Title :
A filtered EM algorithm for joint hidden Markov model and sinusoidal parameter estimation
Author :
Krishnamurthy, Vikram ; Elliott, Robert J.
Author_Institution :
CRASyS, Australian Nat. Univ., Canberra, ACT, Australia
fDate :
1/1/1995 12:00:00 AM
Abstract :
Derives finite-dimensional discrete-time filters for estimating the parameters of discrete-time finite-state Markov chains imbedded in a mixture of Gaussian white noise and deterministic signals of known functional form with unknown parameters. The filters that are derived estimate quantities used in the expectation-maximization (EM) algorithm for maximum likelihood (ML) estimation of the Markov chain parameters (transition probabilities and state levels) as well as the parameters of the deterministic interference. 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 filter-based EM algorithm has negligible memory requirements. In comparison, implementing the EM algorithm using smoothed variables (forward-backward variables) requires memory proportional to the number of observations. In addition, the filters are suitable for multiprocessor implementation unlike the forward-backward algorithm
Keywords :
Gaussian noise; autoregressive moving average processes; discrete time filters; filtering theory; hidden Markov models; maximum likelihood estimation; multidimensional digital filters; parameter estimation; white noise; Gaussian white noise; amplitudes; deterministic interference; deterministic signals; discrete-time finite-state Markov chains; expectation-maximization algorithm; filtered EM algorithm; finite-dimensional discrete-time filters; forward-backward variables; frequency components; hidden Markov model; maximum likelihood estimation; memory requirements; multiprocessor implementation; periodic signals; phases; polynomial drift; sinusoidal parameter estimation; smoothed variables; state levels; transition probabilities; Filters; Frequency; Hidden Markov models; Interference; Maximum likelihood estimation; Parameter estimation; Polynomials; Signal processing; State estimation; White noise;
Journal_Title :
Signal Processing, IEEE Transactions on