Pipelined robust M-estimate adaptive second-order Volterra filter against impulsive noise

The main limits on adaptive Volterra filters are their computational complexity in practical implementation and significant performance degradation under the impulsive noise environment. In this paper, a low-complexity pipelined robust M-estimate second-order Volterra (PRMSOV) filter is proposed to reduce the computational burdens of the Volterra filter and enhance the robustness against impulsive noise. The PRMSOV filter consists of a number of extended second-order Volterra (SOV) modules without feedback input cascaded in a chained form. To apply to the modular architecture, the modified normalized least mean M-estimate (NLMM) algorithms are derived to suppress the effect of impulsive noise on the nonlinear and linear combiner subsections, respectively. Since the SOV-NLMM modules in the PRMSOV can operate simultaneously in a pipelined parallelism fashion, they can give a significant improvement of computational efficiency and robustness against impulsive noise. The stability and convergence on nonlinear and linear combiner subsections are also analyzed with the contaminated Gaussian (CG) noise model. Simulations on nonlinear system identification and speech prediction show the proposed PRMSOV filter has better performance than the conventional SOV filter and joint process pipelined SOV (JPPSOV) filter under impulsive noise environment. The initial convergence, steady-state error, robustness and computational complexity are also better than the SOV and JPPSOV filters.     

Hierarchical partial update generalized functional link artificial neural network filter for nonlinear active noise control

To reduce the computational burden of the generalized FLANN (GFLANN) filter for nonlinear active noise control (NANC), a hierarchical partial update GFLANN (HPU-GFLANN) filter is presented in this paper. Based on the principle of divide and conquer, the proposed HPU-GFLANN divides the complex GFLANN filter (i.e., long memory length and large cross-terms selection parameter) into simple small-scale GFLANN modules and then interconnected in a pipelined form. Since those modules are simultaneously performed in a parallelism fashion, there is a significant improvement in computational efficiency. Besides, a hierarchical learning strategy is used to avoid the coupling effect between the nonlinear and linear part of the pipelined architecture. Data-dependent hierarchical M-Max filtered-error LMS algorithm is derived to selectively update coefficients of the HPU-GFLANN filter, which can further reduce the computational complexity. Moreover, the convergence analysis of the NANC system indicates that the proposed algorithm is stable. Computer simulation results verify that the proposed adaptive HPU-GFLANN filter is more effective in nonlinear ANC systems than the FLANN and GFLANN filters.     

基于集员滤波的选择权更新子带有源噪声控制

通过子带自适应滤波结构,可以提高宽带噪声降噪效果,归一化子带自适应滤波（NSAF）通过在每个子带上使用相同的全带自适应滤波器,消除了传统子带结构会在输出端产生混叠分量的问题,具有较好的收敛性能和稳态均方误差。但由于在每个子带上采用相同的全带自适应滤波器,计算量要高于传统子带结构,集员滤波（SMF）技术具有数据选择更新的特点,可有效降低计算复杂度。基于NSAF结构,建立了前馈ANC无延迟结构,并基于集员滤波技术,通过选择部分权更新来进一步减少计算量,仿真验证了该算法对宽带噪声具有更优的降噪效果。     

基于集员滤波的二阶Volterra自适应归一化最小平均P范数算法

针对Volterra非线性滤波算法计算复杂度呈幂级数增加的问题,提出了一种α稳定分布噪声下的基于集员滤波的二阶Volterra自适应滤波新算法。由于集员滤波的目标函数考虑了所有输入和期望输出的信号对,通过误差幅值的p次方的门限判决,更新Volterra滤波器的权向量,不仅有效降低了算法复杂度,而且提高了自适应算法对输入信号相关性的鲁棒性;并推导给出了权向量的更新公式。仿真结果表明,该算法计算复杂度低、收敛速度快,对噪声及输入信号相关性有较强的鲁棒性。     

二阶Volterra变记忆长度LMP算法

针对实际应用中非线性系统记忆长度未知致使Volterra自适应滤波器可能无法达到最优性能的问题,提出一种二阶Volterra变记忆长度LMP算法。利用Volterra滤波器二阶权系数矩阵的对称性和对称矩阵可对角化分解性质,推导得到了一阶权系数与二阶权系数个数相同的信号矢量与权系数矢量内积的二阶Volterra滤波器输出信号表达式;提出了基于DCT的二阶Volterra自适应滤波器（CSVF）及其LMP算法（CSVLMP）;采用FIR抽头长度的自适应调整思想,提出了基于DCT的二阶Volterra变记忆长度LMP算法（CSVMLMP）。记忆长度未知的非线性系统辨识的仿真结果表明,在[α]稳定分布噪声背景下,该算法在收敛速度、稳态性能和计算复杂度之间达到了较好的折中。     

Pipelined functional link artificial recurrent neural network with the decision feedback structure for nonlinear channel equalization

