A class of near optimal JPDA algorithms

The crucial problem in multiple target tracking is the hit-to-track data association. A hit is a received signal from a target or background clutter which provides positional information If an incorrect hit is associated with a track, that track could diverge and prematurely terminate or cause other tracks to also diverge. Most methods for hit-to-track data association fall into two categories: multiple hypothesis tracking (MHT) and joint probabilistic data association (JPDA). Versions of MHT use all or some reasonable hits to update a track and delay the decision on which hit was correct. JPDA uses a weighted sum of the reasonable hits to update a track. These weights are the probability that the hit originated from the target in track. The computational load for the joint probabilities increases exponentially as the number of targets increases and therefore, is not an attractive algorithm when expecting to track many targets. Reviewed here is the JPDA filter and two simple approximations of the joint probabilities which increase linearly in computational load as the number of targets increase. Then a new class of near optimal JPDA algorithms is introduced which run in polynomial time. The power of the polynomial is an input to the algorithm. This algorithm bridges the gap in computational load and accuracy between the very fast simple approximations and the efficient optimal algorithms     

An interior point linear programming approach to two-scan dataassociation

We present an efficient two-scan data association method (TSDA) based on an interior point linear programming (LP) approach. In this approach, the TSDA problem is first formulated as a 3-dimensional assignment problem, and then relaxed to a linear program; the latter is subsequently solved by the highly efficient homogeneous, self-dual interior point LP algorithm. When the LP algorithm generates a fractional optimal solution, we use a technique similar to the joint probabilistic data association method (JPDA) to compute a weighted average of the resulting fractional assignments, and use it to update the states of the existing tracks generated by Kalman filters. Unlike the traditional single scan JPDA method, our TSDA method provides an explicit mechanism for track initiation. Extensive computer simulations have demonstrated that the new TSDA method is not only far more efficient in terms of low computational complexity, but also considerably more accurate than the existing single-scan JPDA method     

Multiple scan joint probabilistic data association

This paper presents a multiple scan or n-scan-back joint probabilistic data association (JPDA) algorithm which addresses the problem of measurement-to-track data association in a multiple target and clutter environment. The standard single scan JPDA algorithm updates a track with weighted sum of the measurements which could have reasonably originated from the target in track. The only information the standard JPDA algorithm uses is the measurements on the present scan and the state vectors and covariance matrices of the present targets. The n-scan-back algorithm presented here uses multiple scans of measurements along with the present target information to produce better weights for data association. The standard JPDA algorithm can utilize a formidable amount of processing power and the n-scan-back version only worsens the problem. Therefore, along with the algorithm presentation, implementations which make this algorithm practical are discussed and referenced. An example is also shown for a few n-scan-back window lengths     

Tracking of multiple maneuvering targets using multiscan JPDA and IMM filtering

The paper considers the problem of tracking multiple maneuvering targets in the presence of clutter using switching multiple target motion models. A novel suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach and the joint probabilistic data association (JPDA) technique. Unlike the standard single-scan JPDA approach, the authors exploit a multiscan joint probabilistic data association (mscan-JPDA) approach to solve the data association problem. The algorithm is illustrated via a simulation example involving tracking of four maneuvering targets and a multiscan data window of length two     

Dynamically adaptable m-best 2-D assignment algorithm andmultilevel parallelization

In recent years, there has been considerable interest within the tracking community in an approach to data association based on the m-best two-dimensional (2D) assignment algorithm. Much of the interest has been spurred by its ability to provide various efficient data association solutions, including joint probabilistic data association (JPDA) and multiple hypothesis tracking (MHT). The focus of this work is to describe several recent improvements to the m-best 2D assignment algorithm. One improvement is to utilize a nonintrusive 2D assignment algorithm switching mechanism, based on a problem sparsity threshold. Dynamic switching between two different 2D assignment algorithms, highly suited for sparse and dense problems, respectively, enables more efficient solutions to the numerous 2D assignment problems generated in the m-best 2D assignment framework. Another improvement is to utilize a multilevel parallelization enabling many independent and highly parallelizable tasks to be executed concurrently, including 1) solving the multiple 2D assignment problems via a parallelization of the m-best partitioning task, and 2) calculating the numerous gating tests, state estimates, covariance calculations, and likelihood function evaluations (used as cost coefficients in the 2D assignment problem) via a parallelization of the data association interface task. Using both simulated data and an air traffic surveillance (ATS) problem based on data from two Federal Aviation Administration (FAA) air traffic control radars, we demonstrate that efficient solutions to the data association problem are obtainable using our improvements in the m-best 2D assignment algorithm     

