Physical Review E
Hidden Markov models
I report on numerical experiments in which a detector reliably found chaotic signals at signal to noise ratios as low as -15 dB. The detector was based on a variant of the hidden Markov models used in speech research. The task was particularly difficult because the Fourier power spectrum of the noise was constructed to match the spectrum of the signal. I review likelihood ratio detectors, limitations on the performance of linear models implied by the broad Fourier power spectra of chaotic signals, and the upper limit that the Kolmogorov-Sinai (KS) entropy of a chaotic system places on the expected log likelihood attainable by any model. I find that KS entropy estimates indicate that even better detection performance is possible.
Fraser, A. M. (1996). Chaos and detection. Physical Review E (Statistical Physics, Plasmas, Fluids, And Related Interdisciplinary Topics), 53(5), 4514-4523.