A computationally efficient speech enhancement method is proposed. Reduction of computations is achieved due to derived properties of block model of autoregressive (AR) signal. Decreasing of filtering error in comparison with traditional Kalman filter is shown. The problem of estimation of speech AR parameters is also considered. A two-phase computationally efficient estimation procedure, based on vector quantization of AR parameters, is proposed. On the first stage the initial approximation for optimal AR parameters is determined on a small number of AR quantums. Then the value of estimate is improved by efficient iterative procedure. The performance of resulting method is evaluated on real speech signals.