Wasserstein bounds for non-linear Gaussian filters

Toni Karvonen; Simo Särkkä

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arXiv · 2503.21643

Wasserstein bounds for non-linear Gaussian filters

Toni Karvonen·Simo Särkkä

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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.

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Toni Karvonen, Simo Särkkä. 2025-03-27. Wasserstein bounds for non-linear Gaussian filters. https://arxiv.org/abs/2503.21643

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