Tracking in Clutter using IMM-IPDA?Based Algorithms

We describe three single-scan probabilistic data association (PDA) based algorithms for tracking manoeuvering targets in clutter. These algorithms are derived by integrating the interacting multiple model (IMM) estimation algorithm with the PDA approximation. Each IMM model a posteriori state estimate probability density function (pdf) is approximated by a single Gaussian pdf. Each algorithm recursively updates the probability of target existence, in the manner of integrated PDA (IPDA). The probability of target existence is a track quality measure, which can be used for false track discrimination. The first algorithm presented, IMM-IPDA, is a single target tracking algorithm. Two multitarget tracking algorithms are also presented. The IMM-JIPDA algorithm calculates a posteriori probabilities of all measurement to track allocations, in the manner of the joint IPDA (JIPDA). The number of measurement to track allocations grows exponentially with the number of shared measurements and the number of tracks which share the measurements. Therefore, IMM-JIPDA can only be used in situations with a small number of crossing targets and low clutter measurement density. The linear multitarget IMM-IPDA (IMM-LMIPDA) is also a multitarget tracking algorithm, which achieves the multitarget capabilities by integrating linear multitarget (LM) method with IMM-IPDA. When updating one track using the LM method, the other tracks modulate the clutter measurement density and are subsequently ignored. In this fashion, LM achieves multitarget capabilities using the number of operations which are linear in the: number of measurements and the number of tracks, and can be used in complex scenarios, with dense clutter and a large number of targets.     

Track segment association, fine-step IMM and initialization with Doppler for improved track performance

In this work we present a new track segment association technique to improve track continuity in large-scale target tracking problems where track breakages are common. A representative airborne early warning (AEW) system scenario, which is a challenging environment due to highly maneuvering targets, close target formations, large measurement errors, long sampling intervals, and low detection probabilities, provides the motivation for the new technique. Previously, a tracker using the interacting multiple model (IMM) estimator combined with an assignment algorithm was shown to be more reliable than a conventional Kalman filter based approach in tracking similar targets but it still yielded track breakages due to the difficult environment. In order to combine the broken track segments and improve track continuity, a new track segment association algorithm using a discrete optimization approach is presented. Simulation results show that track segment association yields significant improvements in mean track life as well as in position, speed, and course rms errors. Also presented is a modified one-point initialization technique with range rate measurements, which are typically ignored by other initialization techniques, and a fine-step IMM estimator, which improves performance in the presence of long revisit intervals. Another aspect that is investigated is the benefit of "deep" (multiframe or N-dimensional, with N > 2) association, which is shown to yield significant benefit in reducing the number of false tracks.     

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SVM算法的虚假航迹识别

针对云雨杂波和主被动干扰导致多雷达传感器产生虚假目标航迹的问题,利用支持向量机(SVM)算法的自主学习能力,通过构建基于数据驱动的判别模型进行虚假航迹识别。针对航迹起始得到的目标潜在航迹,利用人工智能数据驱动、自学习的特点,设计了SVM算法。通过对已标记真假的目标航迹样本进行离线学习,形成虚假航迹识别的SVM分类器,实现了基于数据驱动的判别模型代替先验知识规则约束的固定模型,并在工程应用中,利用SVM分类器在线识别虚假航迹,完成实时剔除。通过实测雷达数据实验验证,该算法的目标虚假航迹准确率高达95%以上,完全满足实际的工程应用需求。相比基于阈值或规则进行硬性判断的传统虚假航迹识别方法,所提出的算法不仅提高了准确率,还具有较高的实时性,能够适应复杂多变的杂波环境,在实际应用中具有更强的适应性和实用性。因此,提出的基于SVM算法的虚假航迹识别方法对于密集杂波场景下的虚假航迹剔除问题具有显著的实际应用价值。     

Tracking multitarget in cluttered environment

A method for multitarget tracking and initiating tracking in a cluttered environment is proposed. The algorithm uses a sliding window of length uT (T is the sampling time) to keep the measurement sequence at time k. Instead of solving a large problem, the entire set of targets and measurements is divided into several clusters so that a number of smaller problems are solved independently. When a set of measurements is received, a new set of data-association hypotheses is formed for all the measurements lying in the validation gates within each cluster from time K-u+1 to K. The probability of each track history is computed, and, choosing the largest of these histories, the target measurement is updated with an adaptive state estimator. A covariance-matching technique is used to improve the accuracy of the adaptive state estimator. In several examples, the algorithm successfully tracks targets over a wide range of conditions     

