Numerically-robust O(N/sup 2/) RLS algorithms using least-squares prewhitening

Authors:
S. C. Douglas
Affiliations:
Dept. of Electr. Eng., Southern Methodist Univ., Dallas, TX, USA
Venue:
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
Year:
2000

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Abstract

We derive two new O(N/sup 2/) algorithms for arbitrary recursive least-squares (RLS) estimation tasks. The algorithms employ a novel update for an inverse square-root factor of the exponentially-windowed input signal autocorrelation matrix that is the least-squares equivalent of a natural gradient prewhitening algorithm. Both of the new RLS algorithms require 4N/sup 2/+O(N) multiply/adds, two divides, and one square root per iteration to implement. We can prove that our new algorithms are numerically-robust, and simulations are used to indicate this fact in fixed-point arithmetic. An algorithm that computes the square-root factorization of the input signal autocorrelation matrix is also described.