# Numerically robust Gaussian state estimation with singular observation noise

arXiv: https://arxiv.org/abs/2503.10279 · HTML: https://mlsanity.com/paper/2503.10279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 3 of 3)

- [Stable Implementation of Probabilistic ODE Solvers](https://mlsanity.com/paper/2012.10106/) (2020)
- [Fenrir: Physics-Enhanced Regression for Initial Value Problems](https://mlsanity.com/paper/2202.01287/) (2022)
- [Numerically Robust Fixed-Point Smoothing Without State Augmentation](https://mlsanity.com/paper/2409.20004/) (2024)

## Abstract (arXiv)

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.