Improved pruning algorithm for Gaussian mixture probability hypothesis density filter

With the increment of the number of Gaussian components, the computation cost increases in the Gaussian mixture probability hypothesis density(GM-PHD) filter. Based on the theory of Chen et al, we propose an improved pruning algorithm for the GM-PHD filter, which utilizes not only the Gaussian components’ means and covariance, but their weights as a new criterion to improve the estimate accuracy of the conventional pruning algorithm for tracking very closely proximity targets. Moreover, it solves the end-less while-loop problem without the need of a second merging step. Simulation results show that this improved algorithm is easier to implement and more robust than the formal ones.

A NEW DATA ASSOCIATION ALGORITHM USING PROBABILITY HYPOTHESIS DENSITY FILTER

Probability Hypothesis Density (PHD) filtering approach has shown its advantages in tracking time varying number of targets even when there are noise,clutter and misdetection. For linear Gaussian Mixture (GM) system,PHD filter has a closed form recursion (GMPHD). But PHD filter cannot estimate the trajectories of multi-target because it only provides identity-free estimate of target states. Existing data association methods still remain a big challenge mostly because they are com-putationally expensive. In this paper,we proposed a new data association algorithm using GMPHD filter,which significantly alleviated the heavy computing load and performed multi-target trajectory tracking effectively in the meantime.

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

THE PROBABILITY HYPOTHESIS DENSITY FILTER WITH EVIDENCE FUSION

The original Probability Hypothesis Density (PHD) filter is a tractable algorithm for Multi-Target Tracking (MTT) in Random Finite Set (RFS) frameworks. In this paper,we introduce a novel Evidence PHD (E-PHD) filter which combines the Dempster-Shafer (DS) evidence theory. The proposed filter can deal with the uncertain information,thus it forms target track. We mainly discusses the E-PHD filter under the condition of linear Gaussian. Research shows that the E-PHD filter has an analytic form of Evidence Gaussian Mixture PHD (E-GMPHD). The final experiment shows that the proposed E-GMPHD filter can derive the target identity,state,and number effectively.

基于高斯混合模型的采煤工作面冲击危险性评价

【目的】深入了解声发射或微震能量分布所蕴含的概率学信息,对于工作面回采过程中的冲击危险性评价具有重要意义。【方法】以陕西大佛寺煤矿4号煤层40111工作面作为工程背景,运用物理相似模拟实验、理论分析、现场监测等相关方法进行分析,研究了声发射监测数据在回采过程中的演化规律,阐明了声发射能量概率分布呈现波动性的物理意义,提出了基于高斯混合模型(Gaussianminture model,GMM)及置信区间的冲击危险性评价指标模型,并由现场微震数据进行验证。【结果和结论】结果表明:回采过程中上覆岩层周期性垮落并伴随声发射能量的集中释放。总能量的概率密度函数呈现多自由度的非对称分布,通过对比残差平方和等多项拟合效果指标,确定高斯混合模型为最佳拟合模型。基于EM(expectation maximization)算法的GMM聚类分析,将声发射事件总能量分布划分为两类:高频低能型和低频高能型,其中低频高能型与冲击事件的突发性和高能量破坏特征一致。依据概率-能量梯度变化特征,对工作面开采过程中冲击危险性进行了评估。研究成果为采煤工作面冲击危险性评价提供了概率学上的创新思路,具有在冲击地压监测预警及后续防治中的潜在应用价值。

无源声呐水下多目标融合跟踪方法

针对海洋环境噪声导致弱目标在不同子频带检测结果差异较大,致使以全频带探测结果为输入的跟踪算法出现性能退化的问题,提出一种子带融合跟踪方法。该方法利用改进的高斯混合概率假设密度滤波器对各频率子带输出的方位估计结果进行跟踪,并采用广义协方差交集准则对子带跟踪结果进行融合,以获得综合各子带信息的跟踪结果。仿真结果表明,所提方法可以提高弱目标在各子带信噪比不均衡情况下的跟踪能力,且运算时间与对比方法较为接近。海试数据处理结果进一步验证了所提方法的有效性。

基于随机有限集的多目标跟踪技术综述

随机有限集理论为多目标跟踪、多传感器融合和态势评估等问题提供了完整、统一的理论框架和解决方案。基于随机有限集的跟踪算法将多目标状态和量测建模为随机有限集,自然地引入航迹起始、终结机制,可实现目标数量和状态的同时估计。通过对随机有限集框架下的概率假设密度、带势概率假设密度、多目标多伯努利滤波器、扩展标签随机集滤波器和泊松多伯努利混合滤波器的研究进展进行详细梳理和综合对比,对基于随机有限集的多目标跟踪领域未来发展方向进行了分析和展望。

Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.

