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It is well known that the high resolution eigensubspace methods for direction estimation will break down when the incoming signals are fully correlated. To alleviate this problem, the array covariance matrix may be preprocessed, using frequency smoothing in connection with the coherent signal-ubspace processing [l]. This paper attempts to provide an adaptive estimator needed for tracking time-varying signal parameters. We found that the new coherently averaged covariance matrix (CACM) can be updated by adding a rank-one matrix whenever newly received array data are available. From this, the coherent noise subspace of the CACM may be adjusted by a new adaptive algorithm, which is based on a constrained least-squares formulation under a noise-whitening preprocessing procedure. The proposed estimator consists of the RLS method followed by the Gram-Schmidt process. In terms of the rate of convergence and the tracking behavior, its performance is better than [2]. Besides, it offers some additional advantages, such as the robustness to rounding errors, the insensitivity to signal statistics and the suitability for real-time processings.G.H. Golub and C.F. Van Loan, Matrix Computations.[ti][7][8] ~~ Baltimore MD : Univ. Press 1983.