A Unified Algorithmic Framework for Distributed Adaptive Signal and Feature Fusion Problems -- Part II: Convergence Properties

TL;DR

This paper analyzes the convergence properties of the distributed adaptive signal fusion (DASF) algorithm, providing conditions, proofs, and enhancements to ensure reliable distributed optimization in wireless sensor networks.

Contribution

It offers a comprehensive convergence analysis of the DASF algorithm, including new procedures to guarantee convergence under broader conditions.

Findings

Convergence conditions are rigorously established.

Procedures to ensure convergence when conditions are not met.

Applicability demonstrated on spatial filtering problems.

Abstract

This paper studies the convergence conditions and properties of the distributed adaptive signal fusion (DASF) algorithm, the framework itself having been introduced in a `Part I' companion paper. The DASF algorithm can be used to solve linear signal and feature fusion optimization problems in a distributed fashion, and is in particular well-suited for solving spatial filtering optimization problems encountered in wireless sensor networks. The convergence conditions and results are provided along with rigorous proofs and analyses, as well as various example problems to which they apply. Additionally, we describe procedures that can be added to the DASF algorithm to ensure convergence in specific cases where some of the technical convergence conditions are not satisfied.