高斯混合粒子Cardinalized概率假设密度滤波被动测角多目标跟踪

为解决目标数未知或随时间变化的多目标跟踪问题,通常将多目标状态和观测数据表示为随机集形式,通过Cardinalized概率假设密度(CPHD)滤波,递推计算目标的强度(即概率假设密度,PHD)及目标数的概率分布.然而对于被动测角的非线性跟踪问题,CPHD无法获得闭合解.为此,本文提出一种新的高斯混合粒子CPHD算法,利用高斯混合近似PHD,避免了用聚类确定目标状态,同时,将拟蒙特卡罗(QMC)积分方法引入计算目标状态的预测和更新分布,取得了良好的效果.

计算高效的分布式多传感器PHD融合方法

基于广义协方差交集(GCI)融合理论,提出一种计算高效的分布式多传感器多目标跟踪算法,其中概率假设密度(PHD)滤波器在每个传感器节点运行,进行滤波处理。GCI用于融合多个PHD时,融合密度包括大量融合假设,这些假设随着高斯分量的数量增加呈指数增长。因此,GCI融合在实际运行中往往难以计算。为了提高多传感器融合的运算效率,文中通过距离度量将高斯分量聚类,然后进行孤立。距离度量可计算出目标融合后的密度权重,丢弃权重可忽略不计的融合假设,就能够构建简化的近似密度函数。分析表明,所提出的融合算法相较于传统的GCI融合算法,计算效率能够呈倍数提升。在先后出现12个目标的仿真场景中,通过实验验证了所提融合算法的有效性。

基于椭圆随机超曲面模型CPHD滤波器的多扩展目标跟踪算法

复杂场景下多扩展目标跟踪在自动驾驶、目标识别等领域具有很高的应用价值。文中提出了一种基于椭圆随机超曲面模型(ERHM)的势概率假设密度(CPHD)滤波器。首先,基于有限集统计理论,利用CPHD滤波器建立多扩展目标的贝叶斯滤波框架;然后,采用ERHM描述扩展目标的量测源分布,并利用无迹变换嵌入CPHD滤波流程;最后,仿真实验结果表明,ERHM-CPHD滤波器对椭圆扩展目标的跟踪性能优于传统的伽马高斯逆威沙特CPHD滤波器,在杂波密度较高、目标新生的位置比较确定的场景或者扩展目标数目较多时,对扩展目标的参数估计更为准确。所提方法在高分辨率雷达多目标跟踪方面具备很好的运用前景。

基于高斯混合模型的物流非高斯随机振动损伤分析

针对公路运输环境中的振动信号具有明显的非高斯性,提出一种非高斯随机振动疲劳损伤分析方法。为了描述振动信号的幅值概率密度分布,采用移动加速度均方根来代表该段信号的振动强度,并引入高斯混合模型对加速度均方根值进行描述。在此基础上结合Tovo-Benasciutti方法和Dirlik方法推导出非高斯宽带频域疲劳损伤计算方法。最后,以雨流计数法作为参考,对不同峭度的实测振动信号进行疲劳损伤分析,结果表明,与传统频域疲劳损伤计算方法相比较,提出的非高斯疲劳损伤方法具有更高的计算精度。该研究对于运输包装件的随机振动加速试验设计有实际意义。

一种改进的GM-C-CPHD空间多目标跟踪算法

随着空间目标的数目急剧上升,提高空间多目标跟踪精度成为必然要求,但空间多目标跟踪存在轨道动力学模型不完善的问题。针对该问题,提出一种改进的高斯混合势概率假设密度滤波(GM-C-CPHD)算法。通过在轨道动力学模型中考虑一个不确定性模型参数,即面质比参数(AMR),基于协方差传递面质比参数对位置、速度状态估计的影响,提高空间目标跟踪精度。仿真分析表明:相对于GM-CPHD滤波器,目标数量的跟踪和状态估计性能均有所提高,具有良好的应用前景。

Probability Distribution of the Hull Motion and Mooring Line Tension of Two Floating Systems

