具有噪声信息与状态模型不确定系统的IMM自适应滤波

卡尔曼滤波器广泛用于解决线性高斯系统的状态估计问题.然而,在实际应用中过程噪声和系统模型参数先验信息未知,且量测受到异常值干扰,给准确估计系统状态带来极大困难.针对具有噪声信息和状态模型不确定的动态系统,提出一种广义交互式多模型自适应滤波算法.该算法设计多个模型并行的方式对系统不确定进行处理,对于每个模型,建立Skew-T分布非对称重尾噪声表示模型,为了解决过程噪声与系统协方差相互耦合难以求解的问题,利用逆威沙特分布对系统预测协方差矩阵进行描述,并通过变分贝叶斯推理递归计算系统状态的后验分布.仿真结果和实验验证表明,在噪声信息和状态模型不确定条件下,所提出算法具有较高的估计精度.     

带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器

为了解决带有色厚尾量测噪声的非线性状态估计问题,本文提出了新的鲁棒高斯近似（Gaussian approximate,GA）滤波器和平滑器.首先,基于状态扩展方法将量测差分后带一步延迟状态和白色厚尾量测噪声的非线性状态估计问题,转化成带厚尾量测噪声的标准非线性状态估计问题.其次,针对量测差分后模型中的噪声尺度矩阵和自由度（Degrees of freedom,DOF）参数未知问题,设计了新的高斯近似滤波器和平滑器,通过建立未知参数和待估计状态的共轭先验分布,并利用变分贝叶斯方法同时估计未知的状态、尺度矩阵、自由度参数.最后,利用目标跟踪仿真验证了本文提出的带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器的有效性以及与现有方法相比的优越性.     

基于领域关系广义混合模型图像分割的研究

针对高斯混合模型不能有效处理复杂噪声图像分割问题,提出了基于领域关系广义混合模型.在高斯混合模型基础上引入形状参数r提高混合模型对不同噪声适应能力,另外该方法结合图像中像素点邻域关系,融入像素点间的互动信息.与混合模型通常采用EM算法估计参数不同,该模型参数估计采用梯度方法,通过最小化负似然对数优化参数.实验结果表明,广义混合模型在处理高斯噪声,重尾噪声,混合噪声以及脉冲噪声图像分割问题都取得了很好的效果.     

利用混合卡尔曼滤波的混沌信号盲估计

针对混沌动力学系统时变参数未知的混沌信号,在含有状态噪声的情况下,利用混合卡尔曼滤波提出一种盲估计算法.对未知参数和混沌状态构成的高维状态进行估计,先利用卡尔曼滤波给出线性高斯部分的最优精确估计,剩余部分利用粒子滤波方法给出次优估计,文中详细研究了高斯噪声以及非高斯噪声下的最优重要性函数选取并推导了重要性权重的计算公式,最终基于有效粒子的最小均方误差准则实现了信号的盲估计.仿真结果表明该算法能有效实现含有状态噪声混沌信号的盲估计,并取得了比基本粒子滤波算法更优的性能.     

Alpha稳定分布随机变量的产生

在实际应用中遇到的大量的非高斯信号或噪声具有显著的尖峰脉冲特性,其概率密度函数的衰减过程比高斯分布要慢,表现出显著的拖尾。而基于广义中心极限定理的Alpha稳定分布描述了信号统计分布的非高斯性和重拖尾性。实现服从Alpha稳定分布随机变量的仿真是开展相关研究的基础。该文由S2参数系下的分布模型的仿真算法导出标准参数系下Alpha稳定分布随机变量的仿真算法。并通过仿真实验证实了该仿真算法的可行性。     

