Frequency tracking using hidden Markov models with amplitude and phase information

It is demonstrated how the hidden Markov model (HMM) frequency tracker can be extended by the addition of amplitude and phase information. The HMM tracker as originally formulated uses a gate of spectral bins from fast Fourier transform (FFT) processing, and associates each cell with a state of the hidden Markov chain. A measurement sequence based on the output of a simple threshold detector forms the input to the HMM tracker. Two extensions to the original tracker are proposed. The first, the HMM/A tracker, incorporates the FFT amplitudes in the cells of the measurement sequence. The second, the HMM/AP tracker, does not use a measurement sequence, but uses instead the FFT amplitude and phase values in all cells within the gate. A comparison of the results obtained in using the three HMM-based trackers with simulated data reveals that the extended trackers outperform the original. An analysis of the effect of parameter mismatch for the three trackers is presented. Their use as detectors is also discussed