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In this paper, the identification of AR processes whose measurements are corrupted by additive noise is considered. An approach to consistent estimation of AR processes is proposed that is based on solving eigenvalue problem. A nonlinear bias compensation equation (BCE) is derived via forward and backward LS predictors. By theoretical analysis, it becomes clear that unbiased estimate of the AR process is one of eigenvectors of a matrix, which consists of stochastic quantities of the output measurements. A method is presented for choosing the estimate from eigenvectors. The proposed algorithm is a batch processing form, it avoids some existing problems in on-line or iterative algorithms such as stability or convergence problems. Simulation results are given to verify the proposed method.