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.

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.

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.

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。

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。

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。

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。

MULTITARGET STATE AND TRACK ESTIMATION FOR THE PROBABILITY HYPOTHESES DENSITY FILTER

The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the es- timates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) ap- proaches are used for the FMM parameter estimation.

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.

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%。

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.

一种基于模糊聚类的PHD航迹维持算法

针对杂波环境下数量变化的多目标航迹关联问题,提出一种基于模糊聚类的PHD航迹维持算法.该算法充分利用多帧信息,对当前时刻状态进行多步预测,并根据惯性进行加权,然后利用模糊聚类求得当前估计属于每条航迹的隶属度,从而得到最终的航迹.与传统的估计与航迹关联算法不同,该算法在更新每条航迹信息时,不仅仅是简单地对相邻帧之间的对数似然比进行求和,而是通过加权聚类等操作综合考虑了多帧信息.实验结果表明,所提算法能够更好地保持目标航迹,即使在目标出现交叉的地方也能达到很好的跟踪精度,具有较强的鲁棒性和优良的航迹维持性能.

改进的多模型粒子PHD和CPHD滤波算法

多模型粒子概率假设密度(Probability hypothesis density,PHD)滤波是一种有效的多机动目标跟踪算法,然而当模型概率过小时,该算法存在粒子退化问题,而且它对目标数的泊松分布假设会夸大目标漏检对其势估计的影响.针对上述问题,本文提出一种改进算法.该算法并不是简单地对模型索引进行采样,而是用粒子拟合目标状态的模型条件PHD强度,在不对噪声做任何先验假设的前提下,通过重采样实现存活粒子的输入交互,提高了滤波性能.在此基础上,进一步将算法在Cardinalized PHD(CPHD)的框架下加以实现,提高其目标数估计精度.仿真实验表明,所提算法在滤波性能和目标数估计精度方面均优于传统的多模型粒子PHD算法,具有良好的工程应用前景.

面向快速多目标跟踪的协同PHD滤波器

考虑到存活目标与新生目标在动态演化特性上的差异性,提出了面向快速多目标跟踪的协同概率假设密度(collaborative probability hypothesis density,CoPHD)滤波框架。该框架利用存活目标的状态信息,将量测动态划分为存活目标量测集与新生目标量测集,在两个量测集分别运用PHD组处理更新基础上建立了处理模块的交互与协同机制,力图在保证跟踪精度的同时提高计算效率。该框架由于采用PHD组处理方式而具有状态自动提取功能。进一步给出了该框架的序贯蒙特卡罗算法实现。仿真结果表明,该算法在计算效率以及状态提取精度上具有明显优势。

PHD粒子滤波中目标状态提取方法研究

采用概率假设密度(PHD)粒子滤波进行多目标跟踪时,各时刻的目标状态表现为大量的加权粒子,需以一定方法从该粒子近似中提取出来。该文提出一种增强的目标状态提取方法,先以k-means算法对粒子进行空间分布的聚类,再于各类中寻找粒子权的峰值位置作为目标状态的估计。仿真结果表明:由于综合利用了粒子的权值和空间分布信息,该算法具有比现有算法更小的目标状态估计误差。

基于PHD滤波和数据关联的多目标跟踪

针对杂波环境下的多目标跟踪,概率假设密度(probability hypothesis density,PHD)滤波不能提供目标航迹信息的问题,提出一种基于PHD滤波和数据关联的多目标跟踪方法。利用PHD滤波消除杂波并得到各个时刻的目标个数和目标状态估计。将PHD滤波的结果重新定义为量测数据,通过数据关联进一步消除虚警和漏警并给出目标航迹。仿真结果表明,该算法可以在有效地提高杂波环境下多目标跟踪精度的同时提供各目标航迹信息。

结合聚类的GM-PHD滤波器辐射源群目标跟踪

群目标跟踪是一种情况更为复杂的多目标跟踪问题,由于军事辐射源目标经常出现雷达关机的情况,因此常用的多目标跟踪方法对于这类辐射源群目标的跟踪效果并不理想。为此,结合聚类技术提出了一种改进的高斯混合概率假设密度(Gaussian mixture-probability hypothesis density,GM-PHD)滤波器跟踪方法。该方法在GM-PHD滤波器的更新过程中,通过引入群中心产生的虚拟量测信息以提高目标跟踪性能,但不进行量测集划分。获得单一个体目标的估计状态后利用Jensen-Shannon divergence计算其相似度,然后再对估计目标进行聚类以实现群目标的跟踪。最后通过对相邻时刻的群中心轨迹点进行关联匹配,从而获得群目标的完整运动轨迹。仿真实验结果表明,所提方法能够对辐射源群目标进行有效跟踪,并具有较好的目标跟踪性能。