# A new kernel-based approach for overparameterized Hammerstein system identification

arXiv: https://arxiv.org/abs/1504.08190 · HTML: https://mlsanity.com/paper/1504.08190/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2015.

## Built on by (most cited first, 1 of 1)

- [Bayes and Biased Estimators Without Hyper-parameter Estimation: Comparable Performance to the Empirical-Bayes-Based Regularized Estimator](https://mlsanity.com/paper/2503.11854/) (2025)

## Abstract (arXiv)

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of p basis functions. We reconstruct the p coefficients of the nonlinearity together with the first n samples of the impulse response of the linear system by estimating an np-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and p coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.