Nested Sampling Approach to Set-membership Estimation

This paper is concerned with set-membership estimation in nonlinear dynamic systems. The problem entails characterizing the set of all possible parameter values such that given predicted outputs match their corresponding measurements within prescribed error bounds. Most existing methods to tackle this problem rely on outer-approximation techniques, which perform poorly when the parameter host set is large due to the curse of dimensionality. An adaptation of nested sampling—a Monte Carlo technique introduced to compute Bayesian evidence—is presented herein. The nested sampling algorithm leverages efficient strategies from Bayesian statistics for generating an inner-approximation of the desired parameter set. Several case studies are presented to demonstrate the approach.