Convergence Performance of the Simplified Set-Membership Affine Projection Algorithm

Set-membership (SM) adaptive filtering is appealing in many practical situations, particularly those with inherent power and computational constraints. The main feature of the SM algorithms is their data-selective coefficient update leading to lower computational complexity and power consumption. The set-membership affine projection (SM-AP) algorithm does not trade convergence speed with misadjustment and computation complexity as many existing adaptive filtering algorithms. In this work analytical results related to the SM-AP algorithm are presented for the first time, providing tools to setup its parameters as well as some interpretation to its desirable features. The analysis results in expressions for the excess mean square error (MSE) in stationary environments and the transient behavior of the learning curves. Simulation results confirm the accuracy of the analysis and the good features of the SM-AP algorithms.     

Steady-State Mean-Square Performance Analysis of a Relaxed Set-Membership NLMS Algorithm by the Energy Conservation Argument

This paper presents an analysis of the steady-state mean-square error (MSE) of the set-membership normalized least-mean square (SM-NLMS) algorithm with relaxation and regularization parameters. These parameters are introduced for the purpose of deriving in a unified way the steady-state MSE performances of the $varepsilon$-normalized least mean square ($varepsilon$-NLMS) algorithm and a special case of the adaptive parallel subgradient projection (PSP) algorithm. The approach of the paper is to employ the energy conservation relation as a starting point of our analysis. This relation enables us to avoid the transient analysis of the SM-NLMS algorithm, which is in general hard due to the nonlinearity of the SM-NLMS algorithm. As a result, a few nonlinear equations whose solutions are theoretical steady-state MSEs are derived, where two types of reasonable assumptions are introduced to overcome the nonlinearity of the SM-NLMS algorithm. Our results are generalizations of well-known results of the steady-state MSE of the $varepsilon$-NLMS. Extensive simulations show the close agreement between our theories and experiments.      

Convergence and Performance Analysis of the Affine Projection Algorithm with Direction Error

A new statistical analysis model is pro-posed to analyze the Affine projection algorithm with di-rection error (AP-DE). Four assum ptions are m ade, which are based on the direction vector for the AP-DE algo-rithm. Under these assumptions, deterministic recursive equations for the weight error and for the m ean-square er-ror are derived. We also analyze the steady-state behavior of the AP-DE algorithm. Simulation results are provided to corroborate the analytical results.     

Adaptive Regularization Matrix for Affine Projection Algorithm

We propose an adaptive regularized affine projection algorithm (AR-APA) with a regularization matrix. Instead of the conventional fixed and weighted identity matrix for regularization, the proposed AR-APA incorporates a nonidentity regularization matrix which is dynamically updated. The adaptation of the regularization matrix is accomplished by the normalized stochastic gradient of mean-square error. Consequently, an efficient and robust APA is derived. Experimental results comparing the proposed AR-APA to the conventional algorithms clearly indicate its superior performance.     

一种指数型变步长仿射投影算法

可变平滑因子的变步长仿射投影算法需要根据投影误差范数的变化确定＂触发点＂,并切换平滑因子,实现较为复杂。为此这里提出了一种改进的指数型变步长仿射投影算法。该方法直接将投影误差的范数通过指数函数映射得到平滑因子,有效降低了实现复杂度。仿真结果表明该算法的均方偏差性能优于变步长仿射投影算法和常规的仿射投影算法。     

一种基于多尺度核学习的仿射投影滤波算法

为了提高强非线性信号的噪声消除和信道均衡能力,在核学习自适应滤波方法的基础上,该文提出一种基于惊奇准则的多尺度核学习仿射投影滤波方法(SC-MKAPA)。在核仿射投影滤波算法的基础上,对核组合函数结构进行改进,将多个不同高斯核带宽作为可变参数,与加权系数共同参与滤波器的更新;利用惊奇准则将计算结果稀疏化,根据仿射投影算法的约束条件对惊奇测度进行改进,简化其方差项,降低了计算的复杂度。将该算法应用于噪声消除、信道均衡以及MG时间序列预测中,与多种自适应滤波算法及核学习自适应滤波算法进行仿真结果的对比分析,验证了该算法的优越性。

     

不定阶变步长仿射投影算法

变步长仿射投影算法因结构简单、收敛速度快等优点而得到广泛重视。然而此算法由于计算量大,其应用受到一定限制。为了降低算法复杂度,利用变阶思想,在迭代过程中对投影阶数进行控制,文章提出一种新的变步长仿射投影算法——不定阶变步长仿射投影算法。该算法根据均方偏差的收敛条件,在迭代过程中不断减小投影阶数。仿真结果表明,该算法在减小计算量的同时还能保证很快的收敛速度和低的失调。     

简化仿射投影算法在回声抵消中的应用

针对通信中的回声抵消,介绍了一种简化的仿射投影算法,通过对仿射投影的简化,减小了算法复杂度,并对算法进行了鲁棒性设计,提高了算法的抗干扰能力和对近端语音的鲁棒性.仿真表明,算法在保持APA算法的收敛速度和信道跟踪能力的同时,具有较高的稳定性和可靠性.     

An Affine Projection Sign Algorithm Robust Against Impulsive Interferences

A new affine projection sign algorithm (APSA) is proposed, which is robust against non-Gaussian impulsive interferences and has fast convergence. The conventional affine projection algorithm (APA) converges fast at a high cost in terms of computational complexity and it also suffers performance degradation in the presence of impulsive interferences. The family of sign algorithms (SAs) stands out due to its low complexity and robustness against impulsive noise. The proposed APSA combines the benefits of the APA and SA by updating its weight vector according to the $L_{1}$-norm optimization criterion while using multiple projections. The features of the APA and the $L_{1}$-norm minimization guarantee the APSA an excellent candidate for combatting impulsive interference and speeding up the convergence rate for colored inputs at a low computational complexity. Simulations in a system identification context show that the proposed APSA outperforms the normalized least-mean-square (NLMS) algorithm, APA, and normalized sign algorithm (NSA) in terms of convergence rate and steady-state error. The robustness of the APSA against impulsive interference is also demonstrated.      

