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

arXiv: https://arxiv.org/abs/2310.06287 · HTML: https://mlsanity.com/paper/2310.06287/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [Partial Excitation in Parameter Learning](https://mlsanity.com/paper/2503.02235/) (2025)

## Abstract (arXiv)

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.