Decoupling noisy multivariate polynomials in nonlinear system identification

In the field of system identification, the last few decades have witnessed a shift from linear to nonlinear system identification. One special type of nonlinear models are the so-called block-oriented models, and more specifically the Wiener-Hammerstein models. When identifying parallel Wiener-Hammerstein systems based on measurements, a noisy coupled multiple input-multiple output polynomial should be decoupled. However, this decoupling problem has solely been studied for the noiseless case, and not yet for the more involved noisy case. By using the covariance matrix of the polynomial coefficients, we have developed a first step towards the decoupling of noisy multivariate polynomials. This overview describes our contribution to the existing algorithm in the noisy case. For small noise levels (up to 10% of the output level), the covariance matrix method gives a reduction in error up to 10 dB between model and simulation. We expect better results after solving a remaining problem in the covariance matrix algorithm.