基于非线性主成分分析的自适应变步长盲源分离算法

算法的迭代步长对于算法的收敛性能有着重要影响。针对固定步长的非线性主成分分析(NPCA)算法不能兼顾收敛速度和估计精度的情形,提出基于梯度的自适应变步长NPCA算法和最优变步长NPCA算法两种自适应变步长算法来改善其收敛性能。特别地,最优变步长NPCA算法通过对代价函数进行一阶线性近似表示,从而计算出当前的最优迭代步长。该算法的迭代步长随估计误差的变化而变化,估计误差大,迭代步长相应大,反之亦然;且不需要人工设置任何参数。仿真结果表明,当算法的估计精度相同时,与固定步长NPCA算法相比,两种自适应变步长NPCA算法相对固定步长NPCA算法都具有更好的收敛速度或跟踪性能,且最优变步长NPCA算法的性能优于基于梯度的自适应变步长NPCA算法。     

一种新的变步长比例仿射投影算法研究

研究比例仿射投影算法,针对自适应算法收敛速度和稳态误差之间的矛盾,提出了一种变步长的改进比例仿射投影算法( VSS- IPAPA).利用后验误差去补偿干扰信号对系统稳态性能的影响,得到了算法新的最优步长准则,根据步长准则以及先验误差与后验误差之间的联系,导出了一种适用于比例仿射投影的步长调节方法.综合了稀疏算法、数据重用方法及变步长的优点.最后通过对改进算法进行仿真,结果表明,在增加少量计算量的情况下,系统的收敛速度和稳态性能有明显的改善,证明了比例仿射投影算法的有效性.     

Optimal variable step-size LMS model and algorithm with independence assumption

To solve the contradiction between convergence rate and steady-state error in least mean square (LMS) algorithm, basing on independence assumption, this paper proposes and proves the optimal step-size theorem from the view of minimizing mean squared error (MSE). The theorem reveals the one-to-one mapping between the optimal step-size and MSE. Following the theorem, optimal variable step-size LMS (OVS-LMS) model, describing the theoretical bound of the convergence rate of LMS algorithm, is constructed. Then we discuss the selection of initial optimal step-size and updating of optimal step-size at the time of unknown system changing. At last an optimal step-size LMS algorithm is proposed and tested in various environments. Simulation results show the proposed algorithm is very close to the theoretical bound.     

基于误差信号峰度的时变步长恒模盲均衡算法

论文针对固定步长恒模盲均衡算法的缺陷,提出了一种自适应时变步长恒模盲均衡算法,采用误差信号的峰度作为步长控制因子。经计算机仿真与理论分析表明,该算法与传统恒模算法相比,收敛速度加快,稳态剩余误差减小。     

Improved variable step-size NLMS adaptive filtering algorithm for acoustic echo cancellation

Acoustic echo canceller (AEC) is used in communication and teleconferencing systems to reduce undesirable echoes resulting from the coupling between the loudspeaker and the microphone. In this paper, we propose an improved variable step-size normalized least mean square (VSS-NLMS) algorithm for acoustic echo cancellation applications based on adaptive filtering. The steady-state error of the NLMS algorithm with a fixed step-size (FSS-NLMS) is very large for a non-stationary input. Variable step-size (VSS) algorithms can be used to decrease this error. The proposed algorithm, named MESVSS-NLMS (mean error sigmoid VSS-NLMS), combines the generalized sigmoid variable step-size NLMS (GSVSS-NLMS) with the ratio of the estimation error to the mean history of the estimation error values. It is shown from single-talk and double-talk scenarios using speech signals from TIMIT database that the proposed algorithm achieves a better performance, more than 3 dB of attenuation in the misalignment evaluation compared to GSVSS-NLMS, non-parametric VSS-NLMS (NPVSS-NLMS) and standard NLMS algorithms for a non-stationary input in noisy environments.     

A variable step-size selective partial update LMS algorithm

Selective partial update of the adaptive filter coefficients has been a popular method for reducing the computational complexity of least mean-square (LMS)-type adaptive algorithms. These algorithms use a fixed step-size that forces a performance compromise between fast convergence speed and small steady state misadjustment. This paper proposes a variable step-size (VSS) selective partial update LMS algorithm, where the VSS is an approximation of an optimal derived one. The VSS equations are controlled by only one parameter, and do not require any a priori information about the statistics of the system environment. Mean-square performance analysis will be provided for independent and identically distributed (i.i.d.) input signals, and an expression for the algorithm steady state excess mean-square error (MSE) will be presented. Simulation experiments are conducted to compare the proposed algorithm with existing full-update VSS LMS algorithms, which indicate that the proposed algorithm performs as well as these algorithms while requiring less computational complexity.     

