Recent paper by Balenzuela et al. presented an exact algorithm for computing the posterior distribution of current and future observations given the current state, $p(x_n|y_n,\ldots ,y_N)$, which is required when computing fixed-interval smoother of the state by a two-filter formula. In this note, it will be shown that their algorithm is equivalent to the backward filter obtained by applying an information filter to the reverse state-space model. Although their algorithm is proposed for complex Gaussian mixture distribution models, in this note, we consider the case of simple state-space models with respect to filter computation.

翻译：Balenzuela等人近期发表了一篇论文，提出了一种精确算法，用于计算给定当前状态下当前及未来观测的后验分布$p(x_n|y_n,\ldots ,y_N)$，该分布在通过双滤波器公式计算状态固定区间平滑器时是必需的。在本注记中，我们将证明该算法等价于对反向状态空间模型应用信息滤波器所获得的后向滤波器。尽管该算法是针对复杂高斯混合分布模型提出的，但在本注记中，我们考虑相对于滤波器计算而言简单的状态空间模型情形。