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.