Novel data association schemes for the probability hypothesis density filter

The probability hypothesis density (PHD) filter is a practical alternative to the optimal Bayesian multi-target Alter based on finite set statistics. It propagates the PHD function, a first-order moment of the full multi-target posterior density. The peaks of the PHD function give estimates of target states. However, the PHD filter keeps no record of target identities and hence does not produce track-valued estimates of individual targets. We propose two different schemes according to which PHD filter can provide track-valued estimates of individual targets. Both schemes use the probabilistic data-association functionality albeit in different ways. In the first scheme, the outputs of the PHD filter are partitioned into tracks by performing track-to-estimate association. The second scheme uses the PHD filter as a clutter filter to eliminate some of the clutter from the measurement set before it is subjected to existing data association techniques. In both schemes, the PHD filter effectively reduces the size of the data that would be subject to data association. We consider the use of multiple hypothesis tracking (MHT) for the purpose of data association. The performance of the proposed schemes are discussed and compared with that of MHT.     

An improved multiple model GM-PHD filter for maneuvering target tracking

In this paper, an improved implementation of multiple model Gaussian mixture probability hypothesis density (MM-GM-PHD) filter is proposed. For maneuvering target tracking, based on joint distribution, the existing MM-GM-PHD filter is relatively complex. To simplify the filter, model conditioned distribution and model probability are used in the improved MM-GM-PHD filter. In the algorithm, every Gaussian components describing existing, birth and spawned targets are estimated by multiple model method. The final results of the Gaussian components are the fusion of multiple model estimations. The algorithm does not need to compute the joint PHD distribution and has a simpler computation procedure. Compared with single model GM-PHD, the algorithm gives more accurate estimation on the number and state of the targets. Compared with the existing MM-GM-PHD algorithm, it saves computation time by more than 30%. Moreover, it also outperforms the interacting multiple model joint probabilistic data association (IMMJPDA) filter in a relatively dense clutter environment.     

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.     

Multiple-Model Probability Hypothesis Density Filter for Tracking Maneuvering Targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.     

PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.     

交互多模型PHD滤波跟踪多目标方法

在机动多目标跟踪问题中,目标数未知或随时间而变化,概率假设密度（PHD）滤波可以在每一时间步估计多目标状态和目标数,但单模型方法不能给出精确的估计。提出了一种交互多模型PHD滤波方法,建立多模型描述多目标运动方式,利用PHD滤波结合多模型跟踪目标运动轨迹。同时,给出了多传感器交互多模型PHD滤波方法,以提高目标跟踪精度。     

Track labeling and PHD filter for multitarget tracking

Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approaches (as, e.g., MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter has been proposed and particle filtering techniques have been developed to implement the PHD filter. In the particle PHD filter, the track labeling problem is not considered, i.e., the PHD is obtained only for a frame at a time, and it is very difficult to perform the multipeak extraction, particularly in high clutter environments. A track labeling method combined with the PHD approach, as well as considering the finite resolution, is proposed here for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD in the resolution cell to get the estimated number and locations of the targets at each time step, and then perform the track labeling ("peak-to-track" association), whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard particle PHD filter. For example, in group target tracking, if we are interested in the motion of a specific target, we can track this target, which is not possible for the standard particle PHD filter, since the standard particle PHD filter does not keep track labels. Using our approach, multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging, and termination     

基于高斯混合概率假设密度滤波的扫描型光学传感器像平面多目标跟踪算法

高斯混合概率假设密度(GM-PHD)滤波是一种基于随机有限集理论的次优贝叶斯多目标跟踪方法,本文研究了该算法在扫描型光学传感器像平面的多目标跟踪问题.针对典型的锥扫模式和推扫模式,根据其扫描特性建立目标的运动模型和测量模型.介绍高斯混合概率假设密度滤波的基本原理.针对原算法在强杂波环境中的低效率问题,借鉴传统多目标跟踪...     

