Localization of multiple disjoint sources with prior knowledge on source locations in the presence of sensor location errors

Sensor location errors are known to be able to degrade the source localization accuracy significantly. This paper considers the problem of localizing multiple disjoint sources where prior knowledge on the source locations is available to mitigate the effect of sensor location uncertainty. The error in the priorly known source location is assumed to follow a zero-mean Gaussian distribution. When a source location is completely unknown, the covariance matrix of its prior location would go to infinity. The localization of multiple disjoint sources is achieved through exploring the time difference of arrival (TDOA) and the frequency difference of arrival (FDOA) measurements. In this work, we derive the Cramér–Rao lower bound (CRLB) of the source location estimates. The CRLB is shown analytically to be able to unify several CRLBs introduced in literature. We next compare the localization performance when multiple source locations are determined jointly and individually. In the presence of sensor location errors, the superiority of joint localization of multiple sources in terms of greatly improved localization accuracy is established. Two methods for localizing multiple disjoint sources are proposed, one for the case where only some sources have prior location information and the other for the scenario where all sources have prior location information. Both algorithms can reach the CRLB accuracy when sensor location errors are small. Simulations corroborate the theoretical developments.     

Maximum contrast analysis for nonnegative blind source separation

In this paper, we propose a maximum contrast analysis (MCA) method for nonnegative blind source separation, where both the mixing matrix and the source signals are nonnegative. We first show that the contrast degree of the source signals is greater than that of the mixed signals. Motivated by this observation, we propose an MCA-based cost function. It is further shown that the separation matrix can be obtained by maximizing the proposed cost function. Then we derive an iterative determinant maximization algorithm for estimating the separation matrix. In the case of two sources, a closed-form solution exists and is derived. Unlike most existing blind source separation methods, the proposed MCA method needs neither the independence assumption, nor the sparseness requirement of the sources. The effectiveness of the new method is illustrated by experiments using X-ray images, remote sensing images, infrared spectral images, and real-world fluorescence microscopy images.     

基于期望极大化算法的航迹起始方法研究

将序列概率比检验(SPRT)和期望极大化(EM)算法相结合,给出了一种解决杂波环境下目标航迹起始问题的新方法。首先,利用两点差分方法建立暂时航迹;然后,针对由于目标真实状态未知导致的应用SPRT算法时似然函数计算上的困难,导出了基于递推EM算法的似然函数计算公式,可以实时且有效地解决其中的不完全数据问题。从而,实现暂时航迹的确认和删除。仿真结果表明文中算法具有良好的性能。     

基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.     

Parameter estimation of two-level nonlinear mixed effects models using first order conditional linearization and the EM algorithm

Multi-level nonlinear mixed effects (ML-NLME) models have received a great deal of attention in recent years because of the flexibility they offer in handling the repeated-measures data arising from various disciplines. In this study, we propose both maximum likelihood and restricted maximum likelihood estimations of ML-NLME models with two-level random effects, using first order conditional expansion (FOCE) and the expectation–maximization (EM) algorithm. The FOCE–EM algorithm was compared with the most popular Lindstrom and Bates (LB) method in terms of computational and statistical properties. Basal area growth series data measured from Chinese fir (Cunninghamia lanceolata) experimental stands and simulated data were used for evaluation. The FOCE–EM and LB algorithms given the same parameter estimates and fit statistics for models that converged by both. However, FOCE–EM converged for all the models, while LB did not, especially for the models in which two-level random effects are simultaneously considered in several base parameters to account for between-group variation. We recommend the use of FOCE–EM in ML-NLME models, particularly when convergence is a concern in model selection.     

Blind source separation with time series variational Bayes expectation maximization algorithm

This paper presents a variational Bayes expectation maximization algorithm for time series based on Attias? variational Bayesian theory. The proposed algorithm is applied in the blind source separation (BSS) problem to estimate both the source signals and the mixing matrix for the optimal model structure. The distribution of the mixing matrix is assumed to be a matrix Gaussian distribution due to the correlation of its elements and the inverse covariance of the sensor noise is assumed to be Wishart distributed for the correlation between sensor noises. The mixture of Gaussian model is used to approximate the distribution of each independent source. The rules to update the posterior hyperparameters and the posterior of the model structure are obtained. The optimal model structure is selected as the one with largest posterior. The source signals and mixing matrix are estimated by applying LMS and MAP estimators to the posterior distributions of the hidden variables and the model parameters respectively for the optimal structure. The proposed algorithm is tested with synthetic data. The results show that: (1) the logarithm posterior of the model structure increases with the accuracy of the posterior mixing matrix; (2) the accuracies of the prior mixing matrix, the estimated mixing matrix, and the estimated source signals increase with the logarithm posterior of the model structure. This algorithm is applied to Magnetoencephalograph data to localize the source of the equivalent current dipoles.     

