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.

Kernel density estimation and marginalized-particle based probability hypothesis density filter for multi-target tracking

In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis density filter algorithm based on marginalized particle and kernel density estimation is proposed, which utilizes the idea of marginalized particle filter to enhance the estimating performance of the PHD. The state variables are decomposed into linear and non-linear parts. The particle filter is adopted to predict and estimate the nonlinear states of multi-target after dimensionality reduction, while the Kalman filter is applied to estimate the linear parts under linear Gaussian condition. Embedding the information of the linear states into the estimated nonlinear states helps to reduce the estimating variance and improve the accuracy of target number estimation. The meanshift kernel density estimation, being of the inherent nature of searching peak value via an adaptive gradient ascent iteration, is introduced to cluster particles and extract target states, which is independent of the target number and can converge to the local peak position of the PHD distribution while avoiding the errors due to the inaccuracy in modeling and parameters estimation. Experiments show that the proposed algorithm can obtain higher tracking accuracy when using fewer sampling particles and is of lower computational complexity compared with the PF-PHD.

Cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion

The GM-PHD framework as recursion realization of PHD filter is extensively applied to multitarget tracking system. A new idea of improving the estimation precision of time-varying multi-target in non-linear system is proposed due to the advantage of computation efficiency in this paper. First,a novel cubature Kalman probability hypothesis density filter is designed for single sensor measurement system under the Gaussian mixture framework. Second,the consistency fusion strategy for multi-sensor measurement is proposed through constructing consistency matrix. Furthermore,to take the advantage of consistency fusion strategy,fused measurement is introduced in the update step of cubature Kalman probability hypothesis density filter to replace the single-sensor measurement. Then a cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion is proposed. Capabilily of the proposed algorithm is illustrated through simulation scenario of multi-sensor multi-target tracking.

Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing

One of the important fields in statistics is testing hypothesis of correlation coefficient. The extension of the idea of testing correlation to fuzzy hypothesis is of great interesting. In this study, we examined the use of fuzzy hypothesis testing approach for the Sequential Probability Ratio Test (SPRT) of correlation coefficient. Use of fuzzy hypothesis testing for correlation coefficient with SPRT is illustrated by an example.

Free clustering optimal particle probability hypothesis density(PHD) filter

As to the fact that it is difficult to obtain analytical form of optimal sampling density and tracking performance of standard particle probability hypothesis density(P-PHD) filter would decline when clustering algorithm is used to extract target states,a free clustering optimal P-PHD(FCO-P-PHD) filter is proposed.This method can lead to obtainment of analytical form of optimal sampling density of P-PHD filter and realization of optimal P-PHD filter without use of clustering algorithms in extraction target states.Besides,as sate extraction method in FCO-P-PHD filter is coupled with the process of obtaining analytical form for optimal sampling density,through decoupling process,a new single-sensor free clustering state extraction method is proposed.By combining this method with standard P-PHD filter,FC-P-PHD filter can be obtained,which significantly improves the tracking performance of P-PHD filter.In the end,the effectiveness of proposed algorithms and their advantages over other algorithms are validated through several simulation experiments.

Riemann Hypothesis, Catholic Information and Potential of Events with New Techniques for Financial and Other Applications

In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions () which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function ζ(s) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.

null hypothesis的汉译问题及其译名选择

根据中国知网中的词典和期刊文献统计,null hypothesis有零假说(设)、原假说(设)、无效假说(设)、虚无假说(设)等18种汉译译名,译名多样且使用混乱。为了更加全面地了解该词的内涵并给出较为合适的译名,文章在对null hypothesis的证伪原则,"小概率事件原则"的运用,"无差异""无关联"内涵的研究,"null""hypothesis"词义和简称"H0"分析的基础之上,辨析了各种译名的合理性,发现将null hypothesis译为"零假说(设)"较为合适。

P值之争与管理学研究:先验概率的意义

P值之争的本质是人们把统计检验和统计推断混淆,直接用统计检验结果来进行统计推断.这导致许多似是而非的理论被接受.统计检验犯错的是假阳性概率.统计推断犯错的是假阳性之反概率.两种概率之间的数值关系受先验概率影响很大.先验概率越高,利用统计检验的结果进行推断所犯错误概率就越小.如果先验概率很小,即使假阳性概率很小,利用该结果进行推断所犯错误概率也很大.本文以管理学研究为例,提出解决该问题的办法是,通过与现实和与理论的双重对话来掌握先验概率,以提高基于统计检验的结果进行统计推断的可靠性.本文的科学哲学意义是,揭示了科学研究是先验与经验相统一的本质,以及科学研究的不充分决定性的特征.

