Frequency line extractor using multiple hidden Markov models

This paper addresses automatic frequency line detection and tracking in lofargrams. Standard sequential detection with nearest neighbour or probabilistic data association with severely limited branching factors suffers from various difficulties due to the low SNR and to the variability of line frequencies and amplitudes. The solution lies, firstly in taking into account as long as possible observed data blocks (batch processing), secondly in delaying the decisions (knowledge of future) and thirdly in using several frequency line variation models in parallel. The HMM algorithm seems well suited to this problem and several frequency line tracking systems have been based on this modelization. In this paper a HMM-based line extractor is described: (1) at the input only spectrum maxima with amplitudes higher than a first detection threshold are taken into account in order to reduce the computational load, the observation being composed of a set of frequencies and amplitudes delivered at each FFT frame, (2) the extractor is block recursive with 50% overlapping, (3) initiation of new tracks is performed by a generalized likelihood ratio (GLR) test using two frequency line variation models, the GLR being estimated by the forward-backward algorithm, (4) the maximum a posteriori (MAP) estimate of each line track is performed by a Viterbi algorithm, for each block the model used for this Viterbi algorithm is chosen from three fixed transition probability matrices by means of the forward algorithm (MAP estimate). The three frequency variation models taken into account in the line extractor are discussed. A special effort has been devoted to prevent strong lines from masking nearby weak lines. Finally the line extractor has been tested on a few complex simulated and real LOFARs.