One of the most general and acknowledged models for background statistics characterization is the family of elliptically symmetric distributions. They account for heterogeneity and non-Gaussianity of real data. Today, although nonGaussian models are assumed for background modeling and design of detectors, the parameters estimation is usually performed using classical Gaussian-based estimators. This letter analyzes robust estimation techniques in a nonGaussian environment and highlights their interest as an alternative to classical procedures for target detection purposes. The goal of this letter is to extend well-known detection methodologies to nonGaussian framework, when the statistical mean is nonnull and unknown. Furthermore, a theoretical closed-form expression for false-alarm regulation is derived and the Constant False Alarm Rate property is pursued to allow the detector to be independent of nuisance parameters. The experimental validation is conducted on simulations.