The statistical and distribution characteristics of the responses of a floater and its mooring lines are essential in designing floating/mooring systems.In general,the dynamic responses of offshore structures obey a Gaussian distribution,assuming that the structural system,and sea loads are linear or weakly nonlinear.However,mooring systems and wave loads are considerably nonlinear,and the dynamic responses of hull/mooring systems are non-Gaussian.In this study,the dynamic responses of two types of floaters,semi-submersible and spar platforms,and their mooring lines are computed using coupled dynamic analysis in the time domain.Herein,the statistical characteristics and distributions of the hull motion and mooring line tension are discussed and compared.The statistical distributions of the dynamic responses have strong non-Gaussianity and are unreasonably fitted by a Gaussian distribution for the two floating and mooring systems.Then,the effects of water depth,wave parameters,and low-frequency and wave-frequency components on the non-Gaussianity of the hull motion,and mooring line tension are investigated and discussed.A comparison of the statistical distributions of the responses with various probability density functions,including the Gamma,Gaussian,General Extreme Value,Weibull,and Gaussian Mixture Model(GMM)distributions,shows that the GMM distribution is better than the others for characterizing the statistical distributions of the hull motion,and mooring line tension responses.Furthermore,the GMM distribution has the best accuracy of response prediction.

Multiple extended target tracking algorithm based on Gaussian surface matrix

In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix（GSM） into the framework of the random finite set（RFS） theory. The Gaussian surface function is constructed first by the measurements, and it is used to define the GSM via a mapping function. We then integrate the GSM with the probability hypothesis density（PHD） filter, the Bayesian recursion formulas of GSM-PHD are derived and the Gaussian mixture implementation is employed to obtain the closed-form solutions. Moreover, the estimated shapes are designed to guide the measurement set sub-partition, which can cope with the problem of the spatially close target tracking. Simulation results show that the proposed algorithm can effectively estimate irregular target shapes and exhibit good robustness in cross extended target tracking.

Convolution Kernels Implementation of Cardinalized Probability Hypothesis Density Filter

The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.

基于GMM-DBC的CSI室内定位算法

针对贝叶斯室内定位技术存在定位精度低及时间复杂度较高的问题,提出了一种基于高斯混合模型和密度聚类(GMM-DBC)的信道状态信息(CSI)定位算法.通过对分模型参数的初次估计构建GMM概率分布模型并进行误差计算;引入确定分模型个数(DSM)策略,结合误差计算结果更新GMM模型参数,减小由模型精度引起的定位误差;基于不同参考点的分布特征,判断参考点间紧密程度,将紧密相连的参考点划为一类,减小搜索范围,降低时间复杂度;根据分簇结果,利用改进的贝叶斯概率算法进行权值计算,得到最终定位结果.实验结果表明:所提算法能较好地提高定位精度,降低时间复杂度.

SRCKF-GM-PHD多目标跟踪算法的优化

针对平方根容积卡尔曼滤波高斯混合概率假设密度(SRCKF-GM-PHD)算法在高杂波条件下对非线性目标跟踪能力弱的问题,文中首先融入改进灰狼算法,实时调节过程噪声Q和量测噪声R。其次,结合改进的渐消因子思想,实时调整SRCKF-GM-PHD算法中的增益矩阵,提高目标的跟踪精度。此外,为避免算法中止,文中提出动态权重调整策略的改进措施,调整算法中的实际输出残差序列的协方差。最终,形成了融合改进灰狼算法和改进渐消因子的SRCKF-GM-PHD算法。仿真分析对比了四种算法的性能,表明了所提算法在跟踪精度方面的有效性和优越性。

基于STCKF-CPHD算法的多RAM类目标跟踪

针对来袭RAM类目标机动能力强、数目多变且受到密集杂波干扰从而导致传统算法跟踪精度下降的问题,提出一种基于势概率假设密度框架下的强跟踪容积卡尔曼滤波算法(STCKF-CPHD)。首先,建立RAM类目标动力学模型,通过一阶马尔可夫过程对目标外弹道质阻比参数进行建模,得到扩维后滤波器的状态空间模型。然后,引入强跟踪技术,设计带时变渐消因子的STCKF滤波器,解决目标机动导致的模型失配问题。最后,在CPHD的框架下,对目标的质阻比、状态、数量进行联合估计。仿真结果表明,所提算法可以对来袭多RAM类目标进行有效跟踪,目标最优子模型分配(OSPA)距离的跟踪精度相较于STCKF-PHD算法提高了15%。

基于高斯混合概率假设滤波的水下目标跟踪算法

为了解决传统水下目标跟踪中目标数目估计不准确、状态估计误差增长过快的问题,提出了一种基于高斯混合概率假设滤波的水下目标跟踪算法。该算法基于双基地观测模型,采用高斯混合概率假设滤波算法处理方位和时延信息,利用粒子群算法处理多普勒频率获得矢量速度,进一步提升算法的跟踪精度。结果表明,该算法能完成在杂波环境下对目标的跟踪,相比传统的关联算法,能够有效地实现目标个数估计和抑制状态误差增长的目的。