随机样本数据的概率表征方法

本文通过算例分析了参数概率表征方法的适用性和有效性.对于非参数概率密度估计,介绍了几种拟合变量概率密度函数的方法,通过算例对比了不同方法的拟合效果.

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。

改进的邻近目标GM-PHD跟踪算法

针对目标跟踪系统在邻近目标场景下难以进行精确估计的问题,提出一种改进的邻近目标GM-PHD跟踪算法。该算法通过构建基于预测权值和速度参数的自适应门限,有效避免了杂波对算法更新步骤带来的巨大迭代负担。同时,我们充分考虑了目标邻近时量测的可能分布情况,针对目标与量测的“一对零”和“一对多”现象,提出了一种新的权重分配修正方法。结果表明,目标邻近时,改进后的算法在目标数和目标状态估计方面均优于传统算法,能够显著提高跟踪准确度。

采用统计线性回归的改进ATBI-GMPHD滤波

提出一种改进的自适应新生目标GM-PHD算法。该算法以存活目标的量测更新权值构建“似然函数”,通过该函数确定量测来源并对新生目标权值做重分配,有效解决了归一化失衡问题。在量测方程高度非线性情况下,引入统计线性回归方法对量测方程进行线性化近似,求解新生目标预测均值和协方差。仿真结果表明,在新生目标信息先验缺失时,改进后的算法具有良好的跟踪精度和较低的计算量。

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。

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。

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。

Multiple model PHD filter for tracking sharply maneuvering targets using recursive RANSAC based adaptive birth estimation

An algorithm to track multiple sharply maneuvering targets without prior knowledge about new target birth is proposed. These targets are capable of achieving sharp maneuvers within a short period of time, such as drones and agile missiles.The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems. However, the standard PHD filter operates on the single dynamic model and requires prior information about target birth distribution, which leads to many limitations in terms of practical applications. In this paper,we introduce a nonzero mean, white noise turn rate dynamic model and generalize jump Markov systems to multitarget case to accommodate sharply maneuvering dynamics. Moreover, to adaptively estimate newborn targets’information, a measurement-driven method based on the recursive random sampling consensus (RANSAC) algorithm is proposed. Simulation results demonstrate that the proposed method achieves significant improvement in tracking multiple sharply maneuvering targets with adaptive birth estimation.

基于航迹概率假设密度的多传感器多目标跟踪

针对基于概率假设密度(probability hypothesis density,PHD)的分布式多传感器多目标跟踪(distributed multi-sensor multi-target tracking,DMMT)存在无法形成航迹、计算复杂度高、目标漏检等问题。本文基于航迹PHD后验估计提出了一种DMMT方法。为此,首先构建了各节点估计航迹间相似性度量矩阵,并采用匈牙利算法实现最优航迹匹配;其次采用协方差逆准则对关联航迹实现并行融合;最后基于概率生成泛函推导了一种鲁棒的DMMT方法。仿真实验验证了所提算法在目标状态估计精度、计算有效性和实时性方面的优势。

基于分布式PMHT的多传感器多目标跟踪

在目标跟踪领域,概率多假设跟踪(probability multiple hypothesis tracking,PMHT)算法作为一种批处理算法,计算量远远小于传统的多假设跟踪算法。当前,PMHT算法的应用受限于集中式处理,本文首先在传统算法的基础上对传感器网络下的算法似然进行了推导,得到多传感器算法下的关联后参数,接着基于共识性处理策略进行了混合共识,最后使用卡尔曼滤波完成了对目标参数的后验估计,使得PMHT算法能够被应用于不包含融合中心的全分布式传感器网络多目标跟踪。实验结果表明,在不同的杂波密度下,分布式PMHT在跟踪误差上相对于单传感器算法有着90%以上的改善效果,与集中式算法相比跟踪性能接近且运算速度更快。

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。