Parallel Hammerstein Models Identification using Sine Sweeps and the Welch Method

Abstract

Linearity is a common assumption for many real life systems. But in many cases, the nonlinear behavior of systems cannot be ignored and has to be modeled and estimated. Among the various classes of nonlinear models present in the literature, Parallel Hammertein Models (PHM) are interesting as they are at the same time easy to understand as well as to estimate when using exponential sine sweeps (ESS) based methods. However, the classical EES-based estimation procedure for PHM relies on a very specific input signal (ESS), which limits its use in practice. A method is proposed here based on the Welch method that allows for PHM estimation with arbitrary sine sweeps (ASS) which are a much broader class of input signals than ESS. Results show that for various ASS, the proposed method provides results that are in excellent agreement with the ones obtained with the classical ESS method.