A New Affine Projection Algorithm and Its Statistical Behavior

An Affine projection algorithm with Direction error （AP-DE） is presented by redefining the iteration error. Under a measurement-noise-free condition, the iteration error is directly caused by the direction vector. A statistical analysis model is used to analyze the AP-DE algorithm. Deterministic recursive equations for the mean weight error and for the Mean-square error （MSE） in iteration direction are derived. We also analyze the stability of MSE in iteration direction and the optimal step-size for the AP-DE algorithm. Simulation results are provided to corroborate the analytical theory.     

Optimal Regularization Parameter of the Multichannel Filtered- x Affine Projection Algorithm

We discuss the optimal regularization parameter of the Filtered- 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.     

An Affine Projection Adaptive Filtering Algorithm With Selective Regressors

We present a novel affine projection algorithm which reduces complexity by selecting a subset of input regressors at every iteration. The optimal selection of input regressors is derived by comparing the cost functions based on the principle of minimum disturbance. The proposed algorithm shows good convergence performance with various experimental results     

A Stochastic Model for a Pseudo Affine Projection Algorithm

This paper presents a statistical analysis of a Pseudo Affine Projection (PAP) algorithm, obtained from the Affine Projection algorithm (AP) for a step size alpha < 1 and a scalar error signal in the weight update. Deterministic recursive equations are derived for the mean weight and for the mean square error (MSE) for a large number of adaptive taps N compared to the order P of the algorithm. Simulations are presented which show good to excellent agreement with the theory in the transient and steady states. The PAP learning behavior is of special interest in applications where tradeoffs are necessary between convergence speed and steady-state misadjustment.     

Low-Complexity Non-Uniform Penalized Affine Projection Algorithm for Sparse System Identification

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.     

基于可变阶数的集员滤波仿射投影算法

为了解决传统集员滤波仿射投影(SM-AP)算法收敛速度与稳态失调和计量复杂度之间的矛盾,提出一种新的数据选择性仿射投影算法。此算法在传统SM-AP算法的基础上,引入可变阶数(也称数据重用因子),称为基于可变数据重用因子的集员滤波仿射投影(VDRF-SM-AP)算法。通过利用步长提供的信息,此算法可以自动地分配数据重用因子,实现了在初始阶段数据重用因子大,收敛后数据重用因子小的目标,从而既保证了收敛速度又降低了稳态失调。通过理论分析和仿真验证,新算法的整体复杂度比其他传统的SM-AP算法低很多,同时保留了传统的SM-AP算法的快速收敛特性,但是却能达到更小的稳态失调。     

Distributed Estimation Over an Adaptive Incremental Network Based on the Affine Projection Algorithm

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.     

改进仿射投影算法及其在电子回声消除中的应用

在电子回声消除应用中,为提高自适应算法的收敛速度,提出一种改进的仿射投影算法及其快速实现形式.新算法利用回声路径的稀疏结构特征,通过收敛步长控制矩阵,按滤波器各系数幅值大小,等比例地为其指定相应收敛步长,以加快大系数收敛,最终达到加快滤波器整体收敛速度的目的.对新算法进行的统计学分析,为其快速收敛于目标系统的算法特性提供了理论依据.仿真实验表明与传统自适应算法相比,新算法能减小稳态失调并大幅提高收敛速度,其低计算复杂度亦保证了系统的实时性.     

Variable Step Size Affine Projection Algorithm for Adaptive Multiuser DS-CDMA MMSE Receiver

In this paper, we consider the use of affine projection algorithm (APA) for interference suppression in direct sequence code-division multiple-access (DS-CDMA) system. We first derive the multiuser fixed step-size APA (FSS-APA) algorithm. The computational complexity offered by the APA algorithm is linear in terms of the number of taps with additional terms of O (L ²) and a matrix inversion of dimension L, where L is known as the order of the filter. The value of L is chosen very small as compared to the number of filter-taps N _T . We next propose a novel variable step-size APA (VSS-APA) algorithm, which further improves the performance of the FSS-APA algorithm with very small increase in computational complexity as compared to the FSS-APA. It is demonstrated that the performance of the APA based minimum mean-square error (MMSE) receivers is far superior to that of the normalized least-mean-square (NLMS) based receivers. Though, the recursive-least-square (RLS) algorithm based adaptive receivers offer better performance but at the cost of much higher computational complexity.     

仿射不变的中心投影

考虑将区域和轮廓类不变特征提取算法结合:利用中心投影将目标转化为闭曲线,对闭曲线运用轮廓类方法提取不变特征.证明了图像经中心投影所得闭曲线保持仿射变换的结论.介绍了一种利用小波变换进行仿射不变特征提取的算法.对一些汉字、26个大写英文字母等的实验结果表明结论的有效性,与传统方法相比该算法对噪声具有较强的鲁棒性.     

基于M估计变步长自适应仿射投影算法的稳健时延估计

该文提出了一种基于M估计变步长自适应仿射投影方法的稳健时延估计(TDE)算法。该算法将自适应仿射投影算法应用于时延估计,无须事先假定信号和噪声的统计特性,自适应调整自身参数;应用稳健M估计理论,抵消重尾噪声干扰。数值仿真表明,在高斯噪声、非高斯噪声甚至冲激噪声的干扰下,该文算法比高阶统计量法和最小均方自适应法有更强的稳健性和更高的估计精度。