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A Theory on the Convergence Behavior of the affine projection algorithm

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2011年第12期59卷 6233-6239页

作者： Kim, Seong-Eun Lee, Jae-Woo Song, Woo-Jin Pohang Univ Sci & Technol POSTECH Educ Inst Future Informat Technol Pohang 790784 South Korea Pohang Univ Sci & Technol POSTECH Div Elect & Comp Engn Pohang 790784 South Korea

In this paper, we present a theoretical convergence analysis of the affine projection algorithm (APA) based on the arguments of energy conservation. Although the APA and its convergence analysis have been widely studied, the dependency of weight-error vector on past noise is usually neglected for simplicity. To obtain accurate theoretical results for the APA, we here consider the dependency between the weight-error vector and past noise in the mean-square analysis presented by Shin and Sayed in ["Mean-square performance of a family of affine projection algorithms," IEEE Transactions on Signal Processing, vol. 52, no. 1, pp. 90-102, January 2004]. Through this work, we can also theoretically analyze the behavior of the periodic APA, which updates its weights periodically. Simulation results show that our theoretical results coincide closely with simulations.

关键词： Adaptive filter affine projection algorithm energy-conservation mean-square performance analysis

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A noise-resilient affine projection algorithm and its convergence analysis

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SIGNAL PROCESSING 2016年 121卷 94-101页

作者： Kim, Seong-Eun Lee, Jae -Woo Song, Woo-Jin MIT Dept Brain & Cognit Sci E25-618 Cambridge MA 02139 USA Pohang Univ Sci & Technol POSTECH Div Elect Engn Pohang 790784 South Korea

Recently a new normalized least mean square algorithm has been proposed by minimizing the summation of the squared Euclidean norms of the changes between the weight vectors to be updated and the past weight vector. The resultant algorithm exhibits noise resilience in that they prevent the adaptive filter from fluctuating around an optimal solution, but its convergence behavior has not been studied in detail. Thus, we first apply the constrained criterion to an affine projection algorithm (APA) for identifying a highly noisy system by reusing weight vectors. Since the performance of the APA declines under low signal-to-noise ratio (SNR) conditions, this approach is more effective for decreasing the steady-state mean-square deviation (MSD). Then, we analyze the convergence behavior of the proposed APA theoretically using energy conservation arguments. The experimental results show that the proposed theoretical results agree well with the simulation results. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Adaptive filter Normalized least mean square algorithm affine projection algorithm Weight vector reusing Energy conservation Mean-square performance analysis

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On the Convergence Behavior of affine projection algorithm with Direction Error

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ASIAN JOURNAL OF CONTROL 2014年第2期16卷 530-538页

作者： Zhi, Yongfeng Zheng, Xi Li, Ru Northwestern Polytech Univ Dept Automat Control Xian 710072 Shaanxi Peoples R China

An affine projection algorithm with direction error (AP-DE) is presented to solve the nonconformity between the iterated direction of the adaptive filter and the direction caused by the iteration error. A statistical analysis model is shown to analyze the AP-DE algorithm for autoregressive input signals. Deterministic recursive equations for the mean weight error and for the mean-square error in the iterated direction are derived. We also analyze the steady-state mean-square error in the iterated direction for the AP-DE algorithm. Simulation results are provided to corroborate the analytical results.

关键词： statistical analysis Adaptive filter iterated direction affine projection algorithm iteration error

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An affine projection algorithm with a data-selective method of using the condition number

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SIGNAL PROCESSING 2008年第5期88卷 1289-1296页

作者： Lee, Chang Woo Lee, Young Kow Kim, Sang Woo Pohang Univ Sci & Technol Div Elect & Comp Engn Pohang 790784 Gyungbuk South Korea

This paper proposes a novel affine projection (AP) algorithm that offers a data-selective method using the condition number as a criterion for low misalignment. Capable of keeping the condition number of an input data matrix small, the proposed AP algorithm adopts a recently reported technique of E-norm. instead of L-2-norm to reduce the computational burden during the estimation of the condition number. The simulation results show that the proposed algorithm has a lower misalignment than the conventional algorithm in the steady state. (C) 2007 Elsevier B.V. All rights reserved.

关键词： affine projection algorithm condition number misalignment data-selective method

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Augmented affine projection algorithm Based on Error Nonlinearity and Its Simplified Version

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2024年 72卷 2767-2782页

作者： Gu, Yanglong Ni, Jingen Soochow Univ Sch Elect & Informat Engn Suzhou 215006 Peoples R China

The augmented affine projection algorithm (AAPA) has a faster convergence rate than the augmented complex-valued LMS (ACLMS) algorithm for correlated inputs. However, they are both not robust against impulsive interference. This work proposes an improved AAPA based on error nonlinearity, which is implemented with the derivative of the logistic distance metric. To reduce its computational complexity, this work also proposes a simplified version of the improved AAPA using the first-order Taylor approximation of the exponential function that is included in the derivative of logistic distance metric. To study the stochastic behaviors of the improved AAPA and its simplified version, their stability conditions and transient and steady-state performance are analyzed. Simulations are performed in the context of system identification and stereo acoustic echo cancellation to show the merits of the two proposed algorithms and to verify the accuracy of the theory on stability conditions and transient and steady-state performance.

