Hidden Gauss-Markov models for signal classification

Continuous-state hidden Markov models (CS-HMMs) are developed as a tool for signal classification. Analogs of the Baum (1972), Viterbi (1962), and Baum-Welch algorithms are formulated for this class of models. The CS-HMM algorithms are then specialized to hidden Gauss-Markov models (HGMMs) with linear Gaussian state-transition and output densities. A new Gaussian refactorization lemma is used to show that the Baum and Viterbi algorithms for HGMMs are implemented by two different formulations of the fixed-interval Kalman smoother. The measurement likelihoods obtained from the forward pass of the HGMM Baum algorithm and from the Kalman-filter innovation sequence are shown to be equal. A direct link between the Baum-Welch training algorithm and an existing expectation-maximization (EM) algorithm for Gaussian models is demonstrated. A new expression for the cross covariance between time-adjacent states in HGMMs is derived from the off-diagonal block of the conditional joint covariance matrix. A parameter invariance structure is noted for the HGMM likelihood function. CS-HMMs and HGMMs are extended to incorporate mixture densities for the a priori density of the initial state. Application of HGMMs to signal classification is demonstrated with a three-class test simulation.