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This paper describes a new method of accurately estimating the parameters of an autoregressive (AR) process contaminated by high-level white noise. Based on the phase matching technique, it minimizes the difference between the phase of the all-zero model and the phase of the maximum phase signal reconstructed from the power spectrum of the observed signal. The parameters of the AR model are obtained from the finite length sequence of the estimated all-zero model. The proposed method works only when the order of the AR model is known a priori at present. However, since the phase matching technique satisfies the conditions needed to apply the least mean-square method, the AR parameters are estimated accurately even at a low signal-to-noise ratio. With the iterative or noniterative methods as discussed in the recent literature, it is not possible to reconstruct the all-zero model from the power spectrum when there are dips and peaks having no correlation with the poles of original AR signal in the power spectrum. The method proposed in this paper allows one to accurately reconstruct the phase from the power spectrum in such cases. Finally, it is confirmed with computer simulations and experiments that the proposed method is useful for accurate estimation of the AR parameters.