用于稀疏系统辨识的变步长加权零吸引最小平均p范数算法

在α稳定分布噪声背景下,为了提高稀疏系统自适应辨识算法的稳态性能,提出了基于无噪先验误差功率函数的变步长加权零吸引最小平均p范数基本算法(BVSS-RZA-LMP)和变步长加权零吸引最小平均p范数改进算法(IVSS-RZA-LMP).两种算法分别根据无噪先验误差功率和加权的无噪先验误差功率计算新的步长;步长随无噪先验误差功率的减小而逐渐减小.当算法达到稳态时, IVSS-RZA-LMP算法不再调整权矢量,改进了BVSSRZA-LMP算法稳态性能.α稳定分布噪声背景下的系统辨识仿真结果表明,当系统较稀疏时, IVSS-RZA-LMP算法能够在较快收敛的情况下获得非常小的稳态误差.     

一种新的变步长自适应滤波算法研究

针对滤波器在亚模型(under-modeling)工作状态下定步长自适应算法收敛速度和稳态误差之间的矛盾,提出一种变步长分割式比例仿射投影算法(VSS-SPAPA)。该算法考虑到系统干扰噪声和滤波器权系数个数小于回声路径长度时引起的亚模型噪声对回声消除系统性能的影响,利用后验误差去补偿这两类噪声的负面作用,建立一个新的目标函数,根据该目标函数,导出一种适用于比例仿射投影算法整体步长的调节方法。仿真结果表明:在增加少量计算量的情况下,新算法的收敛速度和稳态性能与定步长比例仿射投影算法以及已有变步长算法相比得到了明显提高。     

New IIR filter-based adaptive algorithm in active noise control applications: Commutation error-introduced LMS algorithm and associated convergence assessment by a deterministic approach

In this study, commutation error (CE) is defined in adaptive infinite impulse response (IIR) filter-based ANC systems. CE is subsequently introduced into a new residual error to develop a new LMS-based ANC algorithm in an aim to liberate the restriction of slow adaptation posed on traditional ANC algorithms. A new deterministic analysis based on a linear time-varying system is performed to investigate convergence properties of the developed algorithm: (1) An optimal step size for the fastest convergence rate can be derived. (2) Given a persistent excitation condition and a step-size constraint, we find that the algorithm is uniformly asymptotically stable. Computer simulations indeed demonstrate a greatly improved convergence rate and efficient ANC performance for the developed algorithm as compared with that using the conventional algorithms. Experimental results verify the enhanced ANC performance in real applications. These together support the new IIR filter-based adaptive algorithm that includes CE for superior ANC performance with respect to the convergence rate and noise reduction level.     

A unified framework for adaptive filter algorithms with variable step-size

Employing a recently introduced framework within which a large number of classical and modern adaptive filter algorithms can be viewed as special cases, we extend this framework to cover block normalized LMS (BNLMS) and normalized data reusing LMS (NDRLMS) adaptive filter algorithms. Accordingly, we develop a generic variable step-size adaptive filter. Variable step-size normalized LMS (VSSNLMS) and VSS affine projection algorithms (VSSAPA) are particular examples of adaptive algorithms covered by this generic variable step-size adaptive filter. In this paper we introduce two new VSS adaptive filter algorithms named the variable step-size BNLMS (VSSBNLMS) and the variable step-size NDRLMS (VSSNDRLMS) based on the generic VSS adaptive filter. The proposed algorithms show the higher convergence rate and lower steady-state mean square error compared to the ordinary BNLMS and NDRLMS algorithms.     

Superior step-size theorem and its application

With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construct a parallel variable step-size LMS filters algorithm. The theoretical model of the proposed algorithm is analyzed in detail. Simulations show the proposed theoretical model is quite close to the optimal variable step-size LMS (OVS-LMS) model. The experimental learning curves of the proposed algorithm also show the fastest convergence and fine tracking performance. The proposed algorithm is therefore a good realization of the OVS-LMS model.     

改进的变步长频域批处理LMS算法

现有的单载波频域均衡技术中的定步长频域批处理LMS（Frequency-Domain Block Least Mean Square,FBLMS）算法,在收敛速度和稳态误差之间存在矛盾。针对这个问题,基于对变步长LMS算法的研究分析,提出了一种新的改进的变步长频域批处理LMS自适应滤波算法,通过变步长因子以及频域权系数抽头泄漏能很好地协调收敛速度和稳态误差之间的矛盾,并且还具有较低的算法复杂度的特点。通过Matlab对提出的新算法进行计算机仿真验证,结果表明该算法有较好的收敛速度和较小的稳态误差。     

Superior step-size theorem and its application-Parallel variable step-size LMS filters algorithm

With independence assumption, this paper proposes and proves the superior step-size theorem on least mean square (LMS) algorithm, from the view of minimizing mean squared error (MSE). Following the theorem we construct a parallel variable step-size LMS filters algorithm. The theoretical model of the proposed algorithm is analyzed in detail. Simulations show the proposed theoretical model is quite close to the optimal variable step-size LMS (OVS-LMS) model. The experimental learning curves of the proposed algorithm also show the fastest convergence and fine tracking performance.The proposed algorithm is therefore a good realization of the OVS-LMS model.     

