重新审视滤波公式的本质，用对数二次似然替代信息参数化。
The two filter formula reconsidered: Smoothing in partially observed Gauss--Markov models without information parametrization
- 改用对数二次似然递推，无需信息参数化
- 简化了平方根算法的实现结构
- 适合需要高效滤波的系统建模者
本文重新审视部分观测高斯-马尔可夫模型中的双滤波公式。传统上该公式以反向时间运行的滤波器形式出现，使用信息形式的高斯密度参数化。然而，反向递推中的量实际上并非分布，而是似然。基于这一观察，本文提出一种基于对数二次似然的递推方法，避免了信息参数化的必要性。特别地，该方法极大简化了算法的平方根形式。此外，还给出了从所提出的似然表示推导路径后验分布前向马尔可夫表示的公式。
原文摘要 · Abstract (English)
In this article, the two filter formula is re-examined in the setting of partially observed Gauss--Markov models. It is traditionally formulated as a filter running backward in time, where the Gaussian density is parametrized in ``information form''. However, the quantity in the backward recursion is strictly speaking not a distribution, but a likelihood. Taking this observation seriously, a recursion over log-quadratic likelihoods is formulated instead, which obviates the need for ``information'' parametrization. In particular, it greatly simplifies the square-root formulation of the algorithm. Furthermore, formulae are given for producing the forward Markov representation of the a posteriori distribution over paths from the proposed likelihood representation.
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