Numerically robust Gaussian state estimation with singular observation noise

• URL: http://arxiv.org/abs/2503.10279v1
• Date: Thu, 13 Mar 2025 11:43:53 GMT
• Title: Numerically robust Gaussian state estimation with singular observation noise
• Authors: Nicholas Krämer, Filip Tronarp,
• Abstract summary: This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise.<n>We analyse the proposed method's computational savings and numerical robustness and validate our findings in a series of simulations.
• Score: 10.487920339867953
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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