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

A Note on the Relation Between Balenzela's Algorithm for Two-Filter Formula for Smoothing and Information Filter