The Quadrature Gaussian Sum Filter and Smoother for Wiener Systems

TL;DR

This paper introduces a Gaussian Sum Filter and smoothing method for Wiener systems that improves accuracy and computational efficiency by using Gauss-Legendre quadrature, outperforming traditional techniques.

Contribution

A novel Gaussian Sum Filter and two-filter smoothing strategy for Wiener systems based on Gauss-Legendre quadrature approximation.

Findings

Outperforms traditional filters in accuracy and efficiency

Balances computational load with estimation precision

Enhances control and system identification applications

Abstract

Block-Oriented Nonlinear (BONL) models, particularly Wiener models, are widely used for their computational efficiency and practicality in modeling nonlinear behaviors in physical systems. Filtering and smoothing methods for Wiener systems, such as particle filters and Kalman-based techniques, often struggle with computational feasibility or accuracy. This work addresses these challenges by introducing a novel Gaussian Sum Filter for Wiener system state estimation that is built on a Gauss-Legendre quadrature approximation of the likelihood function associated with the output signal. In addition to filtering, a two-filter smoothing strategy is proposed, enabling accurate computation of smoothed state distributions at single and consecutive time instants. Numerical examples demonstrate the superiority of the proposed method in balancing accuracy and computational efficiency compared to traditional approaches, highlighting its benefits in control, state estimation and system identification, for Wiener systems.