Decentralized consensus finite-element Kalman filter for field estimation

TL;DR

This paper introduces a scalable decentralized finite-element Kalman filter for spatially distributed systems, enabling efficient field estimation through domain decomposition, local filtering, and iterative consensus, with proven stability and demonstrated effectiveness.

Contribution

It presents a novel decentralized Kalman filtering approach combining finite element spatial discretization and the parallel Schwarz method for consensus, with stability proof and simulation validation.

Findings

Proven stability of the distributed filter.

Effective temperature field estimation demonstrated.

Scalable approach suitable for large spatial domains.

Abstract

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.