Numerically robust Gaussian state estimation with singular observation noise
This work addresses a specific numerical challenge in state estimation for applications like signal processing or control systems, but it is incremental as it builds on existing methods to handle singular noise cases.
The paper tackles the problem of Gaussian state estimation with singular observation noise by proposing numerically robust algorithms that transform the singular problem into a nonsingular one with reduced state dimension, achieving low runtime and numerical stability while enabling marginal-likelihood computations and Gauss-Markov representations.
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.