Numerically robust Gaussian state estimation with singular observation noise

2025-03-13

AI Summary

To address numerical instability and high computational complexity in Gaussian state estimation under singular observation noise, this paper proposes a dimensionality-reduction estimation framework based on basis transformation and Bayesian updating. By constructing an orthogonal basis, the original high-dimensional singular problem is projected onto a low-dimensional nonsingular subspace, where stable Bayesian filtering is performed while preserving exact representations of the posterior marginal likelihood and the Gaussian–Markov structure. This work establishes, for the first time, a unified estimation paradigm under singular noise that simultaneously guarantees numerical robustness, significantly reduced computational complexity (theoretically proven), and statistical completeness. Comprehensive simulations demonstrate that the method maintains high estimation accuracy, rapid convergence, and strong stability across diverse ill-conditioned noise scenarios.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Develops robust algorithms for Gaussian state estimation
• Transforms singular noise problems into nonsingular ones
• Ensures numerical stability and computational efficiency

Innovation

• Combines basis changes with Bayes' rule
• Transforms singular to nonsingular estimation problem
• Ensures low runtime and numerical stability