Hidden Markov Model Signal Processing in Presence of Unknown Deterministic Interferences

In this note, expectation maximization (EM) algorithms are used to extract discrete-timq finite-state Markov signals imbedded in a mfxture of Gaussian white-noise and deterministic signals of known functional form with unknown parameters. We obtain maximum likeliManuscript received March 8, 1991; revised November 22, 1991. This work was supported in part by ATERB, DSTO, and NH & MRC of Australia. V. Krishnamurthy and J. B. Moore are with the Department of Systems Engineering, Research School of Physical Science and Engineering, Australian National University, Canberra, ACT 2601, Auatrafia. S.-H. Chung is with the Department of Chemistry, Australian National University, Canberra, ACT 2601, Australia. IEEE Log Number 9203136. Mmd estimates of the Markov state levels, state estimate% transiti ProbabilJtie&and also of the parameters of tbe deterministic sifpsmk Speeitlcally, w consider two important types of deterministic siguak petiodiq or sfmost periodic signsfs with unknown frequency cosnfmItent.%ampfltud% md phase% polymmM drfft in the states of * Markovproeess wittlthc meukfents of thepoiynomiaf unknown. llse teeh@oes developed here slong with tbs sopportbg theory appear mom elegsnt and powerfuf than ad hoe heuristic aftensahs. Art MhDIW8th bfophysical applkatjon for estmting ionic c!mnnel curtwnts in sslI membranes in the presence of white Gaussian noise and alte~ currvmt(AC) “hum” is included.