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.

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.

Labeled box-particle CPHD filter for multiple extended targets tracking

In multiple extended targets tracking, replacing traditional multiple measurements with a rectangular region of the nonzero volume in the state space inspired by the box-particle idea is exactly suitable to deal with extended targets, without distinguishing the measurements originating from the true targets or clutter.Based on our recent work on extended box-particle probability hypothesis density(ET-BP-PHD) filter, we propose the extended labeled box-particle cardinalized probability hypothesis density(ET-LBP-CPHD) filter, which relaxes the Poisson assumptions of the extended target probability hypothesis density(PHD) filter in target numbers, and propagates not only the intensity function but also cardinality distribution. Moreover, it provides the identity of individual target by adding labels to box-particles. The proposed filter can improve the precision of estimating target number meanwhile achieve targets' tracks. The effectiveness and reliability of the proposed algorithm are verified by the simulation results.

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.

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.

Fast density peak-based clustering algorithm for multiple extended target tracking

The key challenge of the extended target probability hypothesis density (ET-PHD) filter is to reduce the computational complexity by using a subset to approximate the full set of partitions. In this paper, the influence for the tracking results of different partitions is analyzed, and the form of the most informative partition is obtained. Then, a fast density peak-based clustering (FDPC) partitioning algorithm is applied to the measurement set partitioning. Since only one partition of the measurement set is used, the ET-PHD filter based on FDPC partitioning has lower computational complexity than the other ET-PHD filters. As FDPC partitioning is able to remove the spatially close clutter-generated measurements, the ET-PHD filter based on FDPC partitioning has good tracking performance in the scenario with more clutter-generated measurements. The simulation results show that the proposed algorithm can get the most informative partition and obviously reduce computational burden without losing tracking performance. As the number of clutter-generated measurements increased, the ET-PHD filter based on FDPC partitioning has better tracking performance than other ET-PHD filters. The FDPC algorithm will play an important role in the engineering realization of the multiple extended target tracking filter.

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.

Probability hypothesis density filter with adaptive parameter estimation for tracking multiple maneuvering targets

The probability hypothesis density(PHD) filter has been recognized as a promising technique for tracking an unknown number of targets. The performance of the PHD filter, however, is sensitive to the available knowledge on model parameters such as the measurement noise variance and those associated with the changes in the maneuvering target trajectories. If these parameters are unknown in advance, the tracking performance may degrade greatly. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation(APE) method in the PHD filter so that the model parameters, which may be static and/or time-varying, can be estimated jointly with target states. The resulting APE-PHD algorithm is implemented using the particle filter(PF), which leads to the PF-APE-PHD filter. Simulations show that the newly proposed algorithm can correctly identify the unknown measurement noise variances, and it is capable of tracking multiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches.

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ET-PHD滤波器和变分贝叶斯近似的扩展目标跟踪算法

针对未知测量噪声协方差情况下的多扩展目标跟踪问题,利用扩展目标概率假设密度(ET-PHD)滤波器和变分贝叶斯(VB)近似理论,提出了一种标准ET-PHD滤波器的扩展方法及其解析的实现方法。首先,根据标准ETPHD滤波器的目标状态方程和测量方程,定义了目标状态和测量噪声协方差的增广状态变量及二者的联合转移函数;然后,根据标准ET-PHD滤波器,构建了扩展的ET-PHD滤波器的预测和更新公式;最后,在线性高斯假设的条件下,利用高斯和逆伽马(IG)混合分布表示目标的联合后验强度函数,从而给出了扩展ET-PHD滤波器的解析实现。仿真结果表明:所提算法能提供可靠的跟踪结果,可有效地处理未知测量噪声协方差环境中的多扩展目标跟踪问题。

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ET-PHD的自适应联合跟踪与分类算法

针对新生目标强度先验未知的扩展目标(Extended target, ET)联合跟踪与分类(Joint tracking and classification,JTC)问题,提出一种基于扩展目标概率假设密度(Extended target-probability hypothesis density, ET-PHD)滤波器的自适应联合跟踪与分类算法,并给出其高斯混合实现方法.算法利用量测信息生成新生目标强度,在滤波预测阶段对存活目标和新生目标分别按照其类别进行传播,再引入属性量测信息,用位置和属性的联合量测似然函数代替单目标位置似然函数,对预测后所有目标强度进行联合更新,之后按照类别进行高斯项的删减与合并,提取相应类别目标的状态集.仿真结果表明,提出的自适应算法改进了概率假设密度滤波器在扩展目标跟踪中的性能.

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。

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。

SMC-PHD based multi-target track-before-detect with nonstandard point observations model

Detection and tracking of multi-target with unknown and varying number is a challenging issue, especially under the condition of low signal-to-noise ratio(SNR). A modified multi-target track-before-detect(TBD) method was proposed to tackle this issue using a nonstandard point observation model. The method was developed from sequential Monte Carlo(SMC)-based probability hypothesis density(PHD) filter, and it was implemented by modifying the original calculation in update weights of the particles and by adopting an adaptive particle sampling strategy. To efficiently execute the SMC-PHD based TBD method, a fast implementation approach was also presented by partitioning the particles into multiple subsets according to their position coordinates in 2D resolution cells of the sensor. Simulation results show the effectiveness of the proposed method for time-varying multi-target tracking using raw observation data.

A novel SMC-PHD filter based on particle compensation

As a typical implementation of the probability hypothesis density(PHD) filter, sequential Monte Carlo PHD(SMC-PHD) is widely employed in highly nonlinear systems. However, the particle impoverishment problem introduced by the resampling step, together with the high computational burden problem, may lead to performance degradation and restrain the use of SMC-PHD filter in practical applications. In this work, a novel SMC-PHD filter based on particle compensation is proposed to solve above problems. Firstly, according to a comprehensive analysis on the particle impoverishment problem, a new particle generating mechanism is developed to compensate the particles. Then, all the particles are integrated into the SMC-PHD filter framework. Simulation results demonstrate that, in comparison with the SMC-PHD filter, proposed PC-SMC-PHD filter is capable of overcoming the particle impoverishment problem, as well as improving the processing rate for a certain tracking accuracy in different scenarios.

基于改进概率假设密度滤波器的非合作双基地雷达目标跟踪

为解决非合作双基地雷达目标跟踪面临的低检测概率和高杂波率问题,提出了改进的概率假设密度滤波器。首先,提出一种新的航迹标识与状态估计方法,并将存活概率定义为与目标状态相关的变量;随后,记录每个候选目标在每一时刻是否有量测的情况,采用序贯概率比检验区分真实目标和由杂波引起的假目标;最后,离线估计目标状态。仿真实验结果表明,所提算法明显提高了非合作双基地雷达目标跟踪的性能,可以有效解决低检测概率和高杂波率问题。

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。

基于概率假设密度滤波方法的多目标跟踪技术综述

概率假设密度(Probability hypothesis density,PHD)滤波方法在多目标跟踪、交通管制、图像处理以及多传感器管理等领域得到了广泛关注.本文对基于PHD滤波方法的多目标跟踪技术的产生、发展及研究现状进行了综述,主要包括PHD滤波器、PHD执行方法、峰值提取及航迹提取技术、多传感器多目标跟踪及多传感器管理、PHD平滑器以及多目标跟踪性能评价指标等,并对PHD滤波器的相关应用进行介绍.最后,基于现有PHD滤波进展,提出了PHD滤波技术在多目标跟踪领域需要重点关注的若干问题.