Stability of FFLS-based diffusion adaptive filter under a cooperative excitation condition

TL;DR

This paper introduces a distributed FFLS algorithm for sensor networks to track time-varying parameters, providing stability analysis under cooperative excitation and Markovian switching graphs without relying on independence or stationarity assumptions.

Contribution

The paper presents a novel distributed FFLS algorithm with stability analysis under cooperative excitation and Markovian switching graphs, extending existing theory to non-independent, non-stationary data.

Findings

Stability of the proposed FFLS algorithm is established under cooperative excitation.

Theoretical results are generalized to Markovian switching directed graphs.

Analysis techniques include stability theory, algebraic graph theory, and Markov chain theory.

Abstract

In this paper, we consider the distributed filtering problem over sensor networks such that all sensors cooperatively track unknown time-varying parameters by using local information. A distributed forgetting factor least squares (FFLS) algorithm is proposed by minimizing a local cost function formulated as a linear combination of accumulative estimation error. Stability analysis of the algorithm is provided under a cooperative excitation condition which contains spatial union information to reflect the cooperative effect of all sensors. Furthermore, we generalize theoretical results to the case of Markovian switching directed graphs. The main difficulties of theoretical analysis lie in how to analyze properties of the product of non-independent and non-stationary random matrices. Some techniques such as stability theory, algebraic graph theory and Markov chain theory are employed to deal with the above issue. Our theoretical results are obtained without relying on the independency or stationarity assumptions of regression vectors which are commonly used in existing literature.