Frequency line tracking using hidden Markov models

Frequency cells comprising a subset, or gate, of the spectral bins from fast Fourier transform (FFT) processing are identified with the states of the hidden Markov chain. An additional zero state is included to allow for the possibility of track initiation and termination. Analytic expressions for the basic parameters of the hidden Markov model (HMM) are obtained in terms of physically meaningful quantities, and optimization of the HMM tracker is discussed. A measurement sequence based on a simple threshold detector forms the input to the tracker. The outputs of the HMM tracker are a discrete Viterbi track, a gate occupancy probability function, and a continuous mean cell occupancy track. The latter provides an estimate of the mean signal frequency as a function of time. The performance of the HMM tracker is evaluated for two sets of simulated data. The HMM tracker is compared to earlier, related trackers, and possible extensions are discussed