Parameter estimation in chaotic noise

The problem of parameter estimation in chaotic noise is considered in this paper. Since a chaotic signal is inherently deterministic, a new complexity measure called the phase space volume (PSV) is introduced for estimation instead of using the conventional probabilistic measures. We show that the unknown parameters of a signal embedded in chaotic noise ran be obtained by minimizing the PSV (MPSV) of the output of an inverse filter of the received signal in a reconstructed phase space. Monte Carlo simulations are carried out to analyze the efficiency of the MPSV method for parameter estimation in chaotic noise. To illustrate the usefulness of the MPSV technique in solving real-life problems, the problem of sinusoidal frequency estimation in real radar clutter (unwanted radar backscatters) is considered. Modeling radar clutter as a chaotic process, we apply the MPSV technique to estimate the sinusoidal frequencies by estimating the coefficients of an autoregressive (AR) spectrum. The results show that the frequency estimates generated by the MPSV method are more accurate than those obtained by the standard least square (LS) technique.