基于l1-范数约束的递归互相关熵的稀疏系统辨识

为了有效解决脉冲噪声环境下的稀疏系统辨识(Sparse system identification, SSI)问题,以l1 -范数为约束构建稀疏递归互相关熵准则(Recursive maximum correntropy criterion, RMCC)算法来解决脉冲噪声对于辨识性能的影响。结合带遗忘算子的互相关熵准则和l1 -范数作为代价函数,推导出一种递归形式的算法,其相对于传统的最大相关熵算法具有快的收敛速度及小的稳态误差。仿真实验结果表明:该算法对于脉冲噪声干扰环境下的SSI问题具有强的鲁棒性。      

鲁棒频域样条优先自适应滤波算法及性能分析

样条自适应滤波结构由线性滤波器和样条插值机制级联组成，是解决Wiener-Hammerstein模型系统辨识的一类有效方案。在非线性系统辨识问题中，随着滤波器阶数增加，将增大时域样条自适应滤波算法的计算复杂度，造成计算效率的降低，且系统附加的非Gaussian噪声会对最小均方算法的样条自适应滤波器性能造成不良影响，导致算法的性能恶化甚至失效。为处理非Gaussian噪声干扰和提高长脉冲响应系统辨识的计算效率，本文结合最大熵准则和频域策略应用于样条自适应滤波器中，并在样条自适应滤波结构中分别采用不同的误差信号对线性部分和非线性部分进行优化，提出了一种鲁棒频域样条优先自适应滤波算法。该算法在滤波前利用非线性系统辨识的不变性原理对未知系统进行优先的有限脉冲响应辨识，可提高非线性系统辨识的精度；通过最大熵准则使算法在非Gaussian噪声环境下具有稳健性，以降低更新过程对大异常值的敏感性；并将线性卷积和线性相关运算通过重叠存储的快速Fourier变换方式进行计算，显著提升了算法的计算效率。此外，本文对所提出的自适应算法进行了收敛性和稳态性能分析，并推导出该算法的理论稳态额外均方误差。最后，通过...     

基于高斯核显性映射的核归一化解相关仿射投影P范数算法

为了降低核仿射投影P范数(KAPP)算法的计算量和存储容量,提高在输入信号强相关时KAPP算法的收敛速度和稳态性能,该文提出基于高斯核显性映射的核归一化解相关APP(KNDAPP-GKEM)算法。该算法利用归一化解相关方法预先解除输入信号的相关性;利用高斯核显式映射方法近似得到显式核函数,消除了对历史数据的依赖,解决了KAPP算法因结构不断生长导致的计算量和存储容量过大的问题。α稳定分布噪声背景下的非线性系统辨识仿真结果表明,在输入信号强相关时KNDAPP-GKEM算法收敛速度快,非线性系统辨识稳态均方误差小,训练所需时间呈线性缓慢增长,有利于实际非线性系统辨识的应用。     

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...     

抗冲激干扰的稀疏惩罚约束遗漏最小均方算法

当被识别系统是稀疏系统时,传统的遗漏最小均方( LLMS )自适应算法收敛性能较差,特别在非高斯噪声环境中,该算法性能进一步恶化甚至算法不平稳收敛。为了解决因信道的稀疏性使算法收敛变慢的问题,对LLMS算法的代价函数分别利用加权詛1-norm和加权零吸引两种稀疏惩罚项进行改进;为了优化算法的抗冲激干扰的性能,利用符号函数对已改进的算法迭代式作进一步改进。同时,将提出的两个算法运用于非高斯噪声环境下的稀疏系统识别,仿真结果显示提出的算法性能优于现存的同类稀疏算法。     

非最小相位ARMA模型的一种自适应辨识算法

本文提出了一种加性有以高斯噪声中因果非最小相位ＡＲＭＡ模型的自适应辨识算法。模型输入假定为非高斯独立同分布随机过程。算法只利用了观测信号的高阶统计量。     

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。     

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.     

