Piecewise fractional Brownian motion for modeling sea clutter

In this paper we mainly study the application of piecewise fractional Brownian motion (PFBM) to modeling radar sea clutter. Because the research objects in nature and man-made systems are usually not perfectly fractal in mathematics, the fractal properties of these researched objects cannot hold in the whole scale interval. Traditionally, the mono-fractal model of sea clutter only makes use of the self-similarity of sea clutter within the scale-invariant interval for parameter estimation but ignores the information contained in the scales outside the scale-invariant interval. The PFBM describes the sea clutter piecewisely in frequency domain, which corresponds to describing the sea clutter in time domain respectively on the large scale and on the fine scale. Combining the physical background, the PFBM model can explain the mechanism of the different roughnesses of a sea clutter time sequence respectively on the large scale and on the fine scale. Subsequently, in the paper, we study the effects of moving targets with different Doppler frequencies on sea clutter. The results show that moving targets can cause different effects on sea clutter respectively on the large scale and on the fine scale.