  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.
