On network topology reconfiguration for remote state estimation

In this paper, we investigate network topology reconfiguration in wireless sensor networks for remote state estimation, where sensor observations are transmitted, possibly via intermediate sensors, to a central gateway/estimator. The time-varying wireless network environment is modelled by the notion of a network state process, which is a randomly time-varying semi- Markov chain and determines the packet reception probabilities of links at different times. For each network state, different network configurations can be used, which govern the network topology and routing of packets. The problem addressed is to determine the optimal network configuration to use in each network state, in order to minimize an expected error covariance measure. Computation of the expected error covariance cost function has a complexity of O(2MΔmax ), where M is the number of sensors and Δmax is the maximum time between transitions of the semi- Markov chain. A sub-optimal method which minimizes the upper bound of the expected error covariance, that can be computed with a reduced complexity of O(2M ), is proposed, which in many cases gives identical results to the optimal method. Conditions for estimator stability under both the optimal and suboptimal reconfiguration methods are derived using stochastic Lyapunov functions. Numerical results and comparisons with other low complexity approaches demonstrate the performance benefits of our approach