Numerically robust Gaussian state estimation with singular observation noise

Nicholas Krämer; Filip Tronarp

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arXiv · 2503.10279

Numerically robust Gaussian state estimation with singular observation noise

Nicholas Krämer·Filip Tronarp

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Abstract

This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a nonsingular one with reduced state dimension. In addition to ensuring low runtime and numerical stability, our proposal facilitates marginal-likelihood computations and Gauss-Markov representations of the posterior process. We analyse the proposed method's computational savings and numerical robustness and validate our findings in a series of simulations.

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Nicholas Krämer, Filip Tronarp. 2025-03-13. Numerically robust Gaussian state estimation with singular observation noise. https://arxiv.org/abs/2503.10279

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