Abstract: In the case of a certain estimated covariance matrix becoming singular in the non-Gaussian clutter context, which is modeled as a spherical invariant random vector, a self-adaptive range-spread target detection is addressed in this paper. We derive the modified maximum likelihood estimation for unknown parameters including non-Gaussian clutter covariance matrix and scatterer amplitudes; then get through with the approximate ML estimation of the texture; and devise a detector, the adaptively modified generalized likelihood ratio test (AMGLRT) . Simulation results show that the AMGLRT had the best performance if the target energy was uniformly distributed, while with increasing number of sensors or decreasing clutter spikiness alsos improve the AMGLRT detection performance. Without secondary data, the AMGLRT detector outperforms the existing common M/K detector.