Distributed interpolatory algorithms for set membership estimation

TL;DR

This paper introduces distributed algorithms for set membership estimation that ensure convergence to a feasible parameter set in networks with bounded measurement errors, demonstrated through a linear regression example.

Contribution

It presents novel distributed projection-based algorithms that are proven to asymptotically estimate parameters within the global feasible set under convexity assumptions.

Findings

Algorithms converge to a point in the global feasible set.

Demonstrated effectiveness on distributed linear regression.

Proved asymptotic properties under convexity assumptions.

Abstract

This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a suitable feasible set. Two distributed algorithms are considered, based on projections of the estimate of each agent onto its local feasible set. The main contribution of the paper is to show that such algorithms are asymptotic interpolatory estimators, i.e. they converge to an element of the global feasible set, under the assumption that the feasible set associated to each measurement is convex. The proposed techniques are demonstrated on a distributed linear regression estimation problem.