Momentum Least Mean Square Paradigm for the Measurement of Nonlinear CARAR System Parameters

Abstract

This study presents a variant of least mean square (LMS) algorithm, i.e., momentum LMS (M-LMS), with faster convergence speed for measuring the system parameter of linear as well as nonlinear control autoregressive autoregressive (CARAR) models. The M-LMS effectively exploits the input/output data by utilizing the previous gradients information in update rule to avoid trapping in local minimum (MNM) and yields better convergence behavior than conventional LMS approach. The speedy convergence of M-LMS is achieved by increasing the proportion of previous gradients but at the cost of little compromise in final steady-state behavior. The correctness of the M-LMS is established by effective optimization of the linear as well as nonlinear CARAR model identification. The robustness of the scheme is verified through accurate measurement of CARAR systems parameters for various noise levels. The statistical analyses based on multiple independent trials through proximity measures in terms of fitness, mean squared error, and Nash Sutcliffe efficiency further validated the superior performance of M-LMS for identification of CARAR models.