脉冲噪声下基于循环相关熵和稀疏重构的宽带信号DOA估计

针对脉冲噪声与同频带干扰并存时宽带信号的波达方向(DOA)估计问题,该文提出一种结合循环相关熵(CCE)与稀疏重构的算法。首先,分析了宽带信源的接收信号模型,并利用循环相关熵的性质构造出对脉冲噪声与同频带干扰具有抑制能力的宽带信号虚拟输出阵列。随后对该虚拟输出阵列进行稀疏表示,并通过归一化迭代硬阈值(NIHT)算法进行稀疏重构,从而估计宽带信号的波达方向。实验结果表明,该算法对脉冲噪声和同频带干扰具有很好的抑制作用,并且相较已有算法在估计性能方面有明显的改善。     

广义复相关熵与相干分布式非圆信号DOA估计

针对相干分布式非圆信号参数估计算法在脉冲噪声环境下性能退化的问题,本文提出了广义复相关熵的概念,并给出了基于广义复相关熵的相干分布式非圆信号DOA（Direction of Arrival）估计方法。该算法首先由分布式信源模型获得入射信号的阵列输出信号,利用信号的非圆特性得到扩展阵列输出信号,再通过扩展阵列输出信号的广义复相关熵矩阵获取信号子空间,避开了传统二阶统计量算法在脉冲噪声下不适应的问题,最后由信号子空间旋转不变特性得到信号的中心波达方向角度。仿真实验结果表明,在Alpha稳定分布噪声条件下,与传统算法相比,本文所提算法具有更好的性能。      

Robust proportionate adaptive filter based on maximum correntropy criterion for sparse system identification in impulsive noise environments

Proportionate-type adaptive filtering (PtAF) algorithms have been successfully applied to sparse system identification. The major drawback of the traditional PtAF algorithms based on the mean square error (MSE) criterion show poor robustness in the presence of impulsive noises or abrupt changes because MSE is only valid and rational under Gaussian assumption. However, this assumption is not satisfied in most real-world applications. To improve its robustness under non-Gaussian environments, we incorporate the maximum correntropy criterion (MCC) into the update equation of the PtAF to develop proportionate MCC (PMCC) algorithm. The mean and mean square convergence performance analysis are also performed. Simulation results in sparse system identification and echo cancellation applications are presented, which demonstrate that the proposed PMCC exhibits outstanding performance under the impulsive noise environments.     

Identification of linear stochastic systems via second- and fourth-order cumulant matching

The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered. The system is not restricted to be minimum phase, and it is allowed to contain all-pass components. A least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed. Knowledge of the probability distribution of the driving noise is not required. An order determination criterion that is a modification of the Akaike information criterion is also proposed. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are presented to illustrate the method.     

An image denoising algorithm for mixed noise combining nonlocal means filter and sparse representation technique

Nonlocal means (NLM) filtering or sparse representation based denoising method has obtained a remarkable denoising performance. In order to integrate the advantages of two methods into a unified framework, we propose an image denoising algorithm through skillfully combining NLM and sparse representation technique to remove Gaussian noise mixed with random-valued impulse noise. In the non-Gaussian circumstance, we propose a customized blockwise NLM (CBNLM) filter to generate an initial denoised image. Based on it, we classify the different noisy pixels according to the three-sigma rule. Besides, an overcomplete dictionary is trained on the initial denoised image. Then, a complementary sparse coding technique is used to find the sparse vector for each input noisy patch over the overcomplete dictionary. Through solving a more reasonable variational denoising model, we can reconstruct the clean image. Experimental results verify that our proposed algorithm can obtain the best denoising performance, compared with some typical methods.     

The Data-Reusing MCC-Based Algorithm and Its Performance Analysis

Maximum correntropy criterion (MCC) provides a robust optimality criterion for non-Gaussian sig-nal processing. In this paper, the weight update equation of the conventional MCC-based adaptive filtering algorithm is modified by reusing the past K input vectors, forming a class of data-reusing MCC-based algorithm, called DR-MCC algorithm. Comparing with the conventional MCC-based algorithm, the DR-MCC algorithm provides a much better convergence performance when the input data is correlated. The mean-square stability bound of the DR-MCC algorithm has been studied theoretically. For both Gaussian noise case and non-Gaussian noise case, the ex-pressions for the steady-state Excess mean square error (EMSE) of DR-MCC algorithm have been derived. The re-lationship between the data-reusing order and the steady-state EMSEs is also analyzed. Simulation results are in agreement with the theoretical analysis.     

