On observability and optimal gain design for distributed linear filtering and prediction

TL;DR

This paper introduces a novel distributed filtering algorithm that combines consensus and innovations, leveraging a new weaker notion of observability to optimize estimation accuracy in sparse multi-agent sensor networks.

Contribution

It proposes a new distributed observability concept and derives optimal gain matrices via a distributed algebraic Riccati equation for improved filtering.

Findings

The proposed algorithm outperforms existing methods in sparse networks.

Optimal gains minimize mean-squared estimation error.

Distributed observability is weaker than traditional assumptions.

Abstract

This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by the consensus+innovations type of distributed estimation approaches, this paper proposes a novel algorithm that fuses the concepts of consensus and innovations. The paper introduces a definition of distributed observability, required by the proposed algorithm, which is a weaker assumption than that of global observability and connected network assumptions combined together. Following first principles, the optimal gain matrices are designed such that the mean-squared error of estimation is minimized at each agent and the distributed version of the algebraic Riccati equation is derived for computing the gains.