平方根变步长lp范数LMS算法的稀疏系统辨识

针对稀疏未知系统的辨识问题,提出了一种基于lp(0相似文献   

一种稀疏系统辨识的子带自适应滤波算法

利用改进的多带结构子带自适应滤波(IMSAF)算法辨识具有稀疏特性的未知系统.代价函数引入加权的l1范数作为附加约束,并结合次梯度分析方法推导出新的更新方程.根据加权矩阵选取的不同,提出了两个li范数约束的IMSAF算法:l1-IMSAF和l1-RIMSAF.仿真结果表明,在未知系统具备稀疏特性的条件下,相较于传统的IMSAF算法,两个新算法的收敛性能具有显著提高.     

l0-范数约束的稀疏多径信道分数间隔双模式盲均衡算法

针对深衰落稀疏多径信道下多进制相移键控（Multiple Phase Shift Keying,MPSK）信号的盲均衡问题,提出了一种l₀-范数约束的分数间隔稀疏自适应双模式盲均衡算法.该算法借鉴传统的分数间隔双模式盲均衡算法思想,结合稀疏自适应滤波理论,首先利用l₀-范数对均衡器抽头系数进行稀疏性约束,构造出一种l₀-范数约束的分数间隔双模式最小均方误差代价函数,然后依据梯度下降法推导出盲均衡器抽头系数更新公式,并对迭代步长进行归一化和比例系数化.理论分析和仿真实验表明,与基于门限稀疏化的盲均衡算法、基于分数阶范数的盲均衡算法及分数间隔双模式盲均衡算法相比,本文所提算法在保证较快收敛速度的前提下,能有效降低剩余符号间干扰.本文设计的盲均衡算法为水声通信系统中接收方恢复出发送信号,提供了一种快速有效的方法.     

l0-范数约束的稀疏多径信道RLS常模盲均衡算法

针对稀疏多径信道下MPSK信号的快速盲均衡问题,提出了一种l0-范数约束的递归最小二乘常模盲均衡算法.该算法借鉴传统的递归最小二乘常模盲均衡算法思想,结合稀疏自适应滤波理论,首先利用l0-范数对均衡器抽头系数进行稀疏性约束,构造出一种l0-范数约束的加权最小二乘误差代价函数,然后依据递归最小二乘算法推导出均衡器抽头系数更新公式.该算法发挥递归最小二乘常模算法收敛速度快的优势,并对幅度极小系数附加零点吸引调整,从而实现不同幅度抽头系数的快速收敛.理论分析与仿真结果表明,与现有算法相比,该算法在保证较低剩余符号间干扰的前提下,能有效提高均衡器的收敛速度.     

引入梯度导引似p范数约束的稀疏信道估计算法

为克服l0和l1范数约束的最小均方算法在不同信道稀疏程度下对稀疏信道估计中出现的收敛性能起伏较大等缺点,提出一种新的似p范数约束的最小均方算法,通过在最小均方算法代价函数中引入p值可变的似p范数约束以适应信道的不同稀疏程度,并在验证代价函数凸性的基础上导出p值的梯度导引寻优。文中最后给出仿真实验及其讨论,实验结果表明了新算法的优越性。     

基于稀疏约束最优化的ISAR相位自聚焦成像算法

本文提出了一种基于稀疏约束的ISAR方位自聚焦算法,能够应用于稀疏孔径ISAR成像中。该算法利用ISAR图像的稀疏特征建立最小1范数成像模型,并将相位误差作为模型误差。然后通过数值迭代的方式进行自适应相位误差估计,最终获得聚焦良好的ISAR图像。同时,成像代价函数的建立基于矩阵模型,有利于采用方位FFT和矩阵的Hardmard乘积操作进行快速求解。由于利用稀疏约束,该方法在低信噪比的条件下仍然能够取得良好的聚焦结果。基于仿真数据和实测数据的结果验证了本文算法的有效性。     

