In this paper, we propose sparsity-aware data-selective adaptive filtering algorithms with adjustable penalties. Prior work incorporates a penalty function into the cost function used in the optimization that originat...
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ISBN:
(纸本)9781538618950
In this paper, we propose sparsity-aware data-selective adaptive filtering algorithms with adjustable penalties. Prior work incorporates a penalty function into the cost function used in the optimization that originates the algorithms to improve their performance by exploiting sparsity. However, the strength of the penalty function is controlled by a scalar that is often a fixed parameter. In contrast to prior work, we develop a framework to derive algorithms that automatically adjust the penalty function parameter and the step size to achieve a better performance. Simulations for a system identification application show that the proposed algorithms outperform in convergence speed existing sparsity-aware algorithms.
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal app...
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In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depends on the number of observations and their innovation. The algorithms described herein use an adaptive step-size to accelerate the learning and can offer an excellent tradeoff between convergence speed and steady state, which allows them to solve nonlinear filtering and estimation problems with a large number of parameters without requiring a large computational cost. The data-selective update scheme also limits the number of operations performed and the size of the dictionary created by the kernel expansion, saving computational resources and dealing with one of the major problems of kernel adaptive algorithms. A statistical analysis is carried out along with a computational complexity analysis of the proposed algorithms. Simulations show that the proposed KNLMS algorithms outperform existing algorithms in examples of nonlinear system identification and prediction of a time series originating from a nonlinear difference equation. (C) 2018 Elsevier B.V. All rights reserved.
Adaptive filtering algorithms, which adopt the set-membership strategy, are able to attain good steady-state performance with low computational burden. In general, such advantages are obtained by defining a bounded-er...
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Adaptive filtering algorithms, which adopt the set-membership strategy, are able to attain good steady-state performance with low computational burden. In general, such advantages are obtained by defining a bounded-error. This specification translates into a time-variant step size, chosen in each iteration according to a nonlinear function of the instantaneous error. Unfortunately, this type of nonlinear behaviour hampers the stochastic modelling of these algorithms. This work devises a novel transient analysis of the set-membership Least Mean Squares algorithm. Additionally, a new interpretation is advanced about the implicit optimization problem solved by the algorithm. This explanation is important since it can contribute to the design of new adaptive algorithms. The proposed theoretical analysis provides predictions for: (i) steady-state performance;(ii) transient performance;and (iii) evolution of the update probability. It is noteworthy that the latter influences the computational complexity of the algorithm. Furthermore, we perform a novel comprehensive transient analysis of a set-membership algorithm. In addition, both time-variant transfer functions and deficient-length configurations are addressed. The resulting theoretical estimates are confirmed by simulations.
Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution ...
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ISBN:
(纸本)9781509041176
Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with nonlinearities. Nevertheless, these methods deal with kernel expansions, creating a growing structure also known as dictionary, whose size depends on the number of new inputs. In this paper, we derive the set-membership kernel-based normalized least-mean square (SM-NKLMS) algorithm, which is capable of limiting the size of the dictionary created in stationary environments. We also derive as an extension the set-membership kernel-based affine projection (SM-KAP) algorithm. Finally, several experiments are presented to compare the proposed SM-NKLMS and SM-KAP algorithms to existing methods.
Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution ...
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ISBN:
(纸本)9781509041183
Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with nonlinearities. Nevertheless, these methods deal with kernel expansions, creating a growing structure also known as dictionary, whose size depends on the number of new inputs. In this paper, we derive the set-membership kernel-based normalized least-mean square (SM-NKLMS) algorithm, which is capable of limiting the size of the dictionary created in stationary environments. We also derive as an extension the set-membership kernel-based affine projection (SM-KAP) algorithm. Finally, several experiments are presented to compare the proposed SM-NKLMS and SM-KAP algorithms to existing methods.
This paper presents a new set-membership proportionate normalized subband adaptive filter (SM-PNSAF) algorithm, named IAF-SM-PNSAF algorithm, by assigning an individual-activation-factor for each filter coefficient in...
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ISBN:
(纸本)9781509063529
This paper presents a new set-membership proportionate normalized subband adaptive filter (SM-PNSAF) algorithm, named IAF-SM-PNSAF algorithm, by assigning an individual-activation-factor for each filter coefficient instead of a common one for all filter coefficients as in the standard SM-PNSAF. The proposed IAF-SM-PNSAF algorithm obtains a large improvement in terms of the convergence rate and tracking capability for highly sparse system as compared to the NSAF, PNSAF, SM-PNSAF and SM-IPNSAF algorithms. Simulation results verify the superiority of the proposed IAF-SM-PNSAF algorithm.
A family of adaptive-filtering algorithms that uses a variable step size is proposed. A variable step size is obtained by minimizing the energy of the noise-free a posteriori error signal which is obtained by using a ...
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A family of adaptive-filtering algorithms that uses a variable step size is proposed. A variable step size is obtained by minimizing the energy of the noise-free a posteriori error signal which is obtained by using a known L-1-L-2 minimization formulation. Based on this methodology, a shrinkage affine projection (SHAP) algorithm, a shrinkage least-mean-squares (SHLMS) algorithm, and a shrinkage normalized least-mean-squares (SHNLMS) algorithm are proposed. The SHAP algorithm yields a significantly reduced steady-state misalignment as compared to the conventional affine projection (AP), variable-step-size AP, and set-membership AP algorithms for the same convergence speed although the improvement is achieved at the cost of an increase in the average computational effort per iteration in the amount of 11% to 14%. The SHLMS algorithm yields a significantly reduced steady-state misalignment and faster convergence as compared to the conventional LMS and variable-step-size LMS algorithms. Similarly, the SHNLMS algorithm yields a significantly reduced steady-state misalignment and faster convergence as compared to the conventional normalized least-mean-squares (NLMS) and set-membership NLMS algorithms.
An improved set-membership affine-projection (AP) adaptive-filtering algorithm is proposed. The new algorithm uses two error bounds that are estimated during the learning phase and by this means significantly reduced ...
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An improved set-membership affine-projection (AP) adaptive-filtering algorithm is proposed. The new algorithm uses two error bounds that are estimated during the learning phase and by this means significantly reduced steady-state misalignment is achieved as compared to those in the conventional AP and set-membership AP algorithms while achieving similar convergence speed and re-adaptation capability. In addition, the proposed algorithm offers robust performance with respect to the error bound, projection order, impulsive-noise interference, and in tracking abrupt changes in the underlying system. These features of the proposed algorithm are demonstrated through extensive simulation results in system-identification and echo-cancellation applications.
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