Randomized Approximations of the Image Set of Nonlinear Mappings with Applications to Filtering
Abstract
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a nonlinear function.We introduce minimum-volume approximations which have the characteristic of guaranteeing a low probability of violation, i.e.,we admit for a probability that some points in the image set are not contained in the approximating set,but this probability is kept below a pre-specified threshold.In the second part of the paper, this idea is then exploited to develop a new family of randomized prediction-corrector filters.These filters represent a natural extension and rapprochement of Gaussian and set-valued filters,and bear similarities with modern tools such as particle filters.
Keywords
Cite
@article{arxiv.1507.08032,
title = {Randomized Approximations of the Image Set of Nonlinear Mappings with Applications to Filtering},
author = {Fabrizio Dabbene and Didier Henrion and Constantino Lagoa and Pavel Shcherbakov},
journal= {arXiv preprint arXiv:1507.08032},
year = {2015}
}