Simple adaptive algorithms for Cholesky, LDL/sup T/, QR, and eigenvalue decompositions of autocorrelation matrices for sensor array data

This paper introduces simple adaptive algorithms for tracking the Cholesky, LDL/sup T/, QR, and eigenvalue decompositions of autocorrelation matrices for sensor array data. The proposed algorithms employ multiplicative updates without costly divides, square roots, or cos/sin operations. Analyses of the algorithms using the ordinary differential equation (ODE) method verify that they converge to their respective solutions. Simulations indicate that all of the algorithms perform their respective tasks and that the adaptive Cholesky and LDL/sup T/ algorithms are particularly competitive.