Power-law sensitivity to initial conditions in sea clutter

Understanding the nature of sea clutter is crucial to the successful modeling of sea clutter as well as to facilitate target detection within sea clutter. To this end, an important question to ask is whether sea clutter is stochastic or deterministic. In the past decade, Haykin et al. have carried out analysis of some sea clutter data using chaos theory, and concluded that sea clutter was generated by an underlying chaotic process. Recently, their conclusion has been questioned by a number of researchers. To reconcile ever growing evidence of stochasticity in sea clutter with their chaos hypothesis, Haykin et al. have further suggested that the non-chaotic feature of sea clutter could be due to many types of noise sources in the data. To test this possibility, McDonald and Damini have tried a series of low-pass filters to remove noise; but again they have failed to find any chaotic features. While most of these studies are conducted by comparing measured sea clutter data with simulated stochastic processes, we use the direct dynamical test for deterministic chaos developed by Gao and Zheng to analyze 280 sea clutter data measured under various sea and weather conditions. The method offers a more stringent criterion for detecting low-dimensional chaos, and can simultaneously monitor motions in phase space at different scales. However, no chaotic feature is observed from any of these scales. But more interestingly, we find that sea clutter can be conveniently characterized by the new concept of power-law sensitivity to initial conditions (PSiC), which generalizes the defining property for chaotic dynamics, the exponential sensitivity to initial conditions (ESIC). We show that PSIC offers a powerful method for detecting targets within sea clutter.