On the relation between triangular matrix decomposition and linear prediction

1 January 1983

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE

Vol. 71 (12) , 1459-1460
https://doi.org/10.1109/proc.1983.12800

Abstract

It is shown that the coefficients of linear prediction for a random process and the prediction error variances are related to the covariance matrix through triangular decomposition. In particular, if the covariance matrix is written in the product form LDL^*where L is lower triangular with unit diagonal and D is diagonal, then the rows of L^-1are the coefficients of linear prediction and the elements of D are the prediction error variances.

Keywords

MATRIX DECOMPOSITION
COVARIANCE MATRIX
EQUATIONS
RANDOM PROCESSES
SYMMETRIC MATRICES
RANDOM VARIABLES
GOVERNMENT
VECTORS
NONLINEAR FILTERS