Randomized Approximations of the Image Set of Nonlinear Mappings with Applications to Filtering
Résumé
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithms
for 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.
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