Weak Signal Estimation in Chaotic Clutter Using Model-Based Coupled Synchronization

In this paper, detection and estimation of weak signals in chaotic clutter with unknown dynamics are presented. We achieve this in three steps. First, by using Takens' delay embedding theorem and support vector machines (SVMs), the dynamics of the clutter is modeled by training SVMs with a known data set. Second, we augment the model with coupled chaotic synchronization scheme so that a better estimate of the clutter signal can be estimated. Finally, this estimate is subtracted from the observations, and on the residual signal, we apply standard signal detection/estimation techniques. By analyzing the statistical properties of the residual signal, we show that the strong clutter in the observation is replaced by a weakly colored and nonstationary noise. Efficiency of the new estimator is evaluated by computing the mean square error (MSE) of the estimation. Our studies reveal that, by a proper selection of coupling coefficients, we can lower the MSE significantly.