Smoothing estimation of stochastic processes: Two-filter formulas

Some simple derivations of two-filter-like formulas (in the smoothing problem of linear estimation) are given for general nonstationary processes. Especially, the argument provides a single development for continuous, discrete, and continuous-discrete schemes (here the results are new). It is shown how a wide sense Markovian assumption is required to give the formulas a backwards filter interpretation. While few of the results are new, the simple derivations will be of intuitive value.