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Set-membership adaptive kernel NLMS algorithms: Design and analysis

SIGNAL PROCESSING 2019年 154卷 1-14页

作者： Flores, Andre de Lamare, Rodrigo C. Pontificia Univ Catolica Rio de Janeiro Ctr Telecommun Studies CETUC Rio de Janeiro Brazil Univ York Dept Elect Engn York N Yorkshire England

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.

关键词： adaptive algorithms Set-membership algorithms Data-selective techniques Kernel methods Statistical analysis

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Modeling and simulation of parallel adaptive divide-and-conquer algorithms

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JOURNAL OF SUPERCOMPUTING 2008年第3期43卷 241-255页

作者： Barros, Fernando J. Univ Coimbra Dept Informat Engn P-3030 Coimbra Portugal

Conventional modeling and simulation formalisms only give support to the representation of model behavior, providing no constructs for describing changes in model structure. However, some systems are better modeled by self-reconfigurable formalisms. We have developed the Discrete Flow System Specification (DFSS) to exploit dynamic structure, component-based and hierarchical model construction. Due to structural similarity, dynamic self-configuring DFSS models offer a good description of systems, like adaptive algorithms and reconfigurable computer architectures. In this paper, we present the modeling and simulation of a parallel adaptive divide-and-conquer integration algorithm in the CAOSTALK modeling and simulation framework, a realization of the DFSS formalism.

关键词： simulation dynamic structure models adaptive algorithms

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New centralised adaptive load-shedding algorithms to mitigate power system blackouts

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IET GENERATION TRANSMISSION & DISTRIBUTION 2009年第1期3卷 99-114页

作者： Seyedi, H. Sanaye-Pasand, M. Univ Tehran Sch Elect & Comp Engn Control & Intelligent Proc Ctr Excellence Tehran 14174 Iran

Conventional under-frequency load-shedding scheme is designed to retrieve the balance of generation and consumption following a disturbance. In the conventional load-shedding method, frequency settings, time-delay settings and the amount of load to be shed in each step are constant values. The loads to be shed by this scheme are also constant load feeders and not selected adaptively. This constant non-adaptive load-shedding algorithm is not the most efficient scheme for all power system disturbances. Application of centralised load-shedding algorithms could enhance adaptability of the load-shedding schemes. Two centralised adaptive load-shedding algorithms are proposed. The first algorithm is response-based and the second one is a combination of event-based and response-based methods. The proposed methods are capable of preserving power system instability even for large disturbances and combinational events. They use both frequency and voltage variables to select appropriate amount of load shedding. Parameters of the suggested schemes are also selected adaptively based on the magnitude of the disturbance. Performances of the proposed algorithms are evaluated by the application of the adaptive algorithms to the distributed and dynamic simulated model of a real power system. Obtained simulation results confirm that by using these algorithms various power system blackouts may be prevented.

关键词： adaptive algorithms algorithms load shedding crop load Event-based power systems

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Performance analysis of the low-complexity adaptive channel estimation algorithms over non-stationary multipath Rayleigh fading channels under carrier frequency offsets

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IET COMMUNICATIONS 2022年第9期16卷 988-1004页

作者： Hadei, Sayed A. Hosseini, S. Abolfazl Miri, Mohammadhasan Tarbiat Modates Univ Dept ECE POB 14115-143 Tehran Iran Islamic Azad Univ Tehran Shahr e Rey Branch Yadegar e Imam Khomeini RAH Coll Elect EngnDept Commun Tehran Iran Golestan Univ Dept ECE Golestan Golestan Iran

The use of selective partial updating method for reducing computational complexity of adaptive algorithms has been proposed recently. However, its performance analysis has not been studied as extensively and exactly as LMS or RLS algorithms for time-varying channel estimation. This paper provides performance analysis of the low-complexity family of affine projection algorithms based on selective partial update method on the estimation of multipath Rayleigh fading channels in the presence of carrier frequency offsets (CFO) and random channel variations. The analysis is based on the calculation of the error correlation matrix of the estimation, the mean-square weight error (MSWE) and the mean-square estimation error (MSE) parameters. The analysis does not use strong assumptions like small or large step-size, and explicit closed-form expressions for the MSE of estimation are obtained only from common hypotheses in wireless communication context. In this paper, the optimum step-size parameters minimizing the MSE of estimation are analytically derived without any simplifying assumptions. For the sake of comparison with other analytical approaches, the performance of the introduced algorithms is also investigated using the energy conservation relation. Likewise, for exact performance analysis, all the moment terms that appear in closed form expressions for the MSE of estimation are evaluated. Simulations are conduced to corroborate the presented studies and show that the theoretical results agree well with the simulation results over non-stationary multipath Rayleigh fading channels.

