最大互相关熵多凸组合自适应滤波算法

基于最大互相关熵准则(MCC)的自适应滤波算法在非高斯噪声环境下具有强鲁棒性,得到了广泛应用.然而,传统MCC滤波算法在选择参数时依然受到收敛速度与稳态精度之间固有矛盾的困扰.为解决这一问题,该文提出一类多凸组合MCC算法,能够充分发挥不同参数组合下滤波算法的性能优势,从而获得更好的信道跟踪能力.理论分析得出了所提算法的均值收敛条件和稳态均方误差,同时,仿真实验表明所提算法在对抗高斯和非高斯噪声时均具有收敛快、稳态精度高的特点.     

偏差补偿比例互相关熵算法

为了解决输入信号含有噪声和非高斯输出噪声的稀疏系统辨识问题,本文提出一种偏差补偿比例更新互相关熵算法。基于互相关熵的自适应滤波算法可以消除非高斯噪声的影响, 进一步应用无偏准则来解决含噪输入信号带来的估计偏差问题。另外,将比例更新机制引入算法,通过自适应调节步长参数以增强算法的跟踪性能。仿真结果表明所提算法对于输入信号受噪声干扰和非高斯输出噪声环境下的稀疏系统辨识问题具有强的鲁棒性和稳态性能。      

基于Lawson范数的通用lncosh稀疏自适应算法

该文提出一种通用稀疏系统识别Lawson-lncosh自适应滤波算法,该算法采用系数向量的Lawson范数和误差的lncosh函数构建代价函数。Lawson范数约束引入参数p,实现稀疏约束滤波动态调整,所提算法可以提高稀疏系统识别时的收敛速度,减小了稳态误差。误差的lncosh函数具有良好的抗脉冲噪声性能。然后,算法分析了步长参数的取值范围和参数p对算法性能的影响。计算机仿真结果表明,在高斯信号输入和色信号输入情况下,所提算法的性能要明显优于其他现存算法,且具备稀疏约束可控特性。     

基于双曲正切函数框架的最小均方算法

自适应滤波器在自适应控制、噪声消除、信道均衡、系统辨识以及生物医学等领域的应用中发挥着重要作用。由于其简单性、低计算量和易于实现等特点，其中最流行的自适应滤波算法是最小均方（Least Mean Square,LMS）算法。传统的LMS算法在处理高斯信号时具有良好的收敛性能，然而，针对非高斯信号的处理，自适应LMS算法的收敛性较差，甚至无法收敛。为了改进LMS算法在非高斯噪声干扰下的收敛性，本文通过将传统的LMS算法的代价函数嵌入到双曲正切（Hyperbolic Tangent）函数框架中设计了一种新的代价函数，从而提出了一种鲁棒的双曲正切最小均方（Hyperbolic Tangent Least Mean Square,HTLMS）算法。此外，针对HTLMS算法存在收敛速度与稳态误差相矛盾的问题，本文设计了一种可变λ参数的双曲正切最小均方（Variableλ-parameter Hyperbolic Tangent Least Mean Square,VHTLMS）算法。仿真结果表明，在系统辨识应用场景中，与LMS算法、最大相关熵准则（Generalized Maximum Corr...     

非高斯噪声下基于Wilcoxon范数的变步长符号扩散式仿射投影算法

扩散式仿射投影算法(DAPA)是实现分布式网络参数自适应估计的一种重要方法,该算法在输入信号存在相关性时仍快速收敛,但抑制具有脉冲特性的非高斯噪声能力弱,且固定步长对收敛性有所限制。为此,该文提出了基于Wilcoxon范数的变步长符号扩散式仿射投影算法(VSS-DWAPA)。首先,引入稳健估计理论中抗异常值能力强的Wilcoxon范数作为代价函数并根据其取值特点进行了符号量化,推导出了新的迭代方程;其次,针对固定步长的局限性,采用迭代方式实现了误差信号对步长的控制,在初始阶段和接近收敛阶段选择不同的步长,使算法具有更好的适应性。仿真结果表明,在非高斯噪声下本文的VSS-DWAPA算法在收敛性、跟踪性等方面均优于现有一些扩散式自适应滤波算法,同时在高斯噪声环境下也具有较好的性能。     

非高斯噪声下基于Wilcoxon范数的变步长符号扩散式仿射投影算法

扩散式仿射投影算法(DAPA)是实现分布式网络参数自适应估计的一种重要方法,该算法在输入信号存在相关性时仍快速收敛,但抑制具有脉冲特性的非高斯噪声能力弱,且固定步长对收敛性有所限制.为此,该文提出了基于Wilcoxon范数的变步长符号扩散式仿射投影算法(VSS-DWAPA).首先,引入稳健估计理论中抗异常值能力强的Wilcoxon范数作为代价函数并根据其取值特点进行了符号量化,推导出了新的迭代方程;其次,针对固定步长的局限性,采用迭代方式实现了误差信号对步长的控制,在初始阶段和接近收敛阶段选择不同的步长,使算法具有更好的适应性.仿真结果表明,在非高斯噪声下本文的VSS-DWAPA算法在收敛性、跟踪性等方面均优于现有一些扩散式自适应滤波算法,同时在高斯噪声环境下也具有较好的性能.     