关键词： Adaptive filters Vectors Logistics Measurement Signal processing algorithms Filtering algorithms Noise affine projection algorithm augmented linear model impulsive interference logistic distance metric

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Low-Complexity Non-Uniform Penalized affine projection algorithm for Sparse System Identification

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2016年第5期35卷 1611-1624页

作者： Li, Yingsong Zhang, Chaozhu Wang, Shigang Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Peoples R China Heilongjiang Univ Sch Mech & Elect Engn Harbin 150080 Peoples R China

In this paper, an improved sparse-aware affine projection (AP) algorithm for sparse system identification is proposed and investigated. The proposed sparse AP algorithm is realized by integrating a non-uniform norm constraint into the cost function of the conventional AP algorithm, which can provide a zero attracting on the filter coefficients according to the value of each filter coefficient. Low complexity is obtained by using a linear function instead of the reweighting term in the modified AP algorithm to further improve the performance of the proposed sparse AP algorithm. The simulation results demonstrate that the proposed sparse AP algorithm outperforms the conventional AP and previously reported sparse-aware AP algorithms in terms of both convergence speed and steady-state error when the system is sparse.

关键词： affine projection algorithm Sparse system identification Zero attracting Norm penalty Adaptive filtering

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Combined Regularization Factor for affine projection algorithm Using Variable Mixing Factor

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IEEE ACCESS 2022年 10卷 120630-120639页

作者： Jiang, Menghua Gao, Ying Cai, Zhuoran Xu, Jindong Ou, Shifeng Yantai Univ Sch Phys & Elect Informat Yantai 264005 Peoples R China Yantai Univ Sch Comp & Control Engn Yantai 264005 Peoples R China

The affine projection algorithm with a fixed regularization parameter is subject to a compromise concerning the convergence speed and steady-state misalignment. To address this problem, we propose to employ a variable mixing factor to adaptively combine two different regularization factors in an attempt to put together the best properties of them. The selection of the mixing factor is derived by minimizing the energy of the noise-free a posteriori error, and for the sake of suppressing large fluctuations, a moving-average method is designed for updating the mixing factor. Based on a random walk model, we also prove that the proposed mixing factor is as well available for the non-stationary system. The mathematical analysis including the stability performance, steady-state mean square error, and computational complexity are performed. In practice, we compare with the existing related algorithms in system identification and echo cancellation scenarios, the results illustrate that the proposed algorithm outperforms them with notable margins.

关键词： Adaptive filter affine projection algorithm regularization factor variable mixing factor system identification

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Distributed Estimation Over an Adaptive Incremental Network Based on the affine projection algorithm

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第1期58卷 151-164页

作者： Li, Leilei Chambers, Jonathon A. Lopes, Cassio G. Sayed, Ali H. SARFT Acad Broadcast Planning Beijing 100045 Peoples R China Univ Loughborough Dept Elect & Elect Engn Adv Signal Proc Grp Loughborough LE11 3TU Leics England Univ Sao Paulo Dept Elect Syst Escola Politecn BR-05508 Sao Paulo Brazil Univ Calif Los Angeles Dept Elect Engn Adapt Syst Lab Los Angeles CA 90095 USA

We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton's method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.

关键词： Adaptive filters affine projection algorithm distributed estimation energy conversation

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Fast exact variable order affine projection algorithm

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SIGNAL PROCESSING 2012年第9期92卷 2308-2314页

作者： Ferrer, Miguel Gonzalez, Alberto de Diego, Maria Pinero, Gema Univ Politecn Valencia Audio & Commun Signal Proc Grp GTAC Inst Telecommun & Multimedia Applicat iTEAM Valencia Spain

Variable order affine projection algorithms have been recently presented to be used when not only the convergence speed of the algorithm has to be adjusted but also its computational cost and its final residual error. These kind of affine projection (AP) algorithms improve the standard AP algorithm performance at steady state by reducing the residual mean square error. Furthermore these algorithms optimize computational cost by dynamically adjusting their projection order to convergence speed requirements. The main cost of the standard AP algorithm is due to the matrix inversion that appears in the coefficient update equation. Most efforts to decrease the computational cost of these algorithms have focused on the optimization of this matrix inversion. This paper deals with optimization of the computational cost of variable order AP algorithms by recursive calculation of the inverse signal matrix. Thus, a fast exact variable order AP algorithm is proposed. Exact iterative expressions to calculate the inverse matrix when the algorithm projection order either increases or decreases are incorporated into a variable order AP algorithm leading to a reduced complexity implementation. The simulation results show the proposed algorithm performs similarly to the variable order AP algorithms and it has a lower computational complexity. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Adaptive filters affine projection algorithm Fast algorithm Computational complexity Efficient matrix inversion

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Optimal regularization parameter of the multichannel filtered-x affine projection algorithm

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2007年第10期55卷 4882-4895页

作者： Carini, Alberto Sicuranza, Giovanni L. Univ Urbino Informat Sci & Technol Inst I-61029 Urbino Italy Univ Trieste Dept Elect Elect & Comp Engn I-34127 Trieste Italy

We discuss the optimal regularization parameter of the Filtered-x affine projection (FX-AP) algorithm suitable for feedforward active noise control. While the original FX-AP algorithm always provides a biased estimate of the minimum-mean-square solution, we show that the optimal regularized FX-AP algorithm is capable to eliminate the bias of the asymptotic solution and thus that the regularization parameter can optimize both the convergence speed and the residual MSE of the algorithm. We derive some expressions for the optimal regularization parameter, and we discuss some heuristic estimations of the optimal regularization parameter in practical conditions.

关键词： active noise control affine projection algorithm multichannel adaptive filtering optimal regularization parameter

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