy construction method, and develop a new analytical approach by applying the asymptotic theory of spectral radii of products of non-negative matrices. A necessary and sufficient stability condition is derived in terms of the LTI system parameters and the channel statistics, which is more effective than existing sufficient conditions available in the literature. Explicit scheduling policies with stability guarantees are presented as well. We further extend the analytical framework to cover remote estimation with four alternative network setups and obtain corresponding necessary and sufficient stability conditions.
Although state estimation in networked control systems is a fundamental problem, few efforts have been made to study distributed state estimation via multiple access channels (MACs). In this article, we give a characterization of the zero-error capacity region of an M-input, single-output MAC at any finite block-length. To this end, nonstochastic information-theoretic tools are used to derive the converse and achievability proofs. Next, a tight condition to be able to achieve uniformly bounded state estimation errors over such a MAC is provided. The obtained condition establishes a connection between the intrinsic topological entropies of the linear systems and the zero-error capacity region of the MAC.
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Estimating the occurrence of packet losses in a networked control systems (NCS) can be used to improve the control performance and to detect failures or cyber-attacks. This study considers simultaneous estimation of the plant state and the packet loss occurrences at each time step. After formulation of the problem, two solutions are proposed. In the first one, an input-output representation of the NCS model is used to design a recursive filter for estimation of the packet loss occurrences. This estimation is then used for state estimation through Kalman filtering. In the second solution, a state space model of NCS is used to design an estimator for both the plant state and the packet loss occurrences which employs a Kalman filter. The effectiveness of the solutions is shown during an example and comparisons are made between the proposed solutions and another solution based on the interacting multiple model estimation method.
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.
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