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。      

基于Gabor特征和字典学习的高斯混合稀疏表示图像识别

为了克服图像识别中光照,姿态等变化带来的识别困难,同时提高稀疏表示图像识别的鲁棒性,本文提出了一种基于Gabor特征和字典学习的高斯混合稀疏表示图像识别算法.高斯混合稀疏表示是基于最大似然估计准则,将稀疏保真度表示为余项的最大似然函数,最终识别问题转化为求解加权范数的优化逼近问题.本文算法首先提取图像的Gabor特征;然后对Gabor特征集进行字典学习,由于在学习过程中引入了Fisher准则作为约束,学习得到具有类别标签的新字典;最后使用高斯混合稀疏表示识别方法进行分类识别.在3个公开数据库(人脸数据库AR库和FERET库以及USPS手写数字库)上的实验结果验证了该算法的有效性和鲁棒性.     

尺度不变范数比正则的稀疏DOA估计

波达方向估计(Direction Of Arrival,DOA)通过使用传感器阵列来识别声源方位,而传统的DOA估计方法忽略了声源在空间分布的稀疏性,目前的凸稀疏DOA估计方法和非凸稀疏DOA估计方法所使用的惩罚函数未考虑稀疏度量l₀范数的重要特性——尺度不变性,因此无法精确描述声源的空域稀疏结构,难以获得较高的DOA估计精度.为此,本文首先使用具有尺度不变性的范数比函数来逼近l₀范数,刻画声源空域稀疏结构;接着,针对范数比函数的非凸特性,采用光滑化的思想,构建了平滑的近似函数;然后,构建了基于光滑l_p比l_q范数的稀疏DOA估计模型,开发了基于光滑l_p比l_q范数的稀疏DOA估计算法(Smoothed l_p-Over-l_q regularized Sparse DOA Estimation algorithm,SPOQ-SDOA).大量仿真分析表明,与流行的多快拍DOA估计算法相比,本文提出的算法在不同信噪比和快拍...     

一种变步长最小平均p范数自适应滤波算法

在p稳定分布脉冲噪声背景下,为解决固定步长最小平均p范数(LMP)不能同时满足快收敛速度和低稳态误差的问题,该文提出一种对脉冲噪声具有鲁棒性的变步长最小平均p范数(VSS-LMP)自适应滤波算法.该算法利用改进的变形高斯函数来调节步长,采用移动平均法构造变步长函数,克服了定步长算法稳态误差高及抗噪性能差的问题.VSS-...     

一种稳健的盲稀疏度压缩感知雷达目标参数估计方法

针对压缩感知雷达(Compressive Sensing Radar, CSR)在感知矩阵和目标信息矢量失配时距离-多普勒参数估计性能下降的问题,该文提出一种稳健的盲稀疏度CSR目标参数估计方法。首先建立了CSR系统模型失配时的距离-多普勒2维参数稀疏感知模型,推导了以最小化感知矩阵相干系数(Coherence of Sensing Matrix, CSM)为准则的波形优化目标函数。其次提出了一种新的盲稀疏度CSR目标参数估计方法,通过发射波形,系统模型失配误差和目标信息矢量的相互迭代,逐步校正系统感知矩阵,最终以较高精度估计目标距离-多普勒参数。与传统CSR目标参数估计方法相比,该方法显著降低了CSR系统距离-多普勒参数的估计误差,改善了CSR目标参数估计的准确性和鲁棒性。计算机仿真验证了该方法的有效性。     

On a simple derivation of the complementary matching pursuit

Sparse approximation in a redundant basis has attracted considerable attention in recent years because of many practical applications. The problem basically involves solving an under-determined system of linear equations under some sparsity constraint. In this paper, we present a simple interpretation of the recently proposed complementary matching pursuit (CMP) algorithm. The interpretation shows that the CMP, unlike the classical MP, selects an atom and determines its weight based on a certain sparsity measure of the resulting residual error. Based on this interpretation, we also derive another simple algorithm which is seen to outperform CMP at low sparsity levels for noisy measurement vectors.     

