A variable forgetting factor diffusion recursive least squares algorithm for distributed estimation

Distributed recursive least squares (RLS) algorithms have superior convergence properties compared to the least mean squares (LMS) counterpart. However, with a fixed forgetting factor (FF), they are not suitable for tracking time-varying (TV) parameters. This paper proposes a novel diffusion variable FF RLS (Diff-VFF-RLS) algorithm based on a local polynomial modeling (LPM) of the unknown TV system. The diffusion RLS solution is derived analytically such that the estimation deviation from the true value is investigated. Based on the analysis and the LPM of the TV system, a new optimal VFF formula that tries to minimize the estimation deviation is obtained. Simulations are conducted to verify the theoretical analysis in terms of the steady-state mean square deviation (MSD) and the VFF formula. Results also show that the convergence and tracking performance of the proposed algorithm compares favorably with conventional ones.