Hidden Markov model signal processing in presence of unknown deterministic interferences

Expectation maximization 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. Maximum-likelihood estimates of the Markov state levels, state estimates, transition possibilities, and the parameters of the deterministic signals are obtained. Two types of deterministic signals are considered: 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 and supporting theory appear more elegant and powerful than ad hoc heuristic alternatives. An illustrative application to extracting ionic channel currents in cell membranes in the presence of white Gaussian noise and AC hum is included