Neural solution to the multitarget tracking data associationproblem

The problem of tracking multiple targets in the presence of clutter is addressed. The joint probabilistic data association (JPDA) algorithm has been previously reported to be suitable for this problem in that it makes few assumptions and can handle many targets as long as the clutter density is not very high. However, the complexity of this algorithm increases rapidly with the number of targets and returns. An approximation of the JPDA that uses an analog computational network to solve the data association problem is suggested. The problem is viewed as that of optimizing a suitably chosen energy function. Simple neural-network structures for the approximate minimization of such functions have been proposed by other researchers. The analog network used offers a significant degree of parallelism and thus can compute the association probabilities more rapidly. Computer simulations indicate the ability of the algorithm to track many targets simultaneously in the presence of moderately dense clutter     

多局部节点异步抗差航迹关联算法

为解决航迹异步与系统误差并存情况下的多局部节点航迹关联问题,提出一种基于区间序列离散度的多局部节点异步抗差航迹关联算法。定义区间型数据集的离散信息度量,给出系统误差下航迹序列区间化方法,通过累次积分计算离散度,结合多维分配进行关联判定。针对多局部节点上报目标不完全一致现象,设置零号航迹管理关联质量。与传统算法相比,无需时域配准,可在系统误差下对异步航迹直接关联。仿真结果表明,算法能在局部节点上报目标不完全一致场景下实现有效关联,且正确关联率随局部节点数目的增加或目标密集程度的增大而提高。     

空间多分辨率模糊目标跟踪

提出了一种新的模糊目标跟踪算法--CPDA算法。这个算法在空间多分辨率框架下应用概率数据互联算法,在粗分辨率上实现模糊目标跟踪。在不同虚警密度的模糊目标环境下,利用仿真实验分析了CPDA算法的跟踪性能,同时将其与单分辨率上的联合概率数据互联方法进行了性能比较。仿真结果表明,CPDA算法的跟踪性能在达到与单分辨率上JPDA算法同样性能的条件下,能够以较小的计算量跟踪模糊目标。     

修正的概率数据互联算法

阐明了概率数据互联(PDA)算法能很好地解决密集环境下的目标跟踪问题,在该算法基础上,人们又提出了联合概率数据互联(JPDA)算法和一些基于 PDA 的修正算法。在概率数据互联算法中,有一个很重要的参数就是杂波数密度(或波门内虚假量测期望数)。然而在许多实际情况中,这个参数是很难获取的。针对这一问题,文中提出了一种修正的概率数据互联算法,该算法通过实时地调整这一参数来获得对目标较为准确的估计结果。最后,给出了算法的仿真分析。     

Multisensor covariance control strategies for reducing bias effects in interacting target scenarios

Algorithms are presented for managing sensor information to reduce the effects of bias when tracking interacting targets. When targets are close enough together that their measurement validation gates overlap, the measurement from one target can be confused with another. Data association algorithms such as the joint probabilistic data association (JPDA) algorithm can effectively continue to track targets under these conditions, but the target estimates may become biased. A modification of the covariance control approach for sensor management can reduce this effect. Sensors are chosen based on their ability to reduce the extent of measurement gate overlap as judged by a set of heuristic parameters derived in this work. Monte Carlo simulation results show that these are effective methods of reducing target estimate bias in the JPDA algorithm when targets are close together. An analysis of the computational demands of these algorithms shows that while they are computationally demanding, they are not prohibitively so.     