基于贝叶斯网络理论的时变混合盲源分离算法

以状态空间模型作为信道的变化模型，研究了时变混合情况下非平稳信号的盲分离问题。首先将隐马尔可夫模型（HMM）和混合高斯（MOG）模型结合起来对具有动态结构和复杂分布的非平稳源信号进行建模，然后运用贝叶斯网络理论处理信道时变情况下独立成分分析（ICA）模型中各变量和参数之间的关系，提出了一种基于贝叶斯推断的可同时完成混合矩阵盲估计及源信号盲分离的算法，通过采用逼近方法有效地减小了算法计算量。计算机仿真试验证明本文算法的有效性。     

稳定分布自回归有色噪声及其改进的白化方法

为了解决非高斯白噪声经过线性或非线性系统得到的有色噪声的白化问题,依据稳定分布白噪声的概念及其判断标准,和已有的线性自回归(AR)模型,对已有的迭代重加权最小P范数(IRLP)白化算法进行改进,提出了改进的IIRLP白化算法.对线性自回归稳定有色噪声的模型参数进行估计,并探讨了其白化方法.计算机仿真表明,本文算法较已有的IRLP算法具有更好的韧性及稳健性.     

基于混合Kotz-型分布的多分类人脸识别方法

针对实际人脸图像中含有重尾噪声的问题,提出一种基于混合Kotz-型分布的多分类人脸识别方法。利用Kotz-型分布与广义逆厂分布混合表现出的较厚拖尾特性,结合核方法和概率统计知识,通过调节混合Kotz-型分布中的参数,估计人脸图像中重尾噪声的拖尾情况。分别向ORL人脸库、Yale人脸库、Randface人脸库添加程度不同的重尾噪声,形成新的含有不同程度重尾噪声的人脸库,通过对3个人脸库进行验证,结果表明,该方法能较好地估计人脸图像的拖尾特性,对含有重尾噪声的人脸图像有较高的识别率。     

含局部空间约束的t分布混合模型的点集配准

基于高斯混合模型（Gaussian mixture model,GMM）的点集非刚性配准算法易受重尾点和异常点影响,提出含局部空间约束的t分布混合模型的点集非刚性配准算法. 通过期望最大化（Expectation maximization,EM）框架将高斯混合模型推广为t分布混合模型;把Dirichlet分布作为浮动点的先验权重,并构造含局部空间约束性质的Dirichlet 分布参数. 使用EM算法获得配准参数的闭合解;计算浮动点的自由度,改变其概率密度分布,避免异常点水平估计误差. 实验表明,本文提出的配准算法具有配准误差小、鲁棒性好、抗干扰能力强等优点.     

基于自适应密度估计的系统参数辨识

针对噪声分布未知的ARMAX系统,提出了一种自适应非参数噪声密度估计方法,由估计误差动态调整高斯核函数的全局带宽和局部带宽,实现了未知噪声分布密度的自适应估计;通过极小化似然函数,给出了基于噪声密度估计的参数辨识迭代算法,分析了算法的收敛性并给出了算法收敛的充分条件.仿真结果表明本文提出的算法在系统噪声未知时具有较强的抗噪能力和良好的收敛性.     

Variational Bayesian inference based robust multiple measurement sparse signal recovery

This work concentrates on not only probing into a novel Bayesian probabilistic model to formulate a general type of robust multiple measurement vectors sparse signal recovery problem with impulsive noise, but also developing an improved variational Bayesian method to recover the original joint row sparse signals. In the design of the model, two three-level hierarchical Bayesian estimation procedures are designed to characterize impulsive noise and joint row sparse source signals by means of Gaussian scale mixtures and multivariate generalized t distribution. Those hidden variables, included in signal and measurement models are estimated based on a variational Bayesian framework, in which multiple kinds of probability distributions are adopted to express their features. In the design of the algorithm, the proposed algorithm is a full Bayesian inference approach related to variational Bayesian estimation. It is robust to impulsive noise, since the posterior distribution estimation can be effectively approached through estimating unknown parameters. Extensive simulation results show that the proposed algorithm significantly outperforms the compared robust sparse signal recovery approaches under different kinds of impulsive noises.     