密集杂波背景下的水下多目标跟踪方法

水下多目标跟踪是水声信号处理领域研究的热点和难点问题。高斯混合概率假设密度(Gaussian mixture probability hypothesis density, GM-PHD)滤波器以其高效的计算效率为解决水下多目标跟踪问题提供了保证。然而,GM-PHD滤波器在跟踪目标时需要先验已知新生目标的强度,否则其性能会出现严重退化。针对该问题,提出一种滑动窗两步初始化高斯混合概率假设密度(sliding window two step initialization GM-PHD, SWTSI-GMPHD)滤波器。将提出的滑动窗两步初始化方法嵌入GM-PHD滤波器,利用滑动窗两步初始化方法估计新生目标强度,减少杂波干扰导致跟踪结果中出现的虚假目标。仿真实验表明,在杂波密集环境下,相较于其他跟踪方法,提出方法将跟踪精度提高69.84%,52.62%和41.05%。     

多目标跟踪的核粒子概率假设密度滤波算法

提出一种新的多目标跟踪算法：核粒子概率假设密度滤波算法(KP-PHDF)。算法的创新点在概率假设密度滤波算法(PHDF)的目标状态提取步骤,以粒子概率假设密度滤波算法为框架,并运用结合了mean-shift算法的核密度估计(KDE)理论进行概率假设密度(PHD)分布的二次估计、提取PHD峰值位置作为目标状态估计值。分析与多目标跟踪(MTT)仿真的结果表明,与现有序列蒙特卡罗概率假设密度滤波算法（SMC-PHDF）相比,在相同仿真条件下新算法的估计精度提高30.5%。     

A measurement-driven adaptive probability hypothesis density filter for multitarget tracking

This paper studies the dynamic estimation problem for multitarget tracking. A novel gating strategy that is based on the measurement likelihood of the target state space is proposed to improve the overall effectiveness of the probability hypothesis density(PHD) filter. Firstly, a measurement-driven mechanism based on this gating technique is designed to classify the measurements. In this mechanism, only the measurements for the existing targets are considered in the update step of the existing targets while the measurements of newborn targets are used for exploring newborn targets. Secondly, the gating strategy enables the development of a heuristic state estimation algorithm when sequential Monte Carlo(SMC) implementation of the PHD filter is investigated, where the measurements are used to drive the particle clustering within the space gate.The resulting PHD filter can achieve a more robust and accurate estimation of the existing targets by reducing the interference from clutter. Moreover, the target birth intensity can be adaptive to detect newborn targets, which is in accordance with the birth measurements. Simulation results demonstrate the computational efficiency and tracking performance of the proposed algorithm.     

Multitarget Bayes filtering via first-order multitarget moments

The theoretically optimal approach to multisensor-multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. Even in single-target problems, this optimal filter is so computationally challenging that it must usually be approximated. Consequently, multitarget Bayes filtering will never be of practical interest without the development of drastic but principled approximation strategies. In single-target problems, the computationally fastest approximate filtering approach is the constant-gain Kalman filter. This filter propagates a first-order statistical moment - the posterior expectation - in the place of the posterior distribution. The purpose of this paper is to propose an analogous strategy for multitarget systems: propagation of a first-order statistical moment of the multitarget posterior. This moment, the probability hypothesis density (PHD), is the function whose integral in any region of state space is the expected number of targets in that region. We derive recursive Bayes filter equations for the PHD that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets. We also show that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense.     

多目标跟踪的概率假设密度粒子滤波

在多目标跟踪中,当目标数很大时,目标状态的联合分布的计算量会非常大。如果目标独立运动,可用各目标分别滤波来代替,但这要求考虑数据互联问题。文章介绍一种可以解决计算量问题的方法,只需计算联合分布的一阶矩——概率假设密度(PHD),PHD在任意区域S上的积分是S内目标数的期望值。因未记录目标身份,避免了数据互联问题。仿真中,传感器为被动雷达,目标观测值为距离、角度及速度时,对上述的PHD滤波进行了粒子实现,并对观测值是否相关的不同情况进行比较。PHD粒子滤波应用在非线性模型的多目标跟踪,实验结果表明,滤波可以稳健跟踪目标数为变数的情况,得到了接近真实情况的结果。     

