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

Decoding the `Nature Encoded\u27 Messages for Wireless Networked Control Systems

Because of low installation and reconfiguration cost wireless communication has been widely applied in networked control system (NCS). NCS is a control system which uses multi-purpose shared network as communication medium to connect spatially distributed components of control system including sensors, actuator, and controller. The integration of wireless communication in NCS is challenging due to channel unreliability such as fading, shadowing, interference, mobility and receiver thermal noise leading to packet corruption, packet dropout and packet transmission delay. In this dissertation, the study is focused on the design of wireless receiver in order to exploit the redundancy in the system state, which can be considered as a `nature encoding\u27 for the messages. Firstly, for systems with or without explicit channel coding, a decoding procedures based on Pearl\u27s Belief Propagation (BP), in a similar manner to Turbo processing in traditional data communication systems, is proposed to exploit the redundancy in the system state. Numerical simulations have demonstrated the validity of the proposed schemes, using a linear model of electric generator dynamic system. Secondly, we propose a quickest detection based scheme to detect error propagation, which may happen in the proposed decoding scheme when channel condition is bad. Then we combine this proposed error propagation detection scheme with the proposed BP based channel decoding and state estimation algorithm. The validity of the proposed schemes has been shown by numerical simulations. Finally, we propose to use MSE-based transfer chart to evaluate the performance of the proposed BP based channel decoding and state estimation scheme. We focus on two models to evaluate the performance of BP based sequential and iterative channel decoding and state estimation. The numerical results show that MSE-based transfer chart can provide much insight about the performance of the proposed channel decoding and state estimation scheme. In this dissertation, the study is focused on the design of wireless receiver in order to exploit the redundancy in the system state, which can be considered as a `nature encoding\u27 for the messages. Firstly, for systems with or without explicit channel coding, a decoding procedures based on Pearl\u27s Belief Propagation (BP), in a similar manner to Turbo processing in traditional data communication systems, is proposed to exploit the redundancy in the system state. Numerical simulations have demonstrated the validity of the proposed schemes, using a linear model of electric generator dynamic system. Secondly, we propose a quickest detection based scheme to detect error propagation, which may happen in the proposed decoding scheme when channel condition is bad. Then we combine this proposed error propagation detection scheme with the proposed BP based channel decoding and state estimation algorithm. The validity of the proposed schemes has been shown by numerical simulations. Finally, we propose to use MSE-based transfer chart to evaluate the performance of the proposed BP based channel decoding and state estimation scheme. We focus on two models to evaluate the performance of BP based sequential and iterative channel decoding and state estimation. The numerical results show that MSE-based transfer chart can provide much insight about the performance of the proposed channel decoding and state estimation scheme

Schedule Communication for Decentralized State Estimation

This paper considers decentralized state estimation subject to communication constraints. A group of agents measure the state of a process and obtain their state estimates by exchanging data with each other. Due to the communication constraint, only a few communication channels are available. The main objective of this paper is to allocate these channels among the agents so as to minimize their average estimation errors. We provide optimal allocation strategies for agents having the homogeneous and heterogeneous sensing capabilities, respectively