A sliding-window approximation-based fractional adaptive strategy for Hammerstein nonlinear ARMAX systems

This paper presents a sliding-window approximation-based fractional least mean square (FLMS) algorithm for parameter estimation of Hammerstein nonlinear autoregressive moving average system with exogenous noise. The FLMS algorithm available in the literature makes use of data available at the current iteration only (or memory-less algorithm). This results in poor convergence rate of the algorithm, and the presence of immeasurable noise terms in the information vector makes identification a difficult task. The sliding-window approximation-based fractional LMS (SW-FLMS) algorithm uses not only the current data but also the past data at each iteration. The proposed algorithm uses sliding-window approximation of the expectation where the length of data used by SW-FLMS algorithm determines the size of sliding window. Moreover, a variable convergence approach is also proposed for fast convergence of SW-FLMS algorithm. Compared with the standard FLMS algorithm, the proposed SW-FLMS algorithms can converge at a fast rate to highly accurate parameter estimates. Estimation accuracy and convergence rate of the standard FLMS algorithm and proposed methods are evaluated for 200 independent runs. Simulation results confirm that performance of standard FLMS algorithm can be improved by the use of proposed modifications.