A QRD-Based Array Lattice Form for H∞ Adaptive Filtering (original) (raw)
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IEEE Transactions on Signal Processing, 2001
Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with improved convergence properties are derived. They are based in the cascade lattice structure, which allows the derivation of sufficient conditions for local stability.
A new QRD-based block adaptive algorithm
Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181), 1998
In this paper we present a new robust adaptive algorithm. It is derived from the standard QR Decomposition based RLS (QRD-RLS) algorithm by introducing a non-orthogonal transforni into the update recursion. Instead of updating an upper triangular niatrix, as it is thecase for the QRD-RLS, we adapt an upper triangular block diagonal matrix. The coniplexity of the algorithm, thus obtained, varies from 0 (N2) to 0 (N) when the size of the diagonal blocks decreases. Simulations of the new algorithm have shown a better robustness than the standad QRD-based algorithm in the context of niultichannel 'adaptive filtering with highly intercorrelated channels.
A Practical Form of Exponentially-Weighted H ∞ Adaptive Filters
SICE Journal of Control, Measurement, and System Integration, 2014
This paper examines the problem of exponentially-weighted H ∞ adaptive filtering and shows that its suboptimal solution reduces to a recursive algorithm which is slightly different from the RLS algorithm. Based on this similarity, its fast array form is immediately obtained by following the derivation of the fast RLS array algorithm. Also a theoretical expression for its steady-state mean-square error is provided. Several numerical examples indicate that the exponentially-weighted H ∞ filter can achieve a proper balance between H ∞ and H 2 (least squares) filtering criteria.
Fast QR based IIR adaptive filtering algorithm
International Conference on Acoustics, Speech, and Signal Processing, 1999
In this paper, we present a new QR based algorithm for IIR adaptive filtering. This algorithm achieves a reduction of complexity with regard to the IIR-QR algorithm by using a block reduction transformation. Moreover, this new approach make it possible to directly transform fast FIR algorithm into fast 0 ( N ) versions of the IIR algorithm.
Performance analysis of signed self-orthogonalising adaptive lattice filter
This paper describes the novel signed self-orthogonalizing adaptive lattice filter (SSALF) structure to enhance the slow convergence rate caused by an eigenvalue disparity whilst constraining the level of the convergence rate and the misadjustment required by a specification. The SSALF structure is also implemented by the partial lattice predictor in order to reduce a computational complexity. The performance analysis based on the convergence model of the lattice predictor is given in terms of the mean-squared error and the variance of the reflection coefficient error. Computer simulations are undertaken to verify the performance and the applicability of the proposed filter structure. He has published a book and several papers on the dynamics of neural networks. He has investigated the stability of networks of intelligent agents for British Telecom. His current interest are in models of intelligent agents, where adaptation takes place via neural network learning and evolutionary selection. He is also combining soft computing and economic dynamics.
A Lattice Version of the Multichannel Fast QRD Algorithm Based on A Posteriori Backward Errors
Lecture Notes in Computer Science, 2004
Fast QR decomposition (QRD) RLS algorithms based on backward prediction errors are well known for their good numerical behavior and their low complexity when compared to similar algorithms with forward error update. Although the basic matrix expressions are similar, their application to multiple channel input signals generate more complex equations. This paper presents a lattice version of the multichannel fast QRD algorithm based on a posteriori backward errors updating. This new algorithm comprises scalar operations only; its modularity and pipelinability favors its systolic array implementation.
An unwindowed multichannel lattice filter with orthogonal channels
IEEE Transactions on Signal Processing, 1995
An unwindowed (or covariance) multichannel lattice filter for recursive least-squares estimation is derived. The channels are orthogonalized to eliminate the need for matrix inversion. The channel-orthogonalization process leads to forwardpropagating and backward-propagating blocks in both the lattice filter and the model-parameter construction algorithm. These blocks are particularly suitable for array processing, as illustrated by arrays presented in the paper.
Square-Root-Free QRD-LSL Adaptive Algorithm with Improved Numerical Robustness
Seventh International Conference on Networking (icn 2008), 2008
The QR-decomposition-based least-squares lattice (QRD-LSL) algorithm is one of the most attractive choices for adaptive filters applications, mainly due to its fast convergence rate and good numerical properties. In practice, the square-root-free QRD-LSL (SRF-QRD-LSL) algorithms are frequently employed, especially when fixedpoint digital signal processors (DSPs) are used for implementation. In this context, there are some major limitations regarding the large dynamic range of the algorithm's cost functions. Consequently, hard scaling operations are required, which further reduce the precision of numerical representation and lead to performance degradation. In this paper we propose a SRF-QRD-LSL algorithm based on a modified update of the cost functions, which offers improved numerical robustness. Simulations performed in fixed-point and logarithmic number system (LNS) implementation support the theoretical findings.
Realization of Block Adaptive Filters using Fermat Number Transforms
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