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In the clutter-dominated disturbance modeled as spherically invariant random vectors with the same covariance matrix and possibly correlated texture components, we propose an estimator of covariance matrix, which exploits all secondary data fully and introduces a constraint of matrix trace. Moreover, its adaptive target detection application is investigated. For match between the estimated clutter group size and the actual one, the adaptive normalized matched filter (ANMF) with the new estimator of any number of iterations theoretically ensures the constant false alarm rate (CFAR) property, with respect to the normalized clutter covariance matrix and the statistics of the texture. Furthermore, the simulation results show that it still guarantees the approximate CFAR property for mismatch cases and has an acceptable loss with respect to its nonadaptive counterpart in cases of relevant interest for radar applications. Finally, the effectiveness of ANMF with the proposed estimator is confirmed by Monte Carlo simulation.