A bias‐compensated proportionate NLMS algorithm with noisy input signals

This paper proposes a novel proportionate normalized least‐mean‐squares (PNLMS) algorithm that is robust to input noises. Through compensating for biases due to input noise added at the filter input, the proposed PNLMS algorithm avoids performance deterioration owing to the noisy input signals. Moreover, since the proposed PNLMS algorithm uses a new gain‐distribution matrix, it has a fast convergence rate compared with the existing PNLMS algorithms, even when there is no input noise. The experimental results verify that the proposed PNLMS algorithm enhances the filter performance for sparse system identification in the presence of input noises.     

基于最大相关熵准则的恒模盲均衡算法

针对恒模算法(constant modulus algorithm, CMA)在脉冲噪声环境下性能退化的问题,本文基于最大相关熵准则(maximum correntropy criterion, MCC)对恒模算法中基于最小均方误差(mean square error, MSE)准则的代价函数进行修正,推导出适用于脉冲噪声环境的基于MCC准则的恒模盲均衡算法(MCC_CMA)。该算法利用通信信号的恒模特性,首先得到发送信号与均衡器输出信号模值的误差信号,再通过使模值误差信号的相关熵最大来获得其迭代误差调节项,避免了传统高阶统计量算法在脉冲噪声环境下性能退化的问题。对高斯噪声以及α-稳定分布和混合高斯分布两种脉冲噪声环境下的信道均衡问题的仿真实验表明,相对于经典的自适应恒模盲均衡算法,MCC_CMA算法不依赖噪声的先验知识就能获得较快的收敛速度、较低的剩余码间干扰和误码率,并且在不同脉冲强度的脉冲噪声环境下都能够得到较好的均衡结果,表明MCC_CMA算法具有很好的鲁棒性。      

Closed-loop linear model validation and order estimation usingpolyspectral analysis

Suppose that we perform closed-loop linear system identification using polyspectral analysis given noisy time-domain input-output measurements. In this setup, it is assumed that various disturbances affecting the system are zero-mean stationary Gaussian, whereas the closed-loop system operates under an external (possibly noisy) non-Gaussian input. The closed-loop system must be stable, but it is allowed to be unstable in the open loop. Various techniques have been proposed for system identification using polyspectral analysis. Having obtained a model, how do we know if the fitted model is “good?” This paper is devoted to the problem of statistical model validation using polyspectral analysis. We propose simple statistical tests based on the estimated polyspectrum (integrated bispectrum and/or integrated trispectrum) of an output error signal or the estimated cross-polyspectrum between the external reference and the output error signal. Model order estimation is performed by repeatedly using the model validation procedure. Computer simulation examples are presented in support of the proposed approaches     

New approaches without postprocessing to FIR system identificationusing selected order cumulants

In this paper, we address the problem of identifying the parameters of the nonminimum-phase FIR system from the cumulants of noisy output samples. The system is driven by an unobservable, zero-mean, independent and identically distributed (i.i.d) non-Gaussian signal. The measurement noise may be white Gaussian, colored MA, ARMA Gaussian processes, or even real. For this problem, two novel methods are proposed. The methods are designed by using higher order cumulants with the following advantages. (i) Flexibility: method 1 employs two arbitrary adjacent order cumulants of output, whereas method 2 uses three cumulants of output: two cumulants with arbitrary orders and the other one with an order equal to the summation of the two orders minus one. Because of this flexibility, we can select cumulants with appropriate orders to accommodate different applications. (ii) Linearity: both the formulations in method 1 and method 2 are linear with respect to the unknowns, unlike the existing cumulant-based algorithms. The post-processing is thus avoided. Extensive experiments with ARMA Gaussian and three real noises show that the new algorithms, especially algorithm 1, perform the FIR system identification with higher efficiency and better accuracy as compared with the related algorithms in the literature     

Recursive blind identification of non-Gaussian time-varying ARmodel and application to blind equalisation of time-varying channel

A novel method for the blind identification of a non-Gaussian time-varying autoregressive model is presented. By approximating the non-Gaussian probability density function of the model driving noise sequence with a Gaussian-mixture density, a pseudo maximum-likelihood estimation algorithm is proposed for model parameter estimation. The real model identification is then converted to a recursive least squares estimation of the model time-varying parameters and an inference of the Gaussian-mixture parameters, so that the entire identification algorithm can be recursively performed. As an important application, the proposed algorithm is applied to the problem of blind equalisation of a time-varying AR communication channel online. Simulation results show that the new blind equalisation algorithm can achieve accurate channel estimation and input symbol recovery