Steady State Distributed Kalman Filter

TL;DR

This paper develops an optimal fixed-gain distributed Kalman filter for steady-state estimation in wireless sensor networks, offering improved accuracy and simplicity over existing methods.

Contribution

It introduces a novel offline computation of fixed observer gains based on the asymptotic error covariance, enabling efficient local estimation without online covariance exchange.

Findings

Achieves optimal asymptotic performance among fixed-gain schemes.

Yields lower steady-state error covariance compared to covariance intersection methods.

Demonstrates effectiveness through numerical simulations showing improved accuracy and simplicity.

Abstract

This paper addresses the synthesis of an optimal fixed-gain distributed observer for discrete-time linear systems over wireless sensor networks. The proposed approach targets the steady-state estimation regime and computes fixed observer gains offline from the asymptotic error covariance of the global distributed BLUE estimator. Each node then runs a local observer that exchanges only state estimates with its neighbors, without propagating error covariances or performing online information fusion. Under collective observability and strong network connectivity, the resulting distributed observer achieves optimal asymptotic performance among fixed-gain schemes. In comparison with covariance intersection-based methods, the proposed design yields strictly lower steady state estimation error covariance while requiring minimal communication. Numerical simulations illustrate the effectiveness of the approach and its advantages in terms of accuracy and implementation simplicity.