Separable Least Squares Identification of Wiener Box-Jenkins Models

This paper presents an approach for the identification of a Wiener model, a dynamic linear system followed by a static nonlinearity, in the presence of colored measurement noise. A Box-Jenkins model structure is proposed where the process model consists of a recursive digital filter followed by a polynomial nonlinearity, while the noise model is represented by another recursive digital filter. The prediction error method is implemented using a separable least squares technique in order to estimate the parameters of the linear and nonlinear elements. The parameters of the digital filters are estimated using a second-order iterative optimization method since they appear nonlinearly in the output. After each iteration, the nonlinearity is fitted using linear regression. Monte-Carlo simulation is used to validate the algorithm.