Parametric approaches based on a priori models of the speech are often used in the framework of speech enhancement using a single microphone. When the speech is modeled by means of a stationary autoregressive (AR) process, a frameby- frame approach is usually considered. However, it requires the unbiased estimations of the autoregressive parameters and of the noise variances for the subsequent implementation of a filter (Kalman, Hinf, etc.). The purpose of this paper is twofold. Firstly, we propose to view the AR parameter estimation as an errors-in-variables issue. Secondly, we implement an optimal smoothing procedure based on a constrained minimum variance estimation of the signal. Then, we test the procedure based on both steps in the field of speech enhancement.