Numerically robust least-squares lattice-ladder algorithms with direct updating of the reflection coefficients

New time-recursive equations are derived for the reflection coefficients and the ladder gains in the a priori and a posteriori forms of the exact least-squares (LS) lattice-ladder filtering algorithms. The numerical accuracy of the LS lattice-ladder algorithms obtained by use of these new direct time update equations is analyzed and compared to the accuracy resulting from the conventional LS lattice-ladder algorithms. The analysis and a number of simulation results which are presented lead us to conclude that the new a priori and a posteriori forms of the LS lattice-ladder algorithms yield superior performance.