Design of momentum LMS algorithm for control autoregressive autoregressive systems

Abstract

The least mean square (LMS) adaptive algorithm developed by Widrow and Hoff in 1960's has been used widely to solve optimization problems arising in signal processing and control. The LMS adaptive scheme optimizes the fitness function through gradient descent approach and iteratively updates the weight vector using current value of gradient at each iteration. The LMS strategy is famous because of its simplicity and robust performance under different signal conditions but suffers from slow convergence rate. Recently, the parameter identification problem of control autoregressive autoregressive (C-ARAR) like systems has gained esteem research attention and many methods based on stochastic gradient as well as least squares approaches have been proposed for its identification. In this study, a variant of LMS with faster convergence is proposed for system identification of C-ARAR model. The design scheme i.e., momentum LMS (MomLMS), effectively exploits the gradient information by using the proportion of previous gradients for current estimate of the weight vector. The MomLMS method is faster in convergence and less prone to trap in local minimums. The accuracy and convergence of the proposed method is verified through effective identification of C-ARAR system. The adaptive variables obtained through proposed MomLMS algorithm are compared from actual parameters of the C-ARAR system as well as with the results of standard LMS to prove its correctness. The accurate estimation of C-ARAR parameters for different noise levels establishes the robustness of the adaptive strategy. The performance comparison through statistical analysis based on adequate independent runs validates the reliability and effectiveness of the MomLMS method for C-ARAR system identification.