Parameter estimation for Pareto and K distributed clutter with noise

The form of the z log z estimator is derived for both Pareto and K distributed clutter plus noise. When noise is included, numerical zero finding is required to obtain the shape parameter from the estimator, but it still provides a robust and accurate method that is relatively quick to compute. It is compared with two other methods. The method of moments is the simplest and fastest to compute, but less accurate than other methods if the clutter shape parameter is small. A constrained maximum-likelihood (ML) estimator is constructed by maximising the log likelihood function in one dimension to find the shape parameter, while holding the mean power and clutter to noise ratio constant. This estimator is robust and accurate, but relatively slow because numerical integration is required to calculate the likelihood function, along with numerical optimisation to find the maximum. If the noise power is unknown, it can be obtained using the first two intensity moments in combination with either the constrained ML or z log z estimator. These combinations provide more robust and accurate estimates than the third intensity moment.