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In this note we revisit fixed-interval Kalman like smoothing algorithms. We have two results. We first unify the family of existing algorithms by deriving them in a common Bayesian framework; as we shall see, all these algorithms stem from forward and/or backward Markovian properties of the state process, involve one (or two) out of four canonical probability density functions, and can be derived from the systematic use of some generic properties of Gaussian variables which we develop in adoi:10.1109/tac.2008.2007858 fatcat:xhlyt6sghfdz3o5tkc4acobdp4