Kalman Filtering in Triplet Markov Chains

Let x = {xn} _nisinIN be a hidden process, y = {y_n}_nisinIN an observed process, and r = {r_n}_nisinIN some additional process. We assume that t = (x, r, y) is a (so-called "Triplet") vector Markov chain (TMC We first show that the linear TMC model encompasses and generalizes, among other models, the classical state-space systems with colored process and/or measurement noise(s). We next propose restoration Kalman-like filters for arbitrary linear Gaussian (LG) TMC