Tensor Factorization based Estimates of Parallel Wiener Hammerstein Models * *Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through grant RGPIN/06464-2015 and the Fund for Scientic Research (FWO- Vlaanderen), by the Flemish Government (Methusalem), the Belgian Government through the Inter-university Poles of Attraction (IAP VII) Program, by the ERC Advanced Grant SNLSID under contract 320378 and

Abstract

Abstract 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.