Adaptive filtering parameter estimation algorithms for Hammerstein nonlinear systems

•Two filtering based identification methods are discussed for Hammerstein systems.•A filter based recursive least squares method is presented for Hammerstein systems.•A filter based multi-innovation stochastic gradient method is given for comparison.

This paper studies the parameter estimation problems of the Hammerstein nonlinear systems using the adaptive filtering technique. A linear filter based recursive least squares (LF-RLS) identification algorithm with good convergence properties and high parameter estimation accuracy is proposed by filtering the input-output data. A linear filter based multi-innovation stochastic gradient (LF-MISG) algorithm is proposed by the innovation expansion, in order to improve the computational efficiency of the LF-RLS algorithm. Furthermore, a time-varying factor is introduced in the linear filter to improve the convergence speed of the LF-MISG algorithm. The efficiency of the proposed algorithms are shown in comparison with the conventional identification algorithms.