On Stability and Convergence of Distributed Filters

TL;DR

This paper revises the stability and convergence criteria for distributed filters, showing that they are equivalent to centralized filtering conditions, and validates these findings through Kalman filtering simulations.

Contribution

It introduces a general distributed filter framework and demonstrates that stability conditions match those of centralized filters, simplifying design criteria.

Findings

Stability conditions for distributed filters are equivalent to centralized filters.

A general distributed filter is constructed and analyzed.

Simulation validates the theoretical stability results.

Abstract

Recent years have bore witness to the proliferation of distributed filtering techniques, where a collection of agents communicating over an ad-hoc network aim to collaboratively estimate and track the state of a system. These techniques form the enabling technology of modern multi-agent systems and have gained great importance in the engineering community. Although most distributed filtering techniques come with a set of stability and convergence criteria, the conditions imposed are found to be unnecessarily restrictive. The paradigm of stability and convergence in distributed filtering is revised in this manuscript. Accordingly, a general distributed filter is constructed and its estimation error dynamics is formulated. The conducted analysis demonstrates that conditions for achieving stable filtering operations are the same as those required in the centralized filtering setting. Finally, the concepts are demonstrated in a Kalman filtering framework and validated using simulation examples.