一种非视距环境下的目标定位算法

针对机器人、无人机和其他智能系统的位置信息,研究了非视距(non line of sight, NLOS)环境中基于到达时间(time of arrival,TOA)测距的目标定位问题。在建模过程中,通过引入平衡参数来抑制NLOS误差对定位精度的影响,并成功将定位问题的形式与一个广义信赖域子问题(generalized trust region subproblem,GTRS)框架进行耦合。与其他凸优化算法不同的是,本文没有联合估计目标节点的位置和平衡参数,而是采用了一种迭代求精的思想,算法可以用二分法高速有效地进行求解。 所提算法与已有的算法相比,不需要任何关于NLOS路径的信息。此外,与大多数现有算法不同,所提算法的计算复杂度低,能够满足实时定位的需求。仿真结果表明:该算法具有稳定的NLOS误差抑制能力,在定位性能和算法复杂度之间有着很好的权衡。     

基于无线传感器网络的自适应声源定位算法

基于声源能量的无线传感器网络（ WSNs）最大似然定位算法抗噪声干扰能力强,定位精度高,同时适用于多个目标定位,但是计算量大,不适用于实时定位。针对现有算法的缺点,提出了一种基于自适应迭代的最大似然定位算法。该算法将代价函数作为目标函数,在给定的梯度误差范围内自适应地搜索目标位置。为了提高算法的收敛速度和定位精度,提出了基于Sigmoid函数的变步长的搜索算法。仿真实验结果表明：与最大似然定位算法相比,自适应迭代算法运算量小,定位精度高,能满足对目标定位精度和速度要求较高的场合,具有一定的实际应用意义。     

面向微博的情感影响最大化模型

社交网络中影响最大化问题是寻找具有最大影响范围的节点。影响最大化的大部分求解算法仅仅依赖社交网络图。基于微博的转发关系树和微博内容的情感倾向性,以及用户的社交网络图,提出了一个能够刻画用户情感影响的情感影响最大化模型——情感影响分配模型(sentiment influence distribution,SID),证明了SID模型下的情感影响最大化问题是一个NP难问题,给出了一个具有精度保证的贪心算法。在真实的微博数据上的实验结果表明,SID模型能够有效地找出情感影响最大化的节点集,同时具有很高的扩展性。     

稳定分布噪声环境下的EEG-MUSIC源定位

EEG作为一种无损的新医学技术近几年已经被广泛地研究,EEG-MUSIC是一种基于EEG的脑源病灶空间定位算法,它只能在高斯噪声下工作。特殊情况下的脑电传感器阵列数据中可能伴有一种强脉冲噪声,这种噪声可以用α稳定分布描述。稳定分布噪声环境下,传统的EEG-RAP-MUSIC失效。为此用FLOM矩阵代替自相关矩阵,提出了一种适合稳定分布噪声环境的脑源定位新方法FLOM-EEG-RAP-MUSIC。计算机仿真表明,所提出的方法能较好地在稳定分布噪声环境下工作,具有一定的鲁棒性。     

混合空间新型贝叶斯网络模型的图像分割应用研究

现有研究工作没有确定概率向量模型的混合部分比例,所以无法解决MCMC方法的迭代收敛性问题。在具有空间平滑约束的高斯混合模型GMM基础上提出新型贝叶斯网络模型并应用于图像分割领域。模型应用隐Dirichlet分布LDA的概率密度模型和Gauss-Markov随机域MRF的隐Dirichlet参数混合过程来实现参数平滑过程,具有如下优点:针对空间平滑约束规范概率向量模型比例;使用最大后验概率MAP和期望最大化算法EM完成闭合参数的更新操作过程。实验表明,本模型比其他应用GMM方法的图像分割效果好。该模型已成功应用到自然图像和有噪声干扰的自然艺术图像分割过程中。     

