The problem of modeling chaotic nonlinear dynamical systems using hidden Markov models is considered. A hidden Markov model for a class of chaotic systems is developed from noise-free observations of the output of that system. A combination of vector quantization and the Baum-Welch algorithm is used for training. The importance of this combined iterative approach is demonstrated. The model is then used for signal separation and signal detection problems. The difference between maximum likelihood signal estimation and maximum aposteriori signal estimation using a hidden Markov model is illustrated for a nonlinear dynamical system.
In order to effectively deal with quiet source emissions and elevated ambient noise level in littoral waters, it is important that one understand and exploit the underlying signal microstructure. Experiences indicate that thorough understanding of signal structures is a key to designing robust detection and signal processing algorithms. Therefore, classify-before-detect algorithms are designed and their performance evaluated with passive broadband ͑PBB͒ data corrupted by the SWell-EX1 shallow water ambient noise collected near San Diego, CA. The processing strategy is based on ͑1͒ exploitation of any microstructure present in target signature by projecting raw data onto appropriate low-dimensional projection spaces, ͑2͒ identification of key parameters or ''features'' crucial in determining the presence of signal, and ͑3͒ designing a classifier topology that best matches the underlying feature distribution to minimize modeling errors. Full-spectrum signal processing algorithm design is facilitated by the use of an integrated classification paradigm that takes advantage of an inherent relationship between low-dimensional features and classifier architecture. The analysis results based on the classified PBB signal and the SWell-Ex1 ambient noise indicate that taking advantage of the PBB microstructure improves detection performance by an average of 5 to 15 dB over that of a traditional energy detector.
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