  The paper deals with decentralized state estimation for spatially distributed
systems described by linear partial differential equations 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.
Stability of the proposed distributed consensus-based finite element Kalman
filter is mathematically proved and its effectiveness is demonstrated via
simulation experiments concerning the estimation of a bi-dimensional
temperature field.
