Statistical efficiency of structured cpd estimation applied to Wiener-Hammerstein modeling
For researchers in nonlinear system identification, this work provides a statistically efficient method for estimating Wiener-Hammerstein models, though it is an incremental application of existing structured CPD algorithms.
This paper addresses the identification of nonlinear Wiener-Hammerstein systems using structured canonical polyadic decomposition (CPD) of Volterra kernels. The proposed estimators achieve mean-square error close to the Cramer-Rao bound in Monte Carlo simulations.
The computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications. In this paper, we consider the identification of a nonlinear system by means of a Wiener-Hammerstein model, assuming a high-order Volterra kernel of that system has been previously estimated. Such a kernel, viewed as a tensor, admits a CPD with banded circulant factors which comprise the model parameters. To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of structured CPDs. Then, considering the presence of additive white Gaussian noise, we derive a closed-form expression for the Cramer-Rao bound (CRB) associated with this estimation problem. Finally, we assess the statistical performance of the proposed estimators via Monte Carlo simulations, by comparing their mean-square error with the CRB.