解决观测噪声奇异时的高斯状态估计数值不稳问题
Numerically robust Gaussian state estimation with singular observation noise
- 通过基变换结合贝叶斯规则，将奇异问题转为低维非奇异问题
- 计算效率高且数值稳定，支持后验过程的高斯马尔可夫表示
- 适合需要精确推断与稳定计算的系统辨识与信号处理场景
本文提出针对奇异观测噪声下的高斯状态估计的数值稳健算法。方法结合一系列基变换与贝叶斯规则，将原奇异估计问题转化为低维非奇异问题。该方法不仅保证了低运行时间和数值稳定性，还便于后验过程的边际似然计算与高斯-马尔可夫表示。通过理论分析与多组仿真验证了所提方法在计算效率与数值鲁棒性方面的优势。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。