Abstract
We apply a fast adaptive condition estimation scheme, calledACE, to recursive least squares (RLS) computations in signal processing.ACE is fast in the sense that onlyO(n) operations are required forn parameter problems, and is adaptive over time, i.e., estimates at timet are used to produce estimates at timet + 1. RLS algorithms for linear prediction of time series are applied in various fields of signal processing: identification, estimation, and control. However, RLS algorithms are known to suffer from numerical instability problems under finite word-length conditions, due to ill-conditioning. We apply adaptive procedures, linear in the order of the problem, for accurately tracking relevant extreme eigen-values or singular values and the associated condition numbers over timet. In this paper exponentially weighted data windows are considered. The sliding data window case, which involves downdating as well as updating, is considered else-where. Numerical experiments indicate thatACE yields an accurate, yet inexpensive, RLS condition estimator for signal processing applications.
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Research supported by the Air Force under Grant No. AFOSR-88-0285 and by the National Science Foundation under Grant No. DMS-89-02121.
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Pierce, D.J., Plemmons, R.J. Tracking the condition number for RLS in signal processing. Math. Control Signal Systems 5, 23–39 (1992). https://doi.org/10.1007/BF01211974
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DOI: https://doi.org/10.1007/BF01211974