关键词： low-complexity family optimum step-size parameters carrier frequency offsets nonstationary multipath Rayleigh fading channels closed-form expressions exact performance analysis least mean squares methods multipath channels selective partial update method closed form expressions computational complexity channel estimation Rayleigh channels adaptive algorithms low-complexity adaptive channel estimation algorithms affine projection algorithms time-varying channels introduced algorithms adaptive filters random channel variations error correlation matrix selective partial updating method mean-square weight error time-varying channel estimation MSE mean-square estimation error parameters

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SPARSE adaptive TAYLOR APPROXIMATION algorithms FOR PARAMETRIC AND STOCHASTIC ELLIPTIC PDES

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ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 2013年第1期47卷 253-280页

作者： Chkifa, Abdellah Cohen, Albert DeVore, Ronald Schwab, Christoph Univ Paris 06 UMR 7598 Lab Jacques Louis Lions F-75005 Paris France CNRS UMR 7598 Lab Jacques Louis Lions F-75005 Paris France Texas A&M Univ Dept Math College Stn TX 77843 USA Swiss Fed Inst Technol Seminar Appl Math CH-8092 Zurich Switzerland

The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations can be simultaneously approximated in the Hilbert space V - H-0(1) (D) by multivariate sparse polynomials in the parameter vector y with a controlled number N of terms. The convergence rate in terms of N does not depend on the number of parameters in V, which may be arbitrarily large or countably infinite, thereby breaking the curse of dimensionality. However, these approximation results do not describe the concrete construction of these polynomial expansions, and should therefore rather be viewed as benchmark for the convergence analysis of numerical methods. The present paper presents an adaptive numerical algorithm for constructing a sequence of sparse polynomials that is proved to converge toward the solution with the optimal benchmark rate. Numerical experiments are presented in large parameter dimension, which confirm the effectiveness of the adaptive approach.

关键词： Parametric and stochastic PDE's sparse polynomial approximation high dimensional problems adaptive algorithms

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adaptive iterative thresholding algorithms for magnetoencephalography (MEG)

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第2期221卷 386-395页

作者： Fornasier, Massimo Pitolli, Francesca Univ Roma La Sapienza Dipartimento Metodi & Modelli Matemat Sci Applica I-00161 Rome Italy Princeton Univ Program Appl & Computat Math Princeton NJ 08544 USA

We provide fast and accurate adaptive algorithms for the spatial resolution of current densities in MEG. We assume that vector components of the current densities possess a sparse expansion with respect to preassigned wavelets. Additionally, different components may also exhibit common sparsity patterns. We model MEG as all inverse problem with joint sparsity constraints, promoting the coupling of non-vanishing components. We show how to compute solutions of the MEG linear inverse problem by iterative thresholded Landweber schemes. The resulting adaptive scheme is fast, robust, and significantly Outperforms the classical Tikhonov regularization in resolving sparse current densities. Numerical examples are included. (C) 2007 Elsevier B.V. All rights reserved.

关键词： Magnetoencephalography Inverse problems Iterative thresholding adaptive algorithms Matrix compression Wavelets

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Quantitative Assessment of the Efficiency of adaptive Spatial Processing algorithms in Detecting and Tracking the Low-Noise Underwater Vehicles in Various Shipping Conditions

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ACOUSTICAL PHYSICS 2024年第3期70卷 513-520页

作者： Mashoshin, A. I. Melkanovich, V. S. OJSC Concern Cent Res Inst Elektropribor St Petersburg 197046 Russia

The article describes the methodology and presents the results of a model quantitative assessment of the efficiency of solving the problem of detecting and tracking a low-noise underwater object using three algorithms for spatial signal processing at the output of a multielement array-the nonadaptive Bartlett algorithm, the Capon algorithm, and the Capon algorithm, combined with a projection procedure for limiting the signal power of strong local sources.

