Fractional Volterra LMS algorithm with application to Hammerstein control autoregressive model identification

In the present study, strength of fractional-order adaptive signal processing through fractional Volterra least mean square (FV-LMS) algorithm is exploited for Hammerstein nonlinear control autoregressive model (HN-CAR) identification. The FV-LMS method is a generalization of standard V-LMS by taking usual gradient as well as fractional derivative of cost function in the optimization process. The adaptive scheme FV-LMS is applied to HN-CAR systems for different variations of step size parameter, noise and fractional order. Comparative study of the optimized design variables by FV-LMS from true values of HN-CAR model is carried out using performance metrics of fitness and mean square error, to establish its effectiveness. The performance of the proposed scheme is validated through comparison with standard V-LMS based on multiple independent runs of the scheme.