密集杂波环境下的数据关联快速算法

基于联合概率数据互联（JPDA）的思想,提出了一种新的数据关联快速算法（Fast Al-gorithm for Data Association,简称FAFDA算法）.该方法不需象在最优JPDA算法中那样生成所有可能的联合互联假设,因而具有计算量小,易于工程实现的特点。仿真结果表明,与最优JPDA算法相比,FAFDA算法的跟踪性能令人满意,并且在密集杂波环境下可实时、有效地跟踪100批次以上的目标。     

New assignment-based data association for tracking move-stop-move targets

We present a new assignment-based algorithm for data association in tracking ground targets employing evasive move-stop-move maneuvers using ground moving target indicator (GMTI) reports obtained from an airborne sensor. To avoid detection by the GMTI sensor, the targets deliberately stop for some time before moving again. The sensor does not detect a target when the latter's radial velocity (along the line-of-sight from the sensor) falls below a certain minimum detectable velocity (MDV). Even in the absence of move-stop-move maneuvers, the detection has a less-than-unity probability (P/sub D/<1) due to obscuration and thresholding. Then, it is of interest, when a target is not detected, to develop a systematic technique that can distinguish between lack of detection due to P/sub D/<1 and lack of detection due to a stop (or a near stop). Previously, this problem was solved using a variable structure interacting multiple model (VS-IMM) estimator with a stopped target model (VS-IMM-ST) without explicitly addressing data association. We develop a novel "two-dummy" assignment approach for move-stop-move targets that considers both the problem of data association as well as filtering. Typically, in assignment-based data association a "dummy" measurement is used to denote the nondetection event. The use of the standard single-dummy assignment, which does not handle move-stop-move motion explicitly, can result in broken tracks. The new algorithm proposed here handles the evasive move-stop-move motion by introducing a second dummy measurement to represent nondetection due to the MDV. We also present a likelihood-ratio-based track deletion scheme for move-stop-move targets. Using this two-dummy data association algorithm, the track corresponding to a move-stop-move target is kept "alive' during missed detections both due to MDV and due to P/sub D/<1. In addition, one can obtain reductions in both rms estimation errors as well as the total number of track breakages.     

Efficient multisensor fusion using multidimensional dataassociation

We present the development of a multisensor fusion algorithm using multidimensional data association for multitarget tracking. The work is motivated by a large scale surveillance problem, where observations from multiple asynchronous sensors with time-varying sampling intervals (electronically scanned array (ESA) radars) are used for centralized fusion. The combination of multisensor fusion with multidimensional assignment is done so as to maximize the “time-depth” in addition to “sensor-width” for the number S of lists handled by the assignment algorithm. The standard procedure, which associates measurements from the most recently arrived S-1 frames to established tracks, can have, in the case of S sensors, a time-depth of zero. A new technique, which guarantees maximum effectiveness for an S-dimensional data association (S⩾3), i.e., maximum time-depth (S-1) for each sensor without sacrificing the fusion across sensors, is presented. Using a sliding window technique (of length S), the estimates are updated after each frame of measurements. The algorithm provides a systematic approach to automatic track formation, maintenance, and termination for multitarget tracking using multisensor fusion with multidimensional assignment for data association. Estimation results are presented for simulated data for a large scale air-to-ground target tracking problem     

Evaluation of multiple radar target trackers in stressfulenvironments

This paper evaluates the performance of multiple target tracking (MTT) algorithms in real-life stressful radar tracking environments. Real closely spaced maneuver radar data, generated by six F-18 fighters and other targets, were collected jointly by the defence departments of Canada and United States to support this practical MTT algorithm evaluation study. A set of performance metrics was defined here to compare the suboptimal nearest neighbor (SNN), global nearest neighbor (GNN), and various variants of the joint probabilistic data association (JPDA) MTT trackers. Results reveal an interesting result that all these MTT algorithms exhibited very close performance. In addition, the weighted sum approach of the PDA/JPDA trackers which are theoretically effective were observed to perform poorly in tracking closely spaced targets. Overall speaking, the GNN filter based on the Munkres algorithm had the best performance in terms of both tracking performance and robustness     

Tracking of Spawning Targets with Multiple Finite Resolution Sensors

In this paper the problem of tracking multiple spawning targets with multiple finite-resolution sensors is considered and a new algorithm for measurement-to-track association with possibly unresolved measurements is presented. The goal is to initialize new tracks of spawned targets before they are resolved from the mother platform so that one has the ability to carry out early discrimination when they become resolved. The multiple scan data association problem is first formulated as a multidimensional assignment problem with explicit new constraints for the unresolved measurements. Then the top M hypotheses tracking (TMHT) is presented where the state estimates and their covariances are modified based on the M best hypotheses through the assignment solutions. A modification to the assignment problem is developed that leads to a linear programming (LP) where the optimal solution can be a noninteger in [0,1]. The fractional optimal solution is interpreted as (pseudo) probabilities over the N - 1 frame sliding window. The best hard (binary) decision assignment solution and the M best via TMHT are compared with the soft decision solution for 2-D tracking scenarios with various sensor configurations. Based on the simulation results, the soft assignment approach has better track maintenance capability than the single best hard assignment and a performance nearly as good as the TMHT. Its computational load is slightly higher than the single best hard assignment but much lighter than TMHT.     