Robust ISAR imaging based on compressive sensing from noisy measurements

the compressive sensing (CS) based ISAR imaging has exhibited high-resolution imaging quality when faced with limited spatial aperture. However, its performance is significantly dependent on the number of pulses and the noise level. In this paper, from the perspective of promoted sparsity constraint, a novel reconstruction model deducted from Meridian prior (MCS) is proposed. The detailed comparison of the proposed MCS model with the Laplace-prior-based CS model (LCS) is conducted. The Lorentz curve analysis testified the enhanced sparsity of the MCS model. Different from the algorithm for LCS model, in our solution procedure, the variance parameter is iteratively updated until the algorithm converges. Simulations and the ground truth data experiments of ISAR show that, with the decrease of the number of pulses and signal-to-noise ratio, the proposed model exhibits better performance in terms of resolution and amplitude error than that of the LCS model.     

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.     

A modified non-negative LMS algorithm for online system identification

Adaptive filters are useful solutions for system identification problem where an optimization problem is used to formulated the estimation of the unknown model coefficients. The nonnegativity constraint is one of the most frequently used constraint which can be imposed to avoid physically unreasonable solutions and to comply with physical characteristics. In this letter, we propose a new variant of non-negative least mean square (NNLMS) that has a less mean square error (MSE) value and faster convergence rate. We provide both mean weight behavior and transient excess mean-square error analysis for proposed algorithm. Simulation results validate the theoretical analysis and show the effectiveness of our proposed algorithm.     

An unbiased equation error identifier and reduced-orderapproximations

The equation error (EE) identification technique is modified to remove the parameter bias problem induced by uncorrelated measurement errors. The modification replaces a “monic” constraint with a “unit-norm” constraint; the asymptotic solution replaces a normal equation with an eigenequation. The resulting algorithm is simpler than previous schemes, while at the same time preserving the desirable properties of the conventional EE method: simplicity of an on-line algorithm, unimodality of the performance surface, and consistent identification in the sufficient-order case. In the more realistic undermodeled case, a robustness result shows that the mean optimal parameter values of both the monic and unit-norm EE schemes correspond to a stable transfer function for all degrees of undermodeling, and for all stationary output disturbances, provided the input sequence satisfies an autoregressive constraint; otherwise an unstable model may result. Model approximation properties for the undermodeled case are exposed in detail for the case of autoregressive inputs; although both the monic and unit-norm variants provide Pade approximation properties, the unit-norm version is capable of autocorrelation matching properties as as well, and yields the optimal solution to a first- and second-order interpolation problem. Finally, the mismodeling error for the undermodeled case is shown to be a well-behaved function of the Hankel singular values of the unknown system. This modification allows EE methods to be admitted to the class of unbiased identification and approximation techniques     

基于低秩稀疏约束的穿墙雷达成像算法

针对穿墙雷达(TWR)成像过程中墙杂波与成像空间分别具有低秩性和稀疏性的特点,提出了一种基于低秩稀疏约束的穿墙雷达成像算法.所提成像算法通过奇异值软阈值法和l1范数最小化技术进行迭代求解低秩稀疏约束优化问题,实现在墙体强反射波存在的探测环境中基于压缩感知框架对墙后隐蔽目标的准确成像重建.仿真和实验数据的处理结果验证了所提成像算法的有效性和准确性.     

参数自适应调整的稀疏贝叶斯重构算法

稀疏表示模型中的正则化参数由未知的噪声和稀疏度共同决定,该参数的设置直接影响稀疏重构性能的好坏。然而目前稀疏表示问题优化求解算法或依靠主观、或依靠相关先验信息、或经过实验设置该参数,均无法自适应地设置调整该参数。针对这一问题,该文提出一种无需先验信息的参数自动调整的稀疏贝叶斯学习算法。首先对模型中各参数进行概率建模,然后在贝叶斯学习的框架下将参数设置及稀疏求解问题转化为一系列混合L1范数与加权L2范数之和的凸优化问题,最终通过迭代优化得到参数设置和问题求解。由理论推导和仿真实验可知,已知理想参数时,该算法与其它非自动设置参数的迭代重加权算法性能相当,甚至更优;在理想参数未知时,该算法的重构性能要明显优于其它算法。