基于最大熵Kalman滤波的机载SINS自标定技术

针对在机载捷联惯导系统(SINS)自标定过程中,量测噪声呈非高斯分布,导致经典Kalman滤波性能降低的问题,该文提出了基于最大熵Kalman滤波(MCKF)的机载SINS自标定技术。该方法采用最大相关熵准则(MCC)替代经典Kalman滤波的最小均方误差准则,有效利用信号的高阶矩信息,并将其应用于机载SINS自标定系统中。仿真结果表明,在非高斯噪声条件下,该方法能够估计出机载SINS待标定参数,且算法的鲁棒性和误差项估计精度均优于经典Kalman滤波,具有一定的工程应用价值。     

迭代变步长LMS算法及性能分析

针对固定步长LMS(Least Mean Square)算法(FXSSLMS)不能同时满足快速收敛和小稳态失调误差的问题,该文提出了迭代变步长LMS算法(IVSSLMS)。与已有的变步长LMS算法(VSSLMS)不同,该算法的步长因子不再是由输出误差信号控制,而是建立了与迭代时间的改进Logistic函数非线性关系,克服了定步长算法收敛慢及已有变步长算法抗噪声干扰能力差的问题。最后从理论上分析了算法的性能,给出了其参数取值方法。理论分析和仿真均表明,所提算法能够在快速收敛情况下获得小的稳态失调误差,在有色噪声干扰下稳态失调误差比已有算法降低了约7 dB。     

学生t量测分布下鲁棒粒子滤波算法的设计与实现

野值是一种异于总体数据的非高斯量测值,在实际传输中野值的加入常使信号出现厚尾特性。粒子滤波是基于贝叶斯框架的适用于非线性/非高斯系统的一种滤波方法。如果在量测噪声中存在野值会使粒子滤波的精度下降。该文利用学生t分布建模量测噪声模型,结合变分贝叶斯(VB)递推方法设计一种新颖的边缘粒子滤波(MPF-VBM),它在滤波同时可对量测噪声的包括均值在内的全部参数进行实时估计。进一步,利用该估计算法,在量测噪声时变条件下研究了噪声关联的粒子滤波算法(MPF-VBM-COR)。通过对典型单变量增长模型的仿真,验证了所提两种算法相比于已有算法在状态估计上具有更优越的鲁棒性。     

基于q 梯度的仿射投影算法及其稳态均方收敛分析

q梯度是基于q微分的广义梯度。为了进一步提高仿射投影算法(APA)的滤波性能,该文基于最小均方误差准则将q梯度应用于APA进而产生一种新的q-APA,在高斯噪声环境下选择合适的q值可以取得理想的滤波性能。通过理论分析,提出了保证算法收敛的充分条件,并计算出表征滤波性能的稳态额外均方误差(EMSE)。除此之外,为了进一步提高算法的滤波性能,提出一个变q的APA(V-q-APA)。在高斯噪声环境下,将q-APA和V-q-APA应用于系统辨识中。仿真结果表明：与传统的APA和变q的最小化均方(V-q-LMS)算法相比,q-APA和V-q-APA均具有更好的滤波性能。     

New Variable Step-Sizes Minimizing Mean-Square Deviation for the LMS-Type Algorithms

The least-mean-square-type (LMS-type) algorithms are known as simple and effective adaptation algorithms. However, the LMS-type algorithms have a trade-off between the convergence rate and steady-state performance. In this paper, we investigate a new variable step-size approach to achieve fast convergence rate and low steady-state misadjustment. By approximating the optimal step-size that minimizes the mean-square deviation, we derive variable step-sizes for both the time-domain normalized LMS (NLMS) algorithm and the transform-domain LMS (TDLMS) algorithm. The proposed variable step-sizes are simple quotient forms of the filtered versions of the quadratic error and very effective for the NLMS and TDLMS algorithms. The computer simulations are demonstrated in the framework of adaptive system modeling. Superior performance is obtained compared to the existing popular variable step-size approaches of the NLMS and TDLMS algorithms.     

