Wasserstein bounds for non-linear Gaussian filters
Statistics Theory
2026-05-28 v2 Probability
Statistics Theory
Abstract
Most Kalman filters for non-linear systems, such as the unscented Kalman filter, are based on Gaussian approximations. We use Poincar\'e inequalities to bound the Wasserstein distance between the true joint distribution of the prediction and measurement and its Gaussian approximation. The bounds can be used to assess the performance of non-linear Gaussian filters and determine those filtering approximations that are most likely to induce error.
Cite
@article{arxiv.2503.21643,
title = {Wasserstein bounds for non-linear Gaussian filters},
author = {Toni Karvonen and Simo Särkkä},
journal= {arXiv preprint arXiv:2503.21643},
year = {2026}
}
Comments
To appear in IEEE Transactions on Automatic Control