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Factoring the third-order Volterra kernel of a Wiener-Hammerstein model to recover the impulse responses of its two constituent linear systems is a common example in the multilinear algebra literature. Since recent progress in regularization-based system identification has enabled the practical estimation of the third-order Volterra kernel, these tensor factorization based approaches have become attractive. We extend one of these Wiener-Hammerstein factorization methods to the case of the Parallel Wiener-Hammerstein model, since, unlike the WH model, this structure is a universal approximator for Volterra systems. The efficacy of the method is demonstrated using numerical simulations.

In this work, a non-iterative identification approach is presented for estimating a single-input single-output Wiener model, comprising an infinite impulse response discrete transfer function followed by static non-linearity. Global orthogonal basis functions and orthogonal Hermite polynomials are used as expansion bases for the linear subsystem and the non-linearity, respectively. A multi-index based method is used to transform the non-convex optimization over the parameter values into an over-parametrized linear regression. A singular value decomposition based method is then used to project the result of the over-parametrized linear regression onto the class of Wiener models, each comprising a linear element followed by a memoryless non-linearity. The advantages obtained by using orthogonal polynomials are illustrated using a series of simulation examples.

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.

The ARX structure is often used in linear and nonlinear system identification because it is compact and linear in the variables. However, the ARX structure includes a noise model which shares the same poles as the deterministic system which is not always appropriate. In this paper, we consider the extension of an SVM based identification technique for Hammerstein models with ARX linear dynamics proposed by Dhaifallah and Westwick (2008 IFAC World Congress, pp:4999–5004) to include the output-error class of linear system models. The presented algorithm will be compared to the previous Hammerstein ARX approach using simulations.

In this paper, we outline the extension of the MOESP (standing for Multivariable Output Error State sPace model identification and introduced in [1].) family of subspace model identification schemes to Hammerstein type of non-linear systems. One type of identification problem is considered. This type addresses the identification of both the linear dynamic part and the static nonlinearity, where only limited a priori information regarding the structure of the nonlinearity is available. Another (c) type of Hammerstein identification problem, considered in [2], assumes the (polynomial) structure of the static non-linearity to be given and the task here is to identify similarly the linear system dynamics and the unknown proportional constants in the parametrization of the static non-linearity. The improved robustness properties of the algorithms developed in this paper over existing correlation based schemes is illustrated in [2].