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In this paper, a low complexity ESPRIT algorithm based on power method and Orthogonal-triangular (QR) decomposition is presented for direction finding, which does not require a priori knowledge of source number and the predetermined threshold (separates the signal and noise eigen-values). Firstly, according to the estimation of noise subspace obtained by the power method, a novel source number detection method without eigen-decomposition is proposed based on QR decomposition. Furthermore, the eigenvectors of signal subspace can be determined according to Q matrix,and then the directions of signals could be computed by the ESPRIT algorithm. To determine the source number and subspace, the computation complexity of the proposed algorithm is approximated as (2log2 n+ 2.67)M3, where n is the power of covariance matrix and M is the number of array elements. Compared with the Single Vector Decomposition (SVD) based algorithm, it has a substantial computational saving with the approximation performance. The simulation results demonstrate its effectiveness and robustness.