空间约束层次加权Gamma混合模型的SAR图像分割

目的 合成孔径雷达（SAR）图像中像素强度统计分布呈现出复杂的特性,而传统混合模型难以建模非对称、重尾或多峰等特性的分布。为了准确建模SAR图像统计分布并得到高精度分割结果,本文提出一种利用空间约束层次加权Gamma混合模型（HWGaMM）的SAR图像分割算法。方法 采用Gamma分布的加权和定义混合组份;考虑到同质区域内像素强度的差异性和异质区域间像素强度的相似性,采用混合组份加权和定义HWGaMM结构。采用马尔可夫随机场（MRF）建模像素空间位置关系,利用中心像素及其邻域像素的后验概率定义混合权重以将像素邻域关系引入HWGaMM,构建空间约束HWGaMM,以降低SAR图像内固有斑点噪声的影响。提出算法结合M-H（Metropolis-Hastings）和期望最大化算法（EM）求解模型参数,以实现快速SAR图像分割。该求解方法避免了M-H算法效率低的缺陷,同时克服了EM算法难以求解Gamma分布中形状参数的问题。结果 采用3种传统混合模型分割算法作为对比算法进行分割实验。拟合直方图结果表明本文算法具有准确建模复杂统计分布的能力。在分割精度上,本文算法比基于高斯混合模型（GMM）、Gamma分布和Gamma混合模型（GaMM）分割算法分别提高33%,29%和9%。在分割时间上,本文算法虽然比GMM算法多64 s,但与基于Gamma分布和GaMM算法相比较分别快600 s和420 s。因此,本文算法比传统M-H算法的分割效率有很大的提高。结论 提出一种空间约束HWGaMM的SAR图像分割算法,实验结果表明提出的HWGaMM算法具有准确建模复杂统计分布的能力,且具有较高的精度和效率。     

去除乘性噪声的重加权各向异性全变差模型

恢复含乘性噪声的图像是当前图像处理的重要研究课题. 本文提出基于迭代重加权的各向异性全变差(Total variation, TV)模型. 新模型中, 假定乘性噪声服从Gamma分布. 正则项采用加权的各向异性全变差, 其中, 自适应权函数由期望最大(Expectation maximization, EM)算法得到. 新模型在有效去噪的同时, 较好地保留了图像的边缘和细节信息, 同时能够有效地抑制"阶梯效应". 数值实验验证了新模型的效果.     

Three-dimensional localization of multiple acoustic sources in shallow ocean with non-Gaussian noise

In this paper, a low-complexity algorithm SAGE-USL is presented for 3-dimensional (3-D) localization of multiple acoustic sources in a shallow ocean with non-Gaussian ambient noise, using a vertical and a horizontal linear array of sensors. In the proposed method, noise is modeled as a Gaussian mixture. Initial estimates of the unknown parameters (source coordinates, signal waveforms and noise parameters) are obtained by known/conventional methods, and a generalized expectation maximization algorithm is used to update the initial estimates iteratively. Simulation results indicate that convergence is reached in a small number of (≤10) iterations. Initialization requires one 2-D search and one 1-D search, and the iterative updates require a sequence of 1-D searches. Therefore the computational complexity of the SAGE-USL algorithm is lower than that of conventional techniques such as 3-D MUSIC by several orders of magnitude. We also derive the Cramér–Rao Bound (CRB) for 3-D localization of multiple sources in a range-independent ocean. Simulation results are presented to show that the root-mean-square localization errors of SAGE-USL are close to the corresponding CRBs and significantly lower than those of 3-D MUSIC.     

EM‐based adaptive divided difference filter for nonlinear system with multiplicative parameter

This paper is concerned with application of expectation maximization (EM) algorithm for deriving an adaptive version of divided difference filter for joint state estimation and multiplicative parameter identification of nonlinear system with the colored measurement noise. Owing to the fact that there exist a mutual coupling and interaction of state and parameter on each other, it requires a joint or simultaneous estimation of both state and parameter by a mutual iteration, and justly, EM iterates Expectation (E‐)step and Maximization (M‐)step to meet such requirement. Firstly, E‐step involves state filtering and smoothing issues under knowing the previous parameter identification results, which is well solved by resorting to the Gaussian approximation with a trade‐off between accuracy and complexity. Further, such Gaussian approximation estimators are applied for evaluating the condition expectation of complete‐data likelihood function, nonlinearly characterized by the multiplicative parameter needed to be optimized. Secondly, M‐step deals with the maximization of the condition expectation by directly making its derivative as zero to obtain the current general parameter identification equation as the nonlinear integral. Thirdly, by iteratively operating E‐step and M‐step, an adaptive divided difference filter is proposed for joint state estimation and parameter identification by using the second‐order Stirling interpolation to compute the associated nonlinear integral. Finally, the robust performance of the EM‐based adaptive version of divided difference filter to the unknown or time‐varying multiplicative parameter, as compared with the standard augmentation method, is demonstrated by a maneuvering target tracking example. Copyright © 2016 John Wiley & Sons, Ltd.     

