# Wiener system identification with generalized orthonormal basis functions

arXiv: https://arxiv.org/abs/1612.04558 · HTML: https://mlsanity.com/paper/1612.04558/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2016.

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

- [Structured state-space models are deep Wiener models](https://mlsanity.com/paper/2312.06211/) (2023)

## Abstract (arXiv)

Many nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In general, an infinite number of OBFs is needed for an exact representation of the system. This paper considers the approximation of a Wiener system with finite-order infinite impulse response dynamics and a polynomial nonlinearity. We propose to use a limited number of generalized OBFs (GOBFs). The pole locations, needed to construct the GOBFs, are estimated via the best linear approximation of the system. The coefficients of the multivariate polynomial are determined with a linear regression. This paper provides a convergence analysis for the proposed identification scheme. It is shown that the estimated output converges in probability to the exact output. Fast convergence rates, in the order Op(NF^-nrep/2), can be achieved, with NF the number of excited frequencies and nrep the number of repetitions of the GOBFs.