Superior step-size theorem and its application——Parallel variable step-size LMS filters algorithm

In several branches of adaptive filtering algorithms, the least mean square (LMS) algorithm is widely applied in many areas because of its low computational cost, good numerical stability and other features[1]. However, the contradiction between faster convergence and smaller steady-state mean squared error (MSE) affects its performance considerably. Step-size, as the key to the problem, can but offer only one choice of the two demands. Therefore, many variable step-size algorithms were prop…     

一种快速收敛的变步长自适应谐波检测算法

为解决传统固定步长LMS自适应算法在电网谐波检测中存在的收敛速度和稳态误差之间的矛盾,本文提出了一种快速收敛的变步长自适应谐波检测算法。该算法以误差反馈信号、误差信号在总误差信号中所占的比率以及负载电流的相邻两个采样值之差的和作为自适应反馈量,并通过自适应反馈量的相干平均估计来控制步长的更新;同时对系统权值迭代公式进行改进提高收敛速度;并改传统的固定步长变化范围为时变范围,使步长变化更加平滑。该方法在负载突变的情况下有很好的跟踪性能,可有效的提高初始收敛速度、减小稳态失调。仿真分析及实验证明了该算法在谐波检测中的有效性和准确性。     

变步长比例归一化子带自适应滤波算法研究

针对欠定模型条件下定步长比例归一化子带自适应滤波(PNSAF)算法收敛速度和稳态误差之间的矛盾,提出了一种变步长VSS-PNSAF算法。该算法将系统干扰噪声和欠定模型噪声对系统性能的影响考虑进滤波器系数更新过程中,利用后验误差对其进行补偿,根据先验误差与后验误差之间的联系,导出了一种适用于比例归一化子带自适应滤波算法的步长调节方法。该算法综合了子带自适应滤波、比例自适应算法及变步长方法的优点。仿真结果表明:与定步长比例归一化子带自适应滤波算法相比,所提算法具有更低的稳态误差和更快的收敛速度。     

一种改进的变步长LMS自适应算法及分析

现有的变步长LMS算法中,大都采用建立步长因子与误差信号的函数关系的方法,以提高算法的收敛速度和跟踪性能,但由于未考虑输入信号对算法性能的影响,使得当输入信号发生变化后,稳态误差明显增大。为此,在现有算法的基础上,引入了输入信号因子,提出了一种改进算法。该算法可根据瞬时误差和输入信号来调整步长因子,使算法不仅能保持较高的收敛速度和跟踪性能,还可在输入信号变化的情况下,保证较小的稳态误差。理论分析及仿真实验表明新算法的性能优于现有算法。     

L-DACS中的信号分离算法的研究

L波段数字航空通信系统(L-DACS)是未来20年乃至更长时间航空通信需求的航空通信系统。为了解决接收机更好地区别有用信号,通过研究固定步长EASI算法和变步长EASI(VS-EASI)算法,提出一种基于优选估计函数的EASI峭度变步长(Q-EASI)算法。该算法根据信号的分离状态与峭度方差的关系,使步长随峭度方差的变化而变化,从而使收敛速度与稳态误差之间的矛盾得以缓解,并在信号分离的不同阶段使用不同的估计函数,使稳态误差得以减小。仿真验证,新算法相对于传统算法在稳定性和收敛速度上都有较大提高。     

Improved performance of impulse active noise control using active function threshold with absolute harmonic variable step-size algorithm

The Standard (conventional) adaptive algorithms exhibits low convergence rate and minimum noise suppression, or else the system becomes unstable under Gaussian and non-Gaussian (impulsive noise SαS distributions) noise environments. In order to overcome the drawback of traditional algorithms (i.e., to eliminate unwanted noise), the popular algorithm Filtered Cross Minimum Square (FxLMS) is used in Active Noise Control (ANC), not only to improve its efficiency but also to improve its performance. In this paper, we proposed two improvements: first, we proposed a novel method Active threshold function FxLMS (ATFxLMS) being employed in ANC in the paths of primary (reference) and error signals; a second proposal is employing the Variable Step-Size based on Absolute Harmonic Mean (AHMVSS) of error signal. The idea behind this method is that the step-size of the algorithm varies depending on the harmonic mean of error signal obtained from the error location. In comparison to the fixed step-size algorithm, the proposed ATF-AHMVSS provided an improved convergence rate for the desired ANC efficiency. Moreover computational complication of the proposed method was examined as it was found that the proposed algorithm provided stable condition for ANC systems. Computer simulation results are revealed that the proposed (AT & AHMVSS-FxLMS) algorithm have attained excellent performance in terms of convergence speed, noise reduction and minimum steady state error as compared to other existing algorithms under different noise inputs. The results obtained from the proposed algorithm show outperformance compared to traditional adaptive algorithms.     

基于改进仿射投影算法的数字助听器自适应回声消除

提出了一种改进的仿射投影算法。该算法建立了步长因子与误差能量之间一种新的非线性函数关系,根据误差能量的变化自动调整步长因子,以达到加快滤波器收敛速度、降低稳态失调的目的;在对误差能量的估计中提出了遗忘因子选择规则,提高了误差能量估计的准确性。对提出的算法进行的数学分析,为其快速收 敛性提供了理论依据。实验仿真表明,与传统的自适应算法以及固定步长的仿射投影算法相比,提出的改进仿射算法在收敛速度、稳态失调等方面有明显改善。