Modeling sea clutter as a nonstationary and nonextensive random process

Sea clutter is the backscattered returns from a patch of the sea surface illuminated by a radar pulse. It is of great importance to develop statistical models that properly characterize radar clutter returns. A lot of effort has been made to fit various distributions to the observed amplitude data of sea clutter. However, the fitting of those distributions to real sea clutter data is not excellent, and using parameters estimated from those distributions is not very effective for detecting targets within sea clutter. This may be due to the fact that sea clutter data is highly non-stationary. This non-stationarity motivates us to perform distributional analysis on the data obtained by differencing amplitude data of sea clutter. By systematically analyzing differenced data of 280 sea clutter time series measured under various sea and weather conditions, we show that differenced data of sea clutter are well fitted by the Tsallis distribution. The latter is obtained by maximizing the Tsallis entropy, a generalization of the Shannon (or Boltzman-Gibbs) entropy. Interestingly, we find that the nonextensitivity parameters estimated from the Tsallis distribution may be used to help detect low observable targets within sea clutter.