Information theoretic learning with adaptive kernels

This paper presents an online algorithm for adapting the kernel width that is a free parameter in information theoretic cost functions using Renyi's entropy. This kernel computes the interactions between the error samples and essentially controls the nature of the performance surface over which the parameters of the system adapt. Since the error in an adaptive system is non-stationary during training, a fixed value of the kernel width may affect the adaptation dynamics and even compromise the location of the global optimum in parameter space. The proposed online algorithm for adapting the kernel width is derived from first principles and minimizes the Kullback-Leibler divergence between the estimated error density and the true density. We characterize the performance of this novel approach with simulations of linear and nonlinear systems training, using the minimum error entropy criterion with the proposed adaptive kernel algorithm. We conclude that adapting the kernel width improves the rate of convergence of the parameters, and decouples the convergence rate and misadjustment of the filter weights.     

Reduced-complexity transform-domain adaptive algorithm with selective coefficient update

This paper proposes a new low-complexity transform-domain (TD) adaptive algorithm for acoustic echo cancellation. The algorithm is based on decomposing the long adaptive filter into smaller subfilters and employing the selective coefficient update (SCU) approach in each subfilter to reduce computational complexity. The resulting algorithm combines the fast converging characteristic of the TD decomposition technique and the benefits of the SCU of low complexity with minimal performance losses. The improvement in convergence speed comes at the expense of a corresponding increase in misadjustment. To overcome this problem, a hybrid of the proposed algorithm and the standard TD LMS algorithm (TDLMS) is presented. The hybrid algorithm retains the fast convergence speed capabilities of the original algorithm while allowing for low final MSE. Simulations show that the hybrid algorithm offers a superior performance when compared to the standard TDLMS algorithm with less computational overhead.     

一种变步长凸组合自适应滤波器及其均方性能分析

在分析凸组合最小均方(CLMS)算法性能的基础上,提出一种新的变步长凸组合最小均方(VSCLMS)算法。该算法采用一种变步长滤波器替代原CLMS滤波器组中的恒值大步长滤波器,使新的自适应滤波器能够在噪声、时变,甚至非平稳的环境下保持良好的随动性能,并在收敛的各个阶段均保持快速且稳定的均方特性。理论推导与仿真分析分别验证了新算法与原CLMS算法相比不仅有更快的收敛速度,而且稳态均方性能与跟踪性能也有所提高。     

A minimum misadjustment adaptive FIR filter

The performance of an adaptive filter is limited by the misadjustment resulting from the variance of adapting parameters. This paper develops a method to reduce the misadjustment when the additive noise in the desired signal is correlated. Given a static linear model, the linear estimator that can achieve the minimum parameter variance estimate is known as the best linear unbiased estimator (BLUE). Starting from classical estimation theory and a Gaussian autoregressive (AR) noise model, a maximum likelihood (ML) estimator that jointly estimates the filter parameters and the noise statistics is established. The estimator is shown to approach the best linear unbiased estimator asymptotically. The proposed adaptive filtering method follows by modifying the commonly used mean-square error (MSE) criterion in accordance with the ML cost function. The new configuration consists of two adaptive components: a modeling filter and a noise whitening filter. Convergence study reveals that there is only one minimum in the error surface, and global convergence is guaranteed. Analysis of the adaptive system when optimized by LMS or RLS is made, together with the tracking capability investigation. The proposed adaptive method performs significantly better than a usual adaptive filter with correlated additive noise and tracks a time-varying system more effectively     

Convergence performance analysis of an adaptive kernel width MCC algorithm

A fixed kernel width in MCC algorithm imposes a trade-off among robustness, convergence rate and steady-state accuracy. With a variable kernel width, the adaptive kernel width MCC (AMCC) algorithm can improve the learning speed of the MCC algorithm especially when the initial weight vector is far away from the optimal weight vector. In this paper, the steady-state excess mean square error (EMSE) of the AMCC algorithm is studied based on energy conservation relation. In addition, a novel convergence measure called initial convergence rate is introduced to evaluate the convergence speed at the beginning of the learning. Simulation experiments are carried out to verify the theoretical analysis and confirm the desirable performance of the AMCC algorithm in several different non-Gaussian noise environments.     

An adaptive recursive algorithm based on non-quadratic function of the error

In adaptive filtering, several algorithms were developed to get faster convergence and lower misadjustment, but rely on second order statistics which are optimum only for Gaussian signals. In this work we propose a recursive filter by modifying the performance surface to a non-quadratic function applied upon the error. As a result, the equations are simple, elegant, and yielded faster convergence and lower misadjustment when compared to the RLS, keeping equivalent computational cost.     

A Novel Normalized Sign Algorithm for System Identification Under Impulsive Noise Interference

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies.     

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.     

归一化子带自适应滤波器步长控制

定步长子带自适应滤波器必须在快的收敛速度和低的稳态失调之间进行折中。根据自适应滤波器系数向量均方偏差与步长之间的函数关系,该文采用使自适应滤波器系数向量均方偏差在每次迭代更新时最速下降的方法,提出一种步长控制算法来解决上述问题。该算法可以兼得快的收敛速度和低的稳态失调。实验结果验证了该方法的有效性。