Givens rotation based least squares lattice and related algorithms

The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting...

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Vydáno v:IEEE transactions on signal processing Ročník 39; číslo 7; s. 1541 - 1551
Hlavní autor: Ling, F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.07.1991
Témata:
Adaptive filters
Estimation error
Filtering algorithms
Lattices
Least squares approximation
Least squares methods
Numerical stability
Recursive estimation
Signal processing algorithms
Systolic arrays
ISSN:1053-587X
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Shrnutí:The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting the relationship between the Givens algorithms and the recursive modified Gram-Schmidt algorithm, it is shown that the time and order update of any order-recursive LS estimation algorithm can be realized by employing only Givens rotations. Applying this general conclusion to LS estimation of time-series signals results in the Givens-lattice algorithms. Two Givens-lattice algorithms, one with square roots and the other without, are presented. It is shown that the Givens-lattice algorithms are computationally more efficient than the fast QR algorithm of Cioffi (1987). The derivation of other Givens rotation-based LS estimation algorithms and their systolic array implementations are discussed.< >
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ISSN:1053-587X
DOI:10.1109/78.134393