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.     

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。     

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.     

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。     

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.     

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.     

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.     

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。     

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。     

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.     

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.     

Data Association and Track Management for the Gaussian Mixture Probability Hypothesis Density Filter

The Gaussian mixture probability hypothesis density (GM-PHD) recursion is a closed-form solution to the probability hypothesis density (PHD) recursion, which was proposed for jointly estimating the time-varying number of targets and their states from a sequence of noisy measurement sets in the presence of data association uncertainty, clutter, and miss-detection. However the GM-PHD filter does not provide identities of individual target state estimates, that are needed to construct tracks of individual targets. In this paper, we propose a new multi-target tracker based on the GM-PHD filter, which gives the association amongst state estimates of targets over time and provides track labels. Various issues regarding initiating, propagating and terminating tracks are discussed. Furthermore, we also propose a technique for resolving identities of targets in close proximity, which the PHD filter is unable to do on its own.     

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     

Multi-target state estimation and track continuity for the particle PHD filter

Particle filter approaches for approximating the first-order moment of a joint, or probability hypothesis density (PHD), have demonstrated a feasible suboptimal method for tracking a time-varying number of targets in real-time. We consider two techniques for estimating the target states at each iteration, namely k-means clustering and mixture modelling via the expectation-maximization (EM) algorithm. We present novel techniques for associating the targets between frames to enable track continuity.     

未知测量噪声分布下的多目标跟踪算法

 粒子概率假设密度滤波(SMC-PHDF)在进行粒子更新时需要知道测量噪声的概率分布以计算似然函数,这使得SMC-PHDF依赖于测量噪声的概率模型。针对这一点不足,提出一种未知测量噪声分布下的多目标跟踪算法——基于风险评估的概率假设密度滤波(RE-PHDF)。该算法在SMC-PHDF进行概率假设密度(PHD)粒子更新时采用风险函数计算每个PHD粒子的风险值,并通过一个风险评估函数评估每个PHD粒子,然后用评估后的结果更新粒子的权值。由于粒子更新时避免了在多维测量空间中计算似然函数,算法不仅不依赖于测量噪声的概率分布,还可以节省大量计算时间。仿真结果表明：和SMC-PHDF相比,RE-PHDF在未知的复杂测量噪声环境下具有更高的鲁棒性和稳定性;同时,在两种算法跟踪精度接近的情况下,所提算法节省了50%的运行时间。     

Cardinality compensation method based on information-weighted consensus filter using data clustering for multi-target tracking

In this paper, a cardinality compensation method based on Information-weighted Consensus Filter(ICF) using data clustering is proposed in order to accurately estimate the cardinality of the Cardinalized Probability Hypothesis Density(CPHD) filter. Although the joint propagation of the intensity and the cardinality distribution in the CPHD filter process allows for more reliable estimation of the cardinality(target number) than the PHD filter, tracking loss may occur when noise and clutter are high in the measurements in a practical situation. For that reason, the cardinality compensation process is included in the CPHD filter, which is based on information fusion step using estimated cardinality obtained from the CPHD filter and measured cardinality obtained through data clustering. Here, the ICF is used for information fusion. To verify the performance of the proposed method, simulations were carried out and it was confirmed that the tracking performance of the multi-target was improved because the cardinality was estimated more accurately as compared to the existing techniques.     

航空发动机气路故障诊断的SANNWA-PF算法

针对航空发动机非线性、非高斯的特点，提出一种用于航空发动机气路故障诊断的自适应神经网络权值调整粒子滤波（SANNWA PF）算法。该算法根据粒子分布情况确定分裂和调整的粒子数目，进而根据粒子权重采用正态分布的方式进行分裂，采用反向传插(BP)神经网络进行权值调整，缓解了粒子的退化和贫化，具有更强的自适应性能和跟踪能力。通过一维非线性跟踪模型和航空发动机气路故障诊断仿真研究表明:SANNWA PF算法具有良好的非高斯性能，相对粒子滤波一维非线性追踪模型估计精度提高约21%，航空发动机气路故障诊断在高斯噪声和非高斯噪声下分别提高约30%和26%，诊断速度分别提高约7倍和10倍。      

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.     

基于混合粒子滤波的激光惯导系统误差的补偿

针对激光陀螺捷联惯导系统在动态尤其是高动态环境下的姿态误差显著增大的问题,提出了一种基于改进高斯混合粒子滤波的纯方位跟踪算法。算法基于混合粒子的卡尔曼滤波和粒子滤波的特点,用有限的高斯模型来近似后验状态密度、系统噪声和观测噪声的分布通过EM的算法设计实现模型的降阶,一定程度上克服了EM算法迭代的结果需要依赖初始值、可能收敛到局部最大点或可能收敛到参数空间边界的缺点,从而改善了粒子携带信息的衰减问题。通过仿真与试验结合,在纯动态应用环境下的姿态与定位精度补偿效果,与传统Kalman滤波相比,算法在保持高精度估计能力的同时,具有较强的鲁棒性,是解决非线性系统状态估计问题的一种有效方法。     

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。