Hidden Markov model signal processing in presence of unknown deterministic interferences

Expectation maximization (EM) algorithms are used to extract discrete-time finite-state Markov signals imbedded in a mixture of Gaussian white noise and deterministic signals of known functional form with unknown parameters. The authors obtain maximum likelihood estimates of the Markov state levels, state estimates, transition probabilities and also of the parameters of the deterministic signals. Specifically, they consider two important types of deterministic signals: periodic, or almost periodic signals with unknown frequency components, amplitudes and phases; and polynomial drift in the states of the Markov process with the coefficients of the polynomial unknown. The techniques developed here along with the supporting theory appear more elegant and powerful than ad hoc heuristic alternatives