Covariance and autocorrelation methods for vector linear prediction

A novel least-squares formulation of the vector linear prediction (VLP) problem is presented. Based on this formulation, we develop two new design methods for obtaining the optimal vector predictor for frame-adaptive prediction: the covariance method and the autocorrelation method, which bear the names of the corresponding methods in scalar LPC analysis. Our formulation reveals several previously unrecognized properties of the resulting normal equation. Simulation results for VLP of speech waveforms confirm that the two proposed methods indeed give higher prediction gain than previously developed methods.