  Providing flexibility and user-interpretability in nonlinear system
identification can be achieved by means of block-oriented methods. One of such
block-oriented system structures is the parallel Wiener-Hammerstein system,
which is a sum of Wiener-Hammerstein branches, consisting of static
nonlinearities sandwiched between linear dynamical blocks. Parallel
Wiener-Hammerstein models have more descriptive power than their single-branch
counterparts, but their identification is a non-trivial task that requires
tailored system identification methods. In this work, we will tackle the
identification problem by performing a tensor decomposition of the Volterra
kernels obtained from the nonlinear system. We illustrate how the parallel
Wiener-Hammerstein block-structure gives rise to a joint tensor decomposition
of the Volterra kernels with block-circulant structured factors. The
combination of Volterra kernels and tensor methods is a fruitful way to tackle
the parallel Wiener-Hammerstein system identification task. In simulation
experiments, we were able to reconstruct very accurately the underlying blocks
under noisy conditions.
