Title: Numerically robust Gaussian state estimation with singular observation noise Show Chinese title

Title: 具有奇异观测噪声的高斯状态估计的数值鲁棒性

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. Show Chinese abstract

Abstract: 本文提出了针对奇异观测噪声的高斯状态估计的数值鲁棒算法。 我们的方法结合了一系列基变换与贝叶斯规则，将奇异估计问题转化为具有降维的状态的非奇异问题。除了确保较低的运行时间和数值稳定性外，我们的提议还便于边缘似然计算和后验过程的高斯-马尔可夫表示。我们分析了所提出方法的计算节省和数值鲁棒性，并通过一系列仿真验证了我们的发现。