Set-membership parameter estimation based on Voronoi vertices

Abstract

Identification of complex systems often face structural modelling errors and limited or low quality data, which hinder statistical characterisations. An alternative is the set-membership approach, where errors are assumed unknown-but-bounded. Set-membership estimation aims to find a feasible parameter set (FPS), which produces model outputs that fit within given error bounds. Most algorithms are limited to linear models, small number of parameters, or to discrete approximation of the FPS. These limitations hinder parameter estimation for relatively complex systems. We present an efficient sampling-based set-membership algorithm with low computational complexity that improves the coverage of a discrete approximation of the FPS, characterised by hyperspheres from a Voronoi diagram of the parameter space. Additionally, we suggest a measure for set-membership accuracy based on deviations between the given error bounds and the feasible model output set. Our algorithm provides a balance between accuracy and computational complexity, and a tool to investigate practical identifiability.