Outlier-robust truncated maximum likelihood parameter estimators of generalized Pareto distributions

Abstract

Compound-Gaussian model with inverse Gamma-distributed texture is widely used to characterize high-resolution sea clutter and is also referred to as the generalized Pareto (GP) distributions. In real oceanic environments, sea clutter data are often corrupted by a small number of outliers of very high intensity, which are probably from radar returns of ships or reefs. Thus, it is necessary to develop outlier-robust parameter estimators of the amplitude/intensity models of sea clutter for maritime radars. This paper proposes outlier-robust truncated maximum likelihood estimators of the GP distributions. To mitigate the influence of outliers on parameter estimation, the first k largest samples are deleted from the data to generate the right truncated data. The truncated likelihood function (TLF) of the two parameters is derived and the truncated maximum likelihood (TML) equations are given. An iterative algorithm is presented to fast attain the solution of the TML equations and outlier-robust TML estimators are developed, which are a generalization of the ML estimator in the case with outlier in data. The TML estimators are compared with outlier-sensitive estimators and existing outlier-robust estimators. Without outliers in data, the TML estimators have comparable performance with the best ML estimator. With outliers in data, the TML estimators attain higher precision than the existing outlier-robust estimators.