Weighted tensor decomposition for approximate decoupling of multivariate polynomials

In the field of nonlinear system identification, one special type of models are the so-called block-oriented models, and more specifically the Wiener-Hammerstein models. When identifying parallel Wiener-Hammerstein systems, a coupled multiple-input-multiple-output polynomial based on noisy input-output data should be decoupled into a set of single-input-single-output functions. In this work, we will generalize an earlier decoupling algorithm to the case where an exact decoupling does not exist, but there is information regarding the uncertainty available through the covariance matrix of the coefficients of function to be decoupled.