Abstract: In the non-Gaussian clutter modeled as spherically invariant random vectors, for the problems that existing methods of covariance matrix estimation are not fully adaptive and higher computational complexity, an adaptive estimator is devised based on experience (E-AR). Moreover, with E-AR as the initialization matrix for the recursive, the E-ARE is proposed. The E-AR and the E-ARE are only need to implement real number operation, and have lower computational complexity. The constant false alarm rate property to both of the clutter texture components and the normalized clutter covariance matrix of corresponding adaptive normalized matched filters (ANMFs) are proved theoretically, and are also validated by simulation. Finally, the effectiveness of proposed methods are evaluated and compared with the exiting method for the signal to clutter ratio (SCR) loss and the performance of corresponding ANMFs. The results show that proposed methods have the characteristic of faster convergence rate, fewer second data, smaller SCR loss and better performance of corresponding ANMFs.