Compound Gaussian Radar Clutter Model With Positive Tempered Alpha-Stable Texture

The compound Gaussian (CG) family of distributions has achieved great success in modeling sea clutter. This work develops a flexible-tailed CG model with great potential to achieve high generality in clutter modeling, by introducing the positive tempered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-stable (PT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> S) distribution to model clutter texture. The PT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> S distribution exhibits widely tunable tails by tempering the heavy tails of the positive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-stable distribution, and it contains the gamma and inverse Gaussian (IG) distributions as special cases, thus providing greater flexibility in texture modeling. Specifically, we first develop a bivariate isotropic CG-PT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> S complex clutter model that is defined by an explicit characteristic function (CF), based on which the corresponding amplitude model is derived. Then, we prove that the amplitude model can be expressed as a scale mixture of Rayleighs, containing the well-established K and CG-IG clutter models as special cases. Furthermore, we present three estimators for the amplitude model, i.e., the CF-based parametric curve-fitting estimation, the tractable method of high-order moments, and the tractable method of CF derivatives. Finally, real-world sea clutter data analysis indicates the amplitude model's flexibility in modeling clutter data with various tail behaviors.