Identification of Hammerstein nonlinear ARMAX systems using nonlinear adaptive algorithms

In this study, a novel adaptive strategy is designed based on fractional least mean square (LMS) algorithm for parameter estimation of Hammerstein nonlinear autoregressive moving average system with exogenous noise (HN-ARMAX). The design scheme consists of parameterization of HN-ARMAX systems to obtain linear-in-parameter models and to use fractional LMS algorithm for adapting unknown parameter vectors. The performance analysis of the proposed method is carried out based on convergence to the desired values of HN-ARMAX systems, and comparison is made with state-of-the-art kernel LMS and Volterra LMS algorithms. The consistency in terms of accuracy and convergence is established through the results of statistical analysis based on sufficient large number of independent runs rather than single successful run of the algorithm. The performance of proposed scheme is superior due to its strong mathematical foundations, nonlinear weight updating mechanism and more convergence controlling variables but at the cost of bit more computational requirements.