关键词： hydroacoustics multielement array spatial processing adaptive algorithms orthogonal projector simulation

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Improved strong tracking Sage-Husa adaptive algorithm for multi-MEMS IMU data fusion

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Review of Scientific Instruments 2025年第5期96卷 055002页

作者： Li, Kunpeng Wang, Kaixuan Song, Sujing Liu, Xuan He, Xiaowei Hou, Yuqing Tang, Sheng School of Information Science and Technology Northwest University Shannxi Xi’an710127 China

A circuit array of 16 micro-electro-mechanical system inertial measurement unit (IMUs) is developed, and an improved multi-IMU data fusion method based on the strong tracking Sage-Husa adaptive Kalman filter (ST-SHAKF) is proposed to achieve high-precision inertial measurement at low cost. The traditional Sage-Husa adaptive (SHAKF) algorithm is simplified for adaptive parameterization, with improved measurement noise variance estimation to ensure positive-definiteness. Filter divergence is addressed by supplementing the SHAKF with a strong tracking filter to maintain convergence. Dynamic weight allocation via minimum variance estimation enables effective multi-IMU data fusion. Experiments show that the proposed method significantly outperforms the traditional Sage-Husa adaptive Kalman filter in terms of Allan variance and standard deviation. Compared to traditional SHAKF, the proposed method achieves better noise suppression and improved fusion accuracy for both acceleration and angular velocity under both static and dynamic conditions. © 2025 Author(s).

关键词： adaptive algorithms

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adaptive constructive interval disjunction: algorithms and experiments

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CONSTRAINTS 2015年第4期20卷 452-467页

作者： Neveu, Bertrand Trombettoni, Gilles Araya, Ignacio Univ Paris Est Imagine LIGM Paris France Univ Montpellier CNRS LIRMM F-34059 Montpellier France Pontificia Univ Catolica Valparaiso Valparaiso Chile

An operator called CID and an efficient variant 3BCID were proposed in 2007. For the numerical CSP handled by interval methods, these operators compute a partial consistency equivalent to Partition-1-AC for the discrete CSP. In addition to the constraint propagation procedure used to refute a given subproblem, the main two parameters of CID are the number of times the main CID procedure is called and the maximum number of sub-intervals treated by the procedure. The 3BCID operator is state-of-the-art in numerical CSP, but not in constrained global optimization, for which it is generally too costly. This paper proposes an adaptive variant of 3BCID called ACID. The number of variables handled is auto-adapted during the search, the other parameters are fixed and robust to modifications. On a representative sample of instances, ACID appears to work efficiently, both with the HC4 constraint propagation algorithm and with the state-of-the-art Mohc algorithm. Experiments also highlight that it is relevant to auto-adapt only a number of handled variables, instead of a specific set of selected variables. Finally, ACID appears to be the best interval constraint programming operator for solving and optimization, and has been therefore added to the default strategies of the Ibex interval solver.

关键词： Interval methods adaptive algorithms Strong consistency

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A Survey of algorithms and Analysis for adaptive Online Learning

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JOURNAL OF MACHINE LEARNING RESEARCH 2017年第1期18卷 3117-3166页

作者： McMahan, H. Brendan Google Inc 651 N 34TH St Seattle WA 98103 USA

We present tools for the analysis of Follow-The-Regularized-Leader (FTRL), Dual Averaging, and Mirror Descent algorithms when the regularizer (equivalently, proxfunction or learning rate schedule) is chosen adaptively based on the data. Adaptivity can be used to prove regret bounds that hold on every round, and also allows for data-dependent regret bounds as in AdaGrad-style algorithms (e.g., Online Gradient Descent with adaptive per-coordinate learning rates). We present results from a large number of prior works in a unified manner, using a modular and tight analysis that isolates the key arguments in easily re-usable lemmas. This approach strengthens previously known FTRL analysis techniques to produce bounds as tight as those achieved by potential functions or primal-dual analysis. Further, we prove a general and exact equivalence between adaptive Mirror Descent algorithms and a corresponding FTRL update, which allows us to analyze Mirror Descent algorithms in the same framework. The key to bridging the gap between Dual Averaging and Mirror Descent algorithms lies in an analysis of the FTRL-Proximal algorithm family. Our regret bounds are proved in the most general form, holding for arbitrary norms and non-smooth regularizers with time-varying weight.

关键词： online learning online convex optimization regret analysis adaptive algorithms follow-the-regularized-leader mirror descent dual averaging

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