Statistical efficiency of structured cpd estimation applied to Wiener-Hammerstein modeling

TL;DR

This paper investigates the statistical efficiency of structured CPD estimators for Wiener-Hammerstein system identification, deriving the CRB and evaluating estimator performance through simulations.

Contribution

It introduces specialized estimators for structured CPD in Wiener-Hammerstein models and derives the CRB for their performance analysis.

Findings

The derived CRB provides a benchmark for estimator performance.

Monte Carlo simulations show the estimators approach the CRB under certain conditions.

The approach effectively captures the statistical properties of the estimation process.

Abstract

The computation of a structured canonical polyadic decomposition (CPD) is useful to address several important modeling problems in real-world applications. In this paper, we consider the identification of a nonlinear system by means of a Wiener-Hammerstein model, assuming a high-order Volterra kernel of that system has been previously estimated. Such a kernel, viewed as a tensor, admits a CPD with banded circulant factors which comprise the model parameters. To estimate them, we formulate specialized estimators based on recently proposed algorithms for the computation of structured CPDs. Then, considering the presence of additive white Gaussian noise, we derive a closed-form expression for the Cramer-Rao bound (CRB) associated with this estimation problem. Finally, we assess the statistical performance of the proposed estimators via Monte Carlo simulations, by comparing their mean-square error with the CRB.