Robust data clustering by learning multi-metric Lq-norm distances

Unsupervised clustering for datasets with severe outliers inside is a difficult task. In this approach, we propose a cluster-dependent multi-metric clustering approach which is robust to severe outliers. A dataset is modeled as clusters each contaminated by noises of cluster-dependent unknown noise level in formulating outliers of the cluster. With such a model, a multi-metric Lp-norm transformation is proposed and learnt which maps each cluster to the most Gaussian distribution by minimizing some non-Gaussianity measure. The approach is composed of two consecutive phases: multi-metric location estimation (MMLE) and multi-metric iterative chi-square cutoff (ICSC). Algorithms for MMLE and ICSC are proposed. It is proved that the MMLE algorithm searches for the solution of a multi-objective optimization problem and in fact learns a cluster-dependent multi-metric Lq-norm distance and/or a cluster-dependent multi-kernel defined in data space for each cluster. Experiments on heavy-tailed alpha-stable mixture datasets, Gaussian mixture datasets with radial and diffuse outliers added respectively, and the real Wisconsin breast cancer dataset and lung cancer dataset show that the proposed method is superior to many existent robust clustering and outlier detection methods in both clustering and outlier detection performances.     

Blind separation of non-stationary sources using continuous density hidden Markov models

Blind source separation (BSS) has attained much attention in signal processing society due to its ‘blind’ property and wide applications. However, there are still some open problems, such as underdetermined BSS, noise BSS. In this paper, we propose a Bayesian approach to improve the separation performance of instantaneous mixtures with non-stationary sources by taking into account the internal organization of the non-stationary sources. Gaussian mixture model (GMM) is used to model the distribution of source signals and the continuous density hidden Markov model (CDHMM) is derived to track the non-stationarity inside the source signals. Source signals can switch between several states such that the separation performance can be significantly improved. An expectation-maximization (EM) algorithm is derived to estimate the mixing coefficients, the CDHMM parameters and the noise covariance. The source signals are recovered via maximum a posteriori (MAP) approach. To ensure the convergence of the proposed algorithm, the proper prior densities, conjugate prior densities, are assigned to estimation coefficients for incorporating the prior information. The initialization scheme for the estimates is also discussed. Systematic simulations are used to illustrate the performance of the proposed algorithm. Simulation results show that the proposed algorithm has more robust separation performance in terms of similarity score in noise environments in comparison with the classical BSS algorithms in determined mixture case. Additionally, since the mixing matrix and the sources are estimated jointly, the proposed EM algorithm also works well in underdetermined case. Furthermore, the proposed algorithm converges quickly with proper initialization.     

导向矢量失配情况下基于稀疏表示的波达方向估计算法

提出了一种传感器阵列导向矢量失配情况下的基于稀疏表示的信号源波达方向DOA估计算法。针对一些实际环境中噪声重尾现象严重的特点,采用合成圆对称广义高斯噪声分布对其进行模拟。考虑到实际环境中传感器自身运动以及外界环境因素的改变可能会导致传感器导向矢量产生波动,利用加权最小二乘法对波动生成的增益值进行最优估计。然后,构建信号模型的分数低阶矩FLOM矩阵,进行矢量化处理,以提高其数组维数。最后,利用稀疏表示方法重构信号模型,将信号源DOA估计转化为二阶锥规划问题进行求解,并采用奇异值分解降低运算量。仿真结果表明,本算法的信号源DOA估计具有很高的分辨率,且有效地避免了导向矢量失配对DOA估计产生的影响。     

Alpha-stable modeling of noise and robust time-delay estimation inthe presence of impulsive noise

