Kalman filtering using pairwise Gaussian models

An important problem in signal processing consists in recursively estimating an unobservable process x = {x(n)}(nis an element ofIN) from an observed process y = {y(n)}(nis an element ofIN). This is done classically in the framework of Hidden Markov Models (HMM). In the linear Gaussian case, the classical recursive solution is given by the well-known Kalman filter. In this paper, we consider Pairwise Gaussian Models by assuming that the pair (x, y) is Markovian and Gaussian. We show that this model is strictly more general than the HMM, and yet still enables Kalman-like filtering.