基于数据关联的故障快速检测

 多数情况下,快速实时地进行故障检测是很重要的。将故障看做是通过多传感器观测的动态模型,进行多传感器多模型概率数据关联,以各个模型的关联结果和设定的阈值为依据,可以有效地实现故障检测。联合概率数据关联（JPDA）算法是解决多传感器多目标跟踪的一个有效方法,文中通过分析概率数据关联算法,对联合概率数据关联算法进行了改进：（1）通过正确地选择阈值,移除小概率事件,进而建立一个近似的确认矩阵;（2）根据被跟踪目标故障跟踪门的相交情况,将跟踪空间进行数学划分,形成若干相互独立的区域;（3）对同一区域内公共有效量测的概率密度值进行衰减,计算出关联概率。仿真对比表明,本文的改进算法能显著减少计算时间,有效提高故障检测的快速性和实时性。     

纯方位二维目标跟踪的航迹起始算法

 针对传统航迹起始算法在纯方位目标定位和跟踪系统应用中存在的弊端,提出了一种完全基于角度量测的快速航迹起始算法。该方法通过深入分析目标在角度坐标下的运动特性,给出了全新的关联门构造方法。该波门技术有效提高了纯方位二维目标真实量测的确认效率,极大限制了虚假航迹随密集杂波的扩张。利用此波门,通过基于逻辑的方法对仅有角度量测的目标航迹进行扩展。该方法有效地解决了角度坐标系下机动目标的航迹起始分辨率下降的问题,为基于单个被动传感器纯方位跟踪系统进行快速、准确的航迹起始提供了新的思路。仿真结果及实际应用表明了此算法的有效性和实用性。     

一种基于模糊遗传算法的多传感器多目标跟踪数据关联算法

基于模糊遗传算法发展了一种新的数据关联算法。数据关联的静态部分靠一个模糊遗传算法来得出量测组合序列和S-D分配的m个最优解。在数据关联的动态部分，将得到的S-D分配的m个最优解在一个基于多种群模糊遗传算法的动态2D分配算法中依靠一个卡尔曼滤波估计器估计出移动目标各个时刻的状态。这一基于分配的数据关联算法的仿真试验内容为被动式传感器的航迹形成和维持的问题。仿真试验的结果表明该算法在多传感器多目标跟踪中应用的可行性。另外，对算法发展和实时性问题进行了简单讨论。     

基于OSPA距离的航迹关联方法

 提出一种基于最优次模式分配(OSPA)距离的多传感器航迹关联方法,把每一个局部传感器航迹看做一个航迹集合,通过OSPA距离度量各个航迹集合之间的距离,具有最短OSPA距离的航迹属于同一个目标航迹;针对航迹关联实时性的要求,进一步给出具有滑窗的航迹OSPA递推方法。最终结果表明,本文方法不仅可以有效保持航迹的历史信息和几何特征信息,而且可以有效地关联航迹交叉、航迹分叉和航迹异步等问题。通过与加权关联方法、独立序贯方法的仿真比较,证明其在关联精度、异步等几个方面具有比较好的优势。     

基于分段序列离散度的异步航迹关联算法

为解决异步不等速率航迹关联问题，提出一种基于分段序列离散度的异步航迹关联算法。定义分段混合航迹序列的离散信息度量，给出不等长航迹序列分段划分规则，通过计算离散度，利用经典分配法进行关联判定，并针对多义性问题设置二次检验环节。与传统算法相比，不需要时间对准，且具有不受噪声分布影响的特点。仿真结果表明，算法在航迹异步、传感器采样率不同等条件下均能以较高正确率稳定关联，并可有效分辨航迹交叉、分叉和合并等复杂情况，具有明显的优势。