Numerically robust Gaussian state estimation with singular observation noise

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.

@article{krämer2025_2503.10279,
  title={ Numerically robust Gaussian state estimation with singular observation noise },
  author={ Nicholas Krämer and Filip Tronarp },
  journal={arXiv preprint arXiv:2503.10279},
  year={ 2025 }
}