Robust non-recursive AR speech analysis

In this paper a robust non-recursive algorithm for estimating the linear prediction (LP) parameters of autoregressive (AR) speech signal model is proposed. Starting from Huber's robust M-estimation procedure, minimizing the sum of appropriately weighted residuals, a two-step robust LP procedure (RBLP) is derived. In the first step the Huber's convex cost function is selected to give more weights to the bulk of smaller residuals, while down-weighting the small portion of large residuals, and the Newton-type algorithm is used to minimize the adopted criterion. The proposed algorithm takes into account the non-Gaussian nature of the excitation for voiced speech, being characterized by heavier tails of the underlying distribution, which generates high-intensity signal realizations named outliers. The obtained estimates are used as a new start in the weighted least-squares procedure, based on a redescending function of the prediction residuals, which has to cut off the outliers. The experiments on both synthesized and natural speech have shown that the proposed two-step RBLP gives more efficient (less variance) and less biased estimates than the conve