Fractional order Pareto distributions with application to X-band maritime radar clutter

The theory of fractional order calculus is applied to construct variations of the fundamental Pareto clutter model density, used in X-band maritime surveillance radar. Such data are characterised, at high resolution, by spiky clutter returns whose density function possesses heavy tails. By an application of fractional calculus to the Pareto distribution function, together with optimisation applied to determine the fractional derivative order, it is possible to obtain a new model for radar clutter. This is shown to fit real radar clutter returns better than a standard Pareto model. Additionally, it accounts for receiver thermal noise without the complexity of an additional noise distribution.