Convex optimization algorithms for cooperative RSS-based sensor localization

To obtain a global solution for the source location estimates, the cost function of RSS-based sensor localization is relaxed as convex optimization problem which can be solved by interior point method. Weighted squared least square (WSLS) and weighted least square (WLS) based optimization functions are proposed to locate the source nodes. The corresponding semidefinite programming (SDP), second-order cone program (SOCP) and mixed SOC/SDP algorithms are designed by considering the known or unknown transmit powers. The computational complexity of the proposed algorithms is derived by analyzing the number of variables and equality constraints produced in the relaxation. The simulations show that the mixed SOC/SDP runs faster than the SDP, although the algorithms have the approximately equal accuracy performance. Whether the transmit power is known or not, the accuracy performance of the WLS-SDP is better than that of the WSLS-SDP and WSLS-SOC/SDP algorithms. However the computational complexity of the WLS-SDP is greatly larger than that of WSLS-SOC/SDP and WSLS-SDP due to a large number of variables.     

A variable step-size selective partial update LMS algorithm

Selective partial update of the adaptive filter coefficients has been a popular method for reducing the computational complexity of least mean-square (LMS)-type adaptive algorithms. These algorithms use a fixed step-size that forces a performance compromise between fast convergence speed and small steady state misadjustment. This paper proposes a variable step-size (VSS) selective partial update LMS algorithm, where the VSS is an approximation of an optimal derived one. The VSS equations are controlled by only one parameter, and do not require any a priori information about the statistics of the system environment. Mean-square performance analysis will be provided for independent and identically distributed (i.i.d.) input signals, and an expression for the algorithm steady state excess mean-square error (MSE) will be presented. Simulation experiments are conducted to compare the proposed algorithm with existing full-update VSS LMS algorithms, which indicate that the proposed algorithm performs as well as these algorithms while requiring less computational complexity.     

Interactive color image segmentation via iterative evidential labeling

We develop an interactive color image segmentation method in this paper. This method makes use of the conception of Markov random fields (MRFs) and D–S evidence theory to obtain segmentation results by considering both likelihood information and priori information under Bayesian framework. The method first uses expectation maximization (EM) algorithm to estimate the parameter of the user input regions, and the Bayesian information criterion (BIC) is used for model selection. Then the beliefs of each pixel are assigned by a predefined scheme. The result is obtained by iteratively fusion of the pixel likelihood information and the pixel contextual information until convergence. The method is initially designed for two-label segmentation, however it can be easily generalized to multi-label segmentation. Experimental results show that the proposed method is comparable to other prevalent interactive image segmentation algorithms in most cases of two-label segmentation task, both qualitatively and quantitatively.     

Locating the contagion source in networks with partial timestamps

This paper studies the problem of identifying a single contagion source when partial timestamps of a contagion process are available. We formulate the source localization problem as a ranking problem on graphs, where infected nodes are ranked according to their likelihood of being the source. Two ranking algorithms, cost-based ranking and tree-based ranking, are proposed in this paper. Experimental evaluations with synthetic and real-world data show that our algorithms significantly improve the ranking accuracy compared with four existing algorithms.     

基于WKGV-KICA 的盲源信号分离算法

基于核学习的非线性映射能力,提出一种小波核广义方差的核独立成分分析算法WKGV-KICA.小波核函数具有近似正交,适用于信号局部分析的优点.与互信息相联系,将核广义方差作为对比函数对统计独立性进行衡量,可以获得理想的数学特性.将该算法应用于宽范围的盲源分离问题的实例中,并与现有算法进了比较.实验结果表明, WKGV-KICA算法在同等条件下的分离精度更高,而且性能更好.