A new representation of audio noise signals is proposed, based on symmetric α-stable (SαS) distributions in order to better model the outliers that exist in real signals. This representation addresses a shortcoming of the Gaussian model, namely, the fact that it is not well suited for describing signals with impulsive behavior. The α-stable and Gaussian methods are used to model measured noise signals. It is demonstrated that the α-stable distribution, which has heavier tails than the Gaussian distribution, gives a much better approximation to real-world audio signals. The significance of these results is shown by considering the time delay estimation (TDE) problem for source localization in teleimmersion applications. In order to achieve robust sound source localization, a novel time delay estimation approach is proposed. It is based on fractional lower order statistics (FLOS), which mitigate the effects of heavy-tailed noise. An improvement in TDE performance is demonstrated using FLOS that is up to a factor of four better than what can be achieved with second-order statistics     

Maximum correntropy unscented filter

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilising a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for non-linear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearisation regression based on the maximum correntropy criterion is then used to obtain the posterior estimates of the state and covariance matrix. The satisfying performance of the new algorithm is confirmed by two illustrative examples.     

冲击噪声背景下主分量求逆波束形成

关于波束形成器抑制噪声优化问题,在冲击噪声背景下,常规波束形成性能下降,影响通信效果。为解决上述问题,提出一种适用于任意未知统计特性的代数拖尾冲击噪声环境下的归一化的主分量求逆(N-PCI)算法。通过对输入信号进行无穷范数归一化,使变换信号的二阶统计量在代数拖尾的冲击噪声环境下存在且有界,提高了波束形成器在冲击噪声背景下的性能,且无需噪声特征指数的先验信息。仿真结果表明,该算法具有副瓣电平低且干扰抑制能力强的优点,较常规波束形成算法更有效,为设计提供了有效参考。     

基于M估计的非线性鲁棒检测卡尔曼滤波算法

针对传统鲁棒非线性滤波在观测噪声为非高斯强干扰噪声情况下,滤波性能下降的问题,提出一种利用卡方检测法预判断的非线性鲁棒检测滤波算法。该算法通过卡方检测设置门限,剔除突变野值,利用M估计修正量测更新。仿真实验对比了几种典型非线性滤波方法在不同观测噪声环境下的性能。所提算法在非高斯强干扰噪声情况下,比传统鲁棒滤波算法估计精度平均提高了25.5%;估计方差平均减少了18.3%。实验结果表明:所提算法可以抑制观测量非高斯强干扰噪声的影响,提高滤波精度及稳定性。     

基于固定点迭代的Huber鲁棒容积卡尔曼滤波算法

对于非线性系统而言,容积卡尔曼滤波（Cubature Kalman Filter,CKF）算法是处理状态估计问题的一种有效方法,并且其在高斯噪声下可以获得良好的估计性能。然而,当噪声被重尾噪声污染时,其性能通常会急剧下降。为解决此问题,将Huber方法应用于CKF框架中,取代了传统的最小均方误差（Minimum Mean Square Error,MMSE）准则,以提高算法的鲁棒性。在所提算法中,通过将量测方程线性化构造了线性回归模型,并采用固定点迭代的方法求解基于Huber方法的最小化问题。因此,推导了基于固定点迭代的Huber鲁棒CKF（FP-IHCKF）算法,在该算法中先验信息和量测信息通过Huber方法进行了重构。通过对再入目标跟踪问题进行仿真,验证了所提算法的有效性和鲁棒性。     

带一步随机延迟量测非线性序列贝叶斯估计的条件后验克拉美罗下界

为了解决带一步随机延迟量测非线性状态估计器可获得最优性能的评价问题,提出了一种适用于带一步随机延迟量测非线性系统的条件后验克拉美罗下界(Conditional posterior Cramr-Rao lower bound, CPCRLB),且现有的CPCRLB仅是所提出的CPCRLB在延迟概率为零时的一种特例. 为了递归地计算提出的CPCRLB,本文提出了一种带一步随机延迟量测的粒子滤波器(Particle filter, PF),继而推导了提出的CPCRLB 一般近似解和在高斯噪声情况下的特殊近似解. 单变量非平稳增长模型、纯方位跟踪和频率调制信号模型的数值仿真证明了本文提出方法与现有方法相比的有效性和优越性.