Accurate estimation of transfer function of all-pole model system from the signal buried in noise

This paper describes a new method to estimate accurately the parameters of an auto-regressive (AR) process corrupted with high level white noise. It is based on the phase matching by minimizing 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. Since the phase matching technique is satisfactory to the conditions needed in applying the least mean square method, the AR parameters are estimated accurately even at the low signal-to-noise ratio. The iterative or non-iterative methods in the recent literature fail in reconstructing 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. However, the method proposed in this paper is also used for reconstructing the phase from the power spectrum in such cases. Finally, it is confirmed with computer simulations that the proposed method is useful for accurate estimation of the AR parameters.