Segmented chirp features and hidden Gauss-Markov models for transient signal classification

Time-frequency analysis and stochastic modeling techniques are combined in order to characterize and classify transient wandering-tone signals. A feature set is defined for segments of time-domain data. The features measure the chirp rate, center frequency, and amplitude of each segment. These features are calculated using chirped autocorrelations and the fractional Fourier transform. The features are shown to be sufficient for accurately reconstructing wandering-tone signals. Continuous-state hidden Markov models are used to track the features across segments. Analogs of the Baum and Baum-Welch algorithms are formulated for this general class of continuous-state models and then specialized to Gaussian model densities. A unifying theory of hidden Markov models and Kalman filters is presented. The Baum and Viterbi algorithms for Gaussian models are shown to be implemented by two different formulations of the fixed-interval Kalman smoother. The measurement likelihoods obtained from the forward pass of the Baum algorithm and from the Kalman-filter innovation sequence are shown to be equivalent. A direct link between the Baum-Welch algorithm and an existing expectation-maximization algorithm for linear Gaussian models is demonstrated. The general continuous-state and Gaussian models are extended to incorporate mixture densities for the prior probability of the initial state. A new expression for the cross covariance between time-adjacent states is derived from the off-diagonal block of the conditional joint covariance matrix. The stochastic model is shown to capture the essential nature of the class of signals. Classification results are presented for simulated data and for recorded marine-animal vocalizations.