This paper presents a computationally efficient nonlinear adaptive filter by a pipelined functional link artificial decision feedback recurrent neural network (PFLADFRNN) for the design of a nonlinear channel equalizer. It aims to reduce computational burden and improve nonlinear processing capabilities of the functional link artificial recurrent neural network (FLANN). The proposed equalizer consists of several simple small-scale functional link artificial decision feedback recurrent neural network (FLADFRNN) modules with less computational complexity. Since it is a module nesting architecture comprising a number of modules that are interconnected in a chained form, its performance can be further improved. Moreover, the equalizer with a decision feedback recurrent structure overcomes the unstableness thanks to its nature of infinite impulse response structure. Finally, the performance of the PFLADFRNN modules is evaluated by a modified real-time recurrent learning algorithm via extensive simulations for different linear and nonlinear channel models in digital communication systems. The comparisons of multilayer perceptron, FLANN and reduced decision feedback FLANN equalizers have clearly indicated the convergence rate, bit error rate, steady-state error and computational complexity, respectively, for nonlinear channel equalization.     

α稳定分布下Volterra滤波器的自适应数据块算法

基于分数低阶统计量原理提出了α稳定分布下Volterra滤波器的数据块滤波算法。该算法对Volterra滤波器权向量的线性项部分和非线性项部分分别采用不同的收敛因子,克服了传统只采用一个收敛因子的Volterra滤波器算法收敛性能差缺点,利用更多的输入信号和误差信号信息,更好地估计梯度,更精确地调节自适应滤波器权向量,提高了收敛速度。仿真结果验证了该方法的优越性。     

Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α-stable noise

Although the least mean pth power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α-stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean pth power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p-norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α-stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error.     

一种分阶梯度加权平均变步长VLMP算法

通过平滑梯度矢量减小梯度估计误差,采用平滑梯度矢量的欧氏范数和误差信号的分数低阶矩更新步长因子,对一阶和二阶权系数采取分阶迭代更新,得到一种在[α]稳定分布噪声背景下变步长Volterra自适应滤波算法,分析证明了该算法的收敛性能。非线性系统辨识的仿真结果表明,算法较DOVLMP算法具有更快的收敛速度和更小的稳态失调。     

基于并行滤波器的回波抵消技术方案

为了提高数字直放站回波抵消的收敛速度,首先研究了基于自适应滤波器的回波抵消技术,然后对其中的自适应滤波器的递推算法进行改进,形成了两个自适应滤波器并行计算、联合递推更新权值的技术方案。由于调节两个自适应滤波器权值的误差信号产生方式不同,方案可分为两种：方案一将回波抵消后的信号同时作为调节两个滤波器权值的误差信号(同时);方案二将天线接收信号与第一个滤波器输出信号的差值作为调节第一个滤波器权值的误差信号,而将该误差信号与第二个滤波器输出信号的差值作为调节第二个滤波器权值的误差信号(分别)。仿真结果表明,改进技术方案使回波抵消收敛速度提高11.11%~17.78%,从而有效改善了数字直放站回波抵消收敛速度慢的状况。     

Diffusion normalized subband adaptive algorithm for distributed estimation employing signed regressor of input signal

This paper presents a novel diffusion subband adaptive filtering algorithm for distributed estimation over networks. To achieve the low computational load, the signed regressor (SR) approach is applied to normalized subband adaptive filter (NSAF) and two algorithms for diffusion networks are established. The diffusion SR-NSAF (DSR-NSAF) and modified DSR-NSAF (MDSR-NSAF) have fast convergence speed and low steady-state error similar to the conventional DNSAF. In addition, the proposed algorithms have lower computational complexity than DNSAF due to the signed regressor of the network input signals at each node. Also, based on the spatial-temporal energy conservation relation, the mean-square performance of DSR-NSAF is analyzed and the expressions for the theoretical learning curve and steady-state error are derived. The good performance of these algorithms and the validity of the theoretical results are demonstrated by presenting several simulation results.     

An improved block adaptive system for effective feedback cancellation in hearing aids

The hearing aid being a battery operated, portable device requires short processing delay, low computational complexity, with appreciable acoustic feedback cancellation effect. The prediction error method (PEM) and PEM with shadow filter (PEM-SH) based adaptive feedback canceller (AFC) referred as PEMAFC and PEMAFC-SH respectively reduces the amount of bias present in the estimate of feedback path. The available partitioned block frequency domain adaptive filter (PBFAF) based implementation of PEMAFC (PBFAF-P) and PEMAFC-SH (PBFAF-PS), offers a potential option for modelling an adaptive filter with many taps along with short block processing delay. However, the PBFAF suffers from large computational load because of the involvement of computationally expensive gradient constraints in each partition. Though removing or alternately applying the gradient constraint saves some computations but it results in significant performance degradation. With an objective of substantially reducing the computational burden and simultaneously retaining the performance, this paper develops an improved partitioned block Hartley domain adaptive filter (IPBHAF) and then employs it for effective feedback cancellation in hearing aids. Further, the IPBHAF with modified step size (IPBHAF-M) is proposed to achieve both fast convergence and better steady state performance. The simulation based experiments demonstrate the superior performance of IPBHAF-M based implementations of PEMAFC (IPBHAF-MP) and PEMAFC-SH (IPBHAF-MPS) over the PBFAF-P and PBFAF-PS in terms of both computational complexity and feedback cancellation performance.     

