Diffusion recursive least-squares for distributed estimation over adaptive networks

TLDR

Distributed estimation over adaptive networks requires collaborative parameter estimation, yet centralized fusion centers consume excessive energy and incremental strategies necessitate a predefined network cycle. The authors propose a diffusion recursive least‑squares algorithm that enables nodes to communicate only with their nearest neighbors. The algorithm is diffusion RLS, is proven stable, its performance is analyzed against the centralized global solution, and optimal combination weights are derived. The diffusion RLS algorithm imposes no topology constraints, eliminates matrix transmissions or inversions, is stable, and achieves performance comparable to the centralized solution while reducing communication and computational complexity.

Abstract

We study the problem of distributed estimation over adaptive networks where a collection of nodes are required to estimate in a collaborative manner some parameter of interest from their measurements. The centralized solution to the problem uses a fusion center, thus, requiring a large amount of energy for communication. Incremental strategies that obtain the global solution have been proposed, but they require the definition of a cycle through the network. We propose a diffusion recursive least-squares algorithm where nodes need to communicate only with their closest neighbors. The algorithm has no topology constraints, and requires no transmission or inversion of matrices, therefore saving in communications and complexity. We show that the algorithm is stable and analyze its performance comparing it to the centralized global solution. We also show how to select the combination weights optimally.