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.     

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。     

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.     

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.     

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.     

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。     

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。     

高斯非平稳机动目标波达角模型及跟踪

在实际的跟踪情况中,由于环境条件、目标反射截面等因素的变化,回波信号的功率会随时间变化,即不满足通常阵列信号处理中对高斯信号作平稳性的假设。针对复杂运动条件下高斯非平稳目标的跟踪问题,提出了一种新的机动目标波达角(DOA)模型。该模型全面地刻画了高斯非平稳机动目标的动态,并将目标的DOA和信号功率作为状态变量进行了联合考虑,同时运用虚拟阵列的表示方法构建了相应的观测方程。对于建立的新模型,最后采用无迹卡尔曼滤波(UKF)的框架完成了整个跟踪算法。分析和仿真结果表明,当高斯非平稳机动目标之间存在长时间相互接近的情况时,新方法仍然可以获得较好的跟踪性能。     

增广误差模型算法在目标跟踪中的应用

针对目标机动运行过程中,滤波模型与机动状态模型失配的问题,提出了一种新的增广状态误差滤波模型。不同于现有增广方案,该模型从模型失配所致状态滤波误差的角度出发,将状态估计误差增广为一状态量,通过滤波估计后用其校正原状态量。算法分析表明,该增广滤波模型具有自适应调节多重渐消因子的等效特性,增强了对目标的跟踪能力。基于该增广状态误差滤波模型,给出了滤波算法设计并进行了仿真实验。实验结果表明,基于该模型的滤波算法在对机动目标进行跟踪时具有更强的鲁棒性。     

Modified input estimation technique using pseudoresiduals

An adaptive tracking filter for maneuvering targets is proposed using modified input estimation technique. Pseudoresiduals are defined using measurements and the velocity estimate at the hypothesized maneuver onset time. With the pseudoresiduals and a new target model representing transitions of nominal accelerations, a new input estimation method for tracking a maneuvering target is derived. Since the proposed detection technique is more sensitive to maneuvers than previous work, the shorter window length can be employed to detect and compensate target maneuvers. Also shown is that the tracking performance of the proposed filter is similar to that of interacting multiple model method (IMM) with 3 models, while computational loads of our method are drastically reduced     

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.     

机动多目标跟踪问题中关联区域的研究

 本文研究了跟踪多个机动目标时,由滤波算法所获得的新息向量范数的统计性质,关联区域的大小以及接收正确回波的概率。借助拉蒙特卡洛方法,考察了不同的目标状态模型、目标机动加速度及状态噪声方差等因素对所研究的问题的影响。研究表明,文献[1]所提出的机动目标状态模型及相应的自适应算法具有较好的适应目标机动的能力,关联区域的大小及接收正确回波的概率均较为稳定。     

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     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

一种基于三维到达角的无偏伪线性卡尔曼滤波

为了解决大场景下基于三维到达角的目标跟踪问题，提出了一种具有无偏性的伪线性卡尔曼滤波。首先，基于三维到达角信息对目标运动模型与量测模型进行建模；之后，对量测模型进行了伪线性化处理，得到了线性形式的目标量测模型。为了解决伪线性卡尔曼滤波存在的有偏性问题，提出了一种结合EKF（extend Kalman filter）的三维伪线性无偏卡尔曼滤波。仿真实验表明，该模型能够对非机动目标与机动目标有效跟踪，对于百公里级别的目标，当角测量误差从0.1°变化到0.5°，算法在仿真时间结束时均能将绝对位置误差降低至10 km以内，且算法的运行速度与EKF为同一个量级，同时兼顾了抗干扰能力、定位跟踪精度、运行效率的要求，能够为大场景下的目标跟踪提供有效方法。     

一类新型的机动目标跟踪算法

针对机动目标跟踪,提出了基于截断正态概率模型的改进自适应目标跟踪算法,该算法具有结构和计算简单,鲁棒性好的特点,通过仿真结果对比,充分说明了文中所提出的跟踪算法能够较好地弥补传统的Kalman滤波方法在跟踪机动目标时的不足。     

非线性非高斯模型的高斯和PHD滤波算法(英文)

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.     

一类新型机动目标跟踪算法

阐述了当跟踪非机动目标时,传统的Kalman滤波可以得到很好的跟踪精度。但是当日标机动时,传统的Kalman滤波不能对目标的突然变化做出及时的改正和预测,因此跟踪精度很差,甚至出现丢失目标的情况。文中采用的基于截断正态概率模型的改进自适应目标跟踪算法, 其结构和计算简单,鲁棒性好,较好地解决了使用Kalman滤波带来的不足。     

Extended solution to multiple maneuvering target tracking

An improved algorithm for tracking multiple maneuvering targets is presented. This approach is implemented with an approximate adaptive filter consisting of the one-step conditional maximum-likelihood technique together with the extended Kalman filter and an adaptive maneuvering compensator. In order to avoid the extra computational burden of considering events with negligible probability, a validation matrix is defined in the tracking structure. With this approach, data-association and target maneuvering problems can be solved simultaneously. Detailed Monte Carlo simulations of the algorithm for many tracking situations are described. Computer simulation results indicate that this approach successfully tracks multiple maneuvering targets over a wide range of conditions