A hybrid least squares QR-lattice algorithm using a priori errors

Miranda, María Dolores Martínez; Gerken, M.

doi:10.1109/78.650249

Cited by 20 publications

(9 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From (38), we get (39) where are auxiliary parameters given by . Since the Givens rotation annihilates the first nonzero element of the second row, it can be shown that (40) Combining (38) and (40), we have (41) and…”

Section: Givens-based Approximate Qr-ls Algorithmmentioning

confidence: 98%

“…The first class of algorithm recursively updates the inverse of the correlation matrix of the input signal using certain time-and order-recursions [1]- [5], [9]- [11], [21], [22], [39]. The second class of algorithms works directly with the data matrix using QR decomposition (QRD) [Givens rotation or Householder transformation] [6]- [8], [20]- [24], [37], [38], [40]- [42]. Fast RLS algorithms using the QRD usually exhibit better numerical property because of their lower condition number of the system, as compared with that of the input correlation matrix, which is square of that of the data matrix.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved Approximate QR-LS Algorithms for Adaptive Filtering

Chan¹,

Yang²

2004

IEEE Trans. Circuits Syst. II

View full text Add to dashboard Cite

This paper studies a class of ( ) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It reduces to the QR-LMS algorithm proposed by Liu et al. in 1998, when all the normalization constants are chosen as the Euclidean norm of the input signal vector. An improved transform-domain approximate QR-LS (TA-QR-LS) algorithm, where the input signal vector is first approximately decorrelated by some unitary transformations before the normalization, is proposed to improve its convergence for highly correlated signals. The mean weight vectors of the algorithms are shown to converge to the optimal Wiener solution if the weighting factor of the algorithm is chosen between 0 and 1. New Givens rotations-based algorithms for the A-QR-LS, TA-QR-LS, and the QR-LMS algorithms are proposed to reduce their arithmetic complexities. This reduces the arithmetic complexity by a factor of 2, and allows square root-free versions of the algorithms be developed. The performances of the various algorithms are evaluated through computer simulation of a system identification problem and an acoustic echo canceller.Index Terms-Adaptive filtering, approximate QR-LS algorithm, performance analysis, QR-LMS algorithm, square root free Givens based algorithms, transformed domain LMS algorithm.

show abstract

Section: Givens-based Approximate Qr-ls Algorithmmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Improved Approximate QR-LS Algorithms for Adaptive Filtering

Chan¹,

Yang²

2004

IEEE Trans. Circuits Syst. II

View full text Add to dashboard Cite

show abstract

“…A fundamental result in the derivation of the fast QR-RLS has been reported (McWhirter 1983). In recent years, a number of fast QR-RLS algorithms have been introduced, using McWhirter's filter and exploiting forward and backward linear prediction to update the weights (Haykin 1991;Regalia 1993;Yang and Bohme 1992;Morris and Khemaissia 1995;Miranda and Gerken 1997). The purpose of this paper is to introduce a new kind of linearized training algorithm for feedforward neural networks.…”

Section: Introductionmentioning

confidence: 99%

A Fast New Algorithm for a Robot Neurocontroller Using Inverse QR Decomposition

Morris

Khemaissia

2000

The International Journal of Robotics Research

View full text Add to dashboard Cite

A new adaptive neural network controller for robots is presented. The controller is based on direct adaptive techniques. Unlike many neural network controllers in the literature, inverse dynamical model evaluation is not required. A numerically robust, computationally efficient processing scheme for neural network weight estimation is described, namely, the inverse QR decomposition (INVQR). The inverse QR decomposition and a weighted recursive least-squares (WRLS) method for neural network weight estimation is derived using Cholesky factorization of the data matrix. The algorithm that performs the efficient INVQR of the underlying space-time data matrix may be implemented in parallel on a triangular array. Furthermore, its systolic architecture is well suited for VLSI implementation. Another important benefit of the INVQR decomposition is that it solves directly for the time-recursive least-squares filter vector, while avoiding the sequential back-substitution step required by the QR decomposition approaches.

show abstract

“…Starting from the conventional (or O[N 2 ]) QR decomposition method [5], a number of fast algorithms (O[N ]) were derived [4], [8], [6], [9], [1]. It was shown in [1] that these algorithms can be classified in terms of the type of triangularization applied to the input data matrix (upper or lower triangular) and type of error vector (a posteriori or a priori) used in the updating process.…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in [1] that these algorithms can be classified in terms of the type of triangularization applied to the input data matrix (upper or lower triangular) and type of error vector (a posteriori or a priori) used in the updating process. It can be seen from the Gram-Schmidt orthogonalization procedure that an upper triangularization (in [6], [9] the notation adopted in this work) updates the forward prediction errors, whereas, lower triangularization updates backward prediction errors. Table 1 presents the classification used in [1] and introduces how these algorithms will be designated hereafter.…”

Section: Introductionmentioning

confidence: 99%

Fast QR Algorithms Based on Backward Prediction Errors: A New Implementation and Its Finite Precision Performance

Apolinario

Siqueira

Diniz

2003

Circuits Syst Signal Process

View full text Add to dashboard Cite

QR decomposition techniques are well known for their good numerical behavior and low complexity. Fast QRD recursive least squares adaptive algorithms benefit from these characteristics to offer robust and fast adaptive filters. This paper examines two different versions of the fast QR algorithm based on a priori backward prediction errors as well as two other corresponding versions of the fast QR algorithm based on a posteriori backward prediction errors. The main matrix equations are presented with different versions derived from two distinct deployments of a particular matrix equation. From this study, a new algorithm is derived. The discussed algorithms are compared, and differences in computational complexity and in finite-precision behavior are shown.

show abstract

A hybrid least squares QR-lattice algorithm using a priori errors

Cited by 20 publications

References 11 publications

Improved Approximate QR-LS Algorithms for Adaptive Filtering

Improved Approximate QR-LS Algorithms for Adaptive Filtering

A Fast New Algorithm for a Robot Neurocontroller Using Inverse QR Decomposition

Fast QR Algorithms Based on Backward Prediction Errors: A New Implementation and Its Finite Precision Performance

Contact Info

Product

Resources

About