Over-parameterized recursive least squares algorithm with filtering and maximum likelihood for Hammerstein-Wiener nonlinear system identification

This article focuses on the issue of parameter estimation related to Hammerstein-Wiener nonlinear systems. For the input piecewise nonlinear Hammerstein-Wiener systems, the parametric expression of the nonlinear input element is given by introducing a switching function. By using the over-parametrization method, we derive the identification model of the system and develop a maximum likelihood over-parametrization recursive least squares (ML-O-RLS) algorithm toward estimating the unknown parameters in the system. Considering that the actual systems are usually interfered by colored noise, the data filtering technology is used to process the input and output signals on the basis of the over-parametrization identification model. A filtering-based maximum likelihood over-parametrization recursive least squares (F-ML-O-RLS) algorithm is presented for the data filtering identification model to get the estimate of the parameters. The effectiveness of the proposed algorithms are examined in two examples.