Sinusoidal frequency estimation in chaotic noise

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Abstract
The problem of sinusoidal frequency estimation in chaotic noise is considered. Since the chaotic noise is inherently deterministic, a new complexity measure called the phase space volume (PSV) is introduced. The PSV quantifies the complexity of a signal by measuring its volume in a reconstructed phase space. To estimate the sinusoidal frequencies, an autoregressive (AR) model is applied to the received signal and the coefficients are estimated by minimizing the PSV of the prediction error. It is shown that the frequencies can indeed be obtained by this MPSV-AR spectral estimator. To illustrate the efficiency of this new technique, simulated chaotic noise and real-life radar clutter (radar backscatter) are used as background noise for sinusoidal frequency estimation. Basically, we assume that chaos is a good model of background noise and apply the MPSV-AR technique to estimate the frequencies. The usefulness of this approach is evaluated using real-life measurement noise (radar clutter). In both simulated and real noise environments, we observe that the MPSV-AR spectral estimator provides an efficient frequency estimates in terms of both the mean square errors and frequency resolution.

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