Unsharp masking using quadratic filter for the enhancement of fingerprints in noisy background

The paper summarizes the design and implementation of a quadratic edge detection filter based on Volterra series. The filter is employed in an unsharp masking scheme for enhancing fingerprints in a dark and noisy background. The proposed filter can account for much of the polynomial nonlinearities inherent in the input image and can replace the conventional edge detectors like Laplacian, LoG, etc. The application of the new filter is in forensic investigation where enhancement and identification of latent fingerprints are key issues. The enhancement of images by the proposed method is superior to that with unsharp masking scheme employing conventional filters in terms of the visual quality, the noise performance and the computational complexity, making it an ideal candidate for latent fingerprint enhancement.     

Low complexity LMS-type adaptive algorithm with selective coefficient update for stereophonic acoustic echo cancellation

Stereophonic acoustic echo cancellation (SAEC) has brought up recently much attention and found a viable place in a number of hands-free applications. In this paper, we propose an LMS-type algorithm for SAEC based on decomposing the long adaptive filter of each channel of the SAEC system into smaller subfilters. We further reduce the complexity of the algorithm by employing the selective coefficient update (SCU) method in each subfilter. This leads to a significant improvement in the convergence rate of the algorithm with low computational overhead. However, the algorithm has a high final mean-square error (MSE) at steady-state that increases as number of subfilters increases. A combined-error algorithm is presented that achieves fast convergence without compromising the steady state error level. Simulations demonstrate the convergence speed advantages of the combined-error algorithm.     

基于UD分解的自适应扩展集员估计方法

用于非线性椭球估计的扩展集员算法在实际应用中存在着数值稳定性差、计算复杂度高以及滤波器参数难以选择等问题. 本文提出了一种基于 UD 分解的自适应扩展集员估计算法, 用于解决非线性系统时变状态和参数的联合估计和定界问题. 新算法将 UD 分解与序列更新和选择更新策略结合起来, 改进了传统扩展集员算法的数值稳定性和实时性能; 同时, 对滤波器参数进行自适应选择以进一步降低计算复杂度并达到次优估计结果. 仿真实验表明了该算法的有效性和鲁棒性.     

确定采样型强跟踪滤波飞机舵面故障诊断与隔离

为了克服扩展多模型自适应估计中扩展卡尔曼滤波的理论局限性,多重渐消因子强跟踪改进引起的滤波发散现象以及多维高斯故障概率计算量大等问题,本文将一类基于确定解析采样近似方法的非线性次优高斯滤波与多模型自适应估计相结合,提出了改进的多重渐消因子强跟踪非线性滤波快速故障诊断方法.确定采样型滤波克服了扩展卡尔曼滤波的理论局限性;推导了等效多重渐消因子计算方法,避免了非线性系统雅克比矩阵的计算,提高了故障突变时的跟踪性能;提出了基于平方根分解的改进的一步预测协方差更新方程,保证了滤波稳定性;提出了基于欧几里得范数简化的故障概率计算方法,降低了计算量.通过对比仿真验证了3种不同非线性滤波算法及其强跟踪改进算法的有效性,故障诊断方法跟踪性强、速度快、精度高,具有较好的鲁棒性和稳定性.     

Adaptively Combined FIR and Functional Link Artificial Neural Network Equalizer for Nonlinear Communication Channel

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented.     

自适应Voltera滤波的一种快速算法

Ｖｏｌｔｅｒｒａ滤波是非线性自适应信号处理中一种有效的方法．但是其很高的计算复杂度使之在实际应用中有较大的局限性．针对这一问题，本文提出了一种Ｖｏｌｔｅｒｒａ滤波快速算法，可有效地降低计算的复杂度．我们分析对比了现有算法与快速算法的复杂度．文章还给出了一个用Ｖｏｌｔｅｒｒａ自适应模型建模的仿真实例．     

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

The extended set‐membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization‐based adaptive set‐membership filter is developed and applied to nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real‐time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub‐optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

一种新的分割式比例仿射投影算法

针对自适应算法收敛速度和计算复杂度之间的矛盾．提出一种基于集员滤波的分割式比例仿射投影算法（SM-SPAPA）。该算法中只有当参数估计误差大于给定的误差门限时滤波器系数才进行迭代更新,从而能有效地减少滤波器系数的迭代次数。仿真结果表明,由于每次迭代将对误差性能贡献最大的输入信号筛选出来作为输入,从而能加快收敛速度,同时还能够减少算法的运算量。