Multichannel linear prediction models and their convergence property

Abstract

AbstractThis paper considers theoretically the relation between the convergence problem of various algorithms and statistical properties of a signal appearing during construction of a linear prediction system of signals when the time series of the signal is a multiple Gaussian process. Specifically, we consider first the convergence problem of the covariance matrix of a predicted error arising as a linear prediction algorithm applied to the solution of a Yule‐Walker equation.Next, in comparison with the convergence speed of the correlation coefficient matrix of a multiple signal time series, we obtain an evaluation formula for the convergence speed of a covariance matrix of a linear prediction error. Furthermore, we discuss the convergence of an algorithm for constructing an orthonormalized polynomial matrix which corresponds to a transfer function matrix of a whitening filter from a solution of the Yule‐Walker equation. We present a concrete evaluation formula for the convergence speed of the algorithm.