新生目标强度未知的双门限粒子PHD滤波器

传统粒子概率假设密度(PHD)滤波器假定新生目标强度已知,当新生目标在整个观测区域随机出现时不再适用。为解决新生目标强度未知时的多目标跟踪问题,提出了一种基于量测信息的双门限粒子PHD(PHD-DT)滤波器。首先基于似然函数设定门限对存活目标量测进行粗提取,利用上一时刻的目标估计值构建圆形波门进行精细提取,并对门限设定方法进行分析,然后根据提取结果对目标PHD进行分解,得到存活目标和新生目标的PHD预测及更新表达式,最后给出了滤波器的实现方法并同基于量测驱动的PHD(PHD-M)滤波器和Logic+联合概率数据互联(JPDA)方法进行了仿真对比。仿真结果表明,在新生目标强度未知时,PHD-DT可有效避免Logic+JPDA在杂波背景下因航迹起始错误带来的估计误差,并较好地解决了PHD-M的目标数目过估问题,多目标估计性能更优,且杂波越强性能优势越明显。     

Rao-Blackwellized粒子概率假设密度滤波算法

针对多目标跟踪（MTT）,提出一种新的基于随机集的滤波算法,称为Rao-Blackwellized粒子概率假设密度滤波算法（RBP-PHDF）。算法运用Rao-Blackwellized思想,通过挖掘分析“混合线性/非线性模型”的结构,采用序列蒙特卡罗（SMC）方法预测与估计概率假设密度（PHD）迭代式中各个目标的非线性状态,并利用非线性状态粒子中包含的信息,使用卡尔曼滤波器（KF）对线性状态进行预测与估计。以更好地估计PHD进而提高各目标状态估计精度。分析与MTT仿真的结果表明,在相同的仿真条件下,与现有序列蒙特卡罗概率假设密度滤波算法（SMC-PHDF）相比,RBP-PHDF在降低粒子维数、减少计算量的同时,有效提升了估计精度。     

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 tech-nique 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 mul-tiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches.     

Particle flters for probability hypothesis density flter with the presence of unknown measurement noise covariance

In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.     

Multi-EAP:Extended EAP for multi-estimate extraction for SMC-PHD filter

The ability to extract state-estimates for each target of a multi-target posterior, referred to as multi-estimate extraction (MEE), is an essential requirement for a multi-target filter, whose key performance assessments are based on accuracy, computational efficiency and reliability. The probability hypothesis density (PHD) filter, implemented by the sequential Monte Carlo approach, affords a computationally efficient solution to general multi-target filtering for a time-varying num-ber of targets, but leaves no clue for optimal MEE. In this paper, new data association techniques are proposed to distinguish real measurements of targets from clutter, as well as to associate par-ticles with measurements. The MEE problem is then formulated as a family of parallel single-estimate extraction problems, facilitating the use of the classic expected a posteriori (EAP) estima-tor, namely the multi-EAP (MEAP) estimator. The resulting MEAP estimator is free of iterative clustering computation, computes quickly and yields accurate and reliable estimates. Typical sim-ulation scenarios are employed to demonstrate the superiority of the MEAP estimator over existing methods in terms of faster processing speed and better estimation accuracy.     

改进的MMPHD机动目标跟踪方法

基于序列蒙特卡罗方法的经典多模概率假设密度滤波方法及其各种衍生方法,在预测过程中依据多个并行的状态转移模型,通过将大量粒子散布到下一时刻目标所有可能出现的状态空间实现目标状态的捕获,造成计算量大、目标跟踪精度差。为此,提出一种改进的多模粒子概率假设密度机动目标跟踪方法。该方法利用最新量测信息估计目标运动模型概率及模型参数,并将估计得到的目标模型应用到粒子概率假设密度滤波方法的预测过程中生成预测粒子,从而将大部分粒子聚合在目标最可能出现的状态空间邻域中,实现粒子的有效利用。数值仿真表明,所提方法不仅显著地减少了目标丢失个数,而且提高了目标跟踪精度。     

基于标签多伯努利滤波的衍生目标跟踪算法

针对现有随机有限集(RFS)滤波器在低信噪比环境下对衍生目标跟踪性能严重下降的问题,提出了一种基于Delta扩展标签多伯努利(δ-GLMB)滤波器的改进算法。基于随机集理论和伯努利衍生模型,推导了新的预测方程,并采用了假设裁剪及分组手段和多伯努利近似技术以降低算法的计算量。针对假设增多引起的虚警问题,将多帧平滑思想和算法相结合,利用标签信息对新目标进行回溯处理。仿真结果表明,所提算法能对目标数目进行无偏估计,在低探测概率和强杂波环境下性能明显优于概率假设密度(PHD)算法,计算开销在衍生初始阶段增长快于PHD,目标较分散时低于PHD。