Autori
Giorgio Battistelli, Luigi Chisci and Nicola Forti
Abstract
This work deals with fundamental challenges underlying state estimation of spatially distributed systems, described by linear partial differential equations, monitored by wireless sensor networks. First, we address decentralized state estimation from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A fully scalable approach is pursued by decomposing the domain into overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional Kalman filter which exploits the finite element approach for spatial discretization and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains. Both numerical stability of the finite-element approximation and exponential stability of the proposed consensus finite-element Kalman filter have been analysed. Moreover, optimization-based strategies capable of dealing with physical constraints on state and noise variables, are proposed in the case of dynamic field estimation with binary measurements. In addition, point source estimation i.e. the problem of detecting and localizing a concentrated diffusive source as well as estimating its intensity and induced field, is addressed and a novel multiple model filtering approach to source estimation is presented. A further challenge addressed is the design of secure estimation strategies for such monitoring systems that can be subject to cyber-physical attacks.
