Fast Cholesky algorithms and adaptive feedback filters

In this paper, the Fast Cholesky algorithms, both by columns and by rows, are reviewed. It is shown that the algorithms lead naturally to a prediction error feedback filter. In addition, if this filter is used as the whitening filter for a moving average process, it is of fixed order but has time-varying coefficients. Simulation results for the case when the data came from the output of a moving average process driven by white Gaussian noise confirms theoretical results on convergence and stability of the triangular factors. In addition, the bandedness of the process being identified is revealed. Finally, from a VLSI implementation standpoint, it is shown that an array of CORDIC processors may be configured and controlled to factor a covariance matrix. In particular, there exists a method of factorization where the partial correlations associated with the given matrix are stored within the processors.