Tracker and signal processing for the benchmark problem with unresolved targets

Radar signal processing is particularly important in tracking closely spaced targets and targets in the presence of sea-surface-induced multipath. Closely spaced targets can produce unresolved measurements when they occupy the same range cell of the radar. These issues are the salient features of the benchmark problem for tracking unresolved targets combined with radar management, for which this paper presents the only complete solution to date. In this paper a modified version of a recently developed maximum likelihood (ML) angle estimator, which can produce two measurements from a single (unresolved) detection, is presented. A modified generalized likelihood ratio test (GLRT) is also described to detect the presence of two unresolved targets. Sea-surface-induced multipath can produce a severe bias in the elevation angle measurement when the conventional monopulse ratio angle extractor method is used. A modified version of a recently developed ML angle extractor, which produces nearly unbiased elevation angle measurements and significantly improves the track accuracy, is presented. Efficient radar resource allocation algorithms for two closely spaced targets and targets flying close to the sea surface are also presented. Finally, the IMMPDAF (interacting multiple model estimator with probabilistic data association filter modules) is used to track these targets. It is found that a two-model IMMPDAF performs better than the three-model version used in the previous benchmark. Also, the IMMPDAF with a coordinated turn model works better than the one using a Wiener process acceleration model. The signal processing and tracking algorithms presented here, operating in a feedback manner, form a comprehensive solution to the most realistic tracking and radar management problem to date.     

Multiple model PMHT and its application to the benchmark radar tracking problem

The probabilistic multiple hypothesis tracker (PMHT) uses the expectation-maximization (EM) algorithm to solve the measurement-origin uncertainty problem. Here, we explore some of its variants for maneuvering targets and in particular discuss the multiple model PMHT. We apply this PMHT to the six "typical" tracking scenarios given in the second benchmark problem from W. D. Blair and G. A. Watson (1998). The manner in which the PMHT is used to track the targets and to manage radar allocation is discussed, and the results compared with those of the interacting multiple model probabilistic data association filter (IMM/PDAF) and IMM/MHT (multiple hypothesis tracker). The PMHT works well: its performance lies between those of the IMM/PDAF and IMM/MHT both in terms of tracking performance and computational load.     

基于相位相关的部分可辨编队精细起始算法

针对部分可辨条件下编队目标的精细起始难题,提出了一种基于相位相关的部分可辨编队精细起始算法。首先,采用基于坐标映射距离差分的快速群分割与基于编队中心点的预互联对雷达量测进行预处理;然后,利用图像匹配中相位相关特性,将相邻时刻编队结构进行补偿对准,解决了低目标发现概率情况下的编队结构对准问题;最后,采用增加虚拟量测并后验判决的方式,结合最近邻法做编队航迹精细互联,在填补航迹缺失、增加正确航迹的同时抑制虚假航迹的产生。经仿真验证,与修正的逻辑法、基于相对位置矢量的灰色编队精细起始算法相比,本文所提算法在提高航迹正确起始率、抑制虚假航迹方面性能优势显著,且对环境杂波与雷达精度具有较好的鲁棒性,对目标发现概率具有较好的适应性。     

IMMPDAF for radar management and tracking benchmark with ECM

A framework is presented for controlling a phased array radar for tracking highly maneuvering targets in the presence of false alarms (FAs) and electronic countermeasures (ECMs). Algorithms are presented for track formation and maintenance; adaptive selection of target revisit interval, waveform and detection threshold; and neutralizing techniques for ECM, namely, against a standoff jammer (SOJ) and range gate pull off (RGPO). The interacting multiple model (IMM) estimator in combination with the probabilistic data association (PDA) technique is used for tracking. A constant false alarm rate (CFAR) approach is used to adaptively select the detection threshold and radar waveform, countering the effect of jammer-induced false measurements. The revisit interval is selected adaptively, based on the predicted angular innovation standard deviations. This tracker/radar-resource-allocator provides a complete solution to the benchmark problem for target tracking and radar control. Simulation results show an average sampling interval of about 2.5 s while maintaining a track loss less than the maximum allowed 4%     

An interacting multiple model approach for target tracking withglint noise

The application of the interacting multiple model (IMM) estimation approach to the problem of target tracking when the measurements are perturbed by glint noise is considered. The IMM is a very effective approach when the system has discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties. It is shown that this method performs better than the “score function” method. It is also shown that the IMM method performs robustly when the exact prior information of the glint noise is not available     

航迹起始算法研究

针对传统的基于逻辑的航迹起始算法存在的弊端,分别提出了基于一步延迟思想和多假设思想的航迹起始算法。基于一步延迟思想的方法利用相邻2个采样周期的量测信息来选择用于航迹扩展的量测,从而实现航迹扩展的唯一性,可以在保证航迹起始性能的同时有效地降低存储要求。而在基于多假设思想的航迹起始算法中,在候选目标航迹的扩展阶段,采用关联矩阵拆分的办法获得当前多个可行假设,进而实现原假设的扩展与分裂,从而使得扩展后的源于各个候选目标的量测序列之间无共用量测现象。仿真结果表明了算法的有效性。     

Radar Measurement Noise Variance Estimation with Several Targets of Opportunity

A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. A method is presented of determining the measurement noise variances of a sensor, assumed to be constant, by using multiple IMM estimators while tracking targets whose motion is not known---targets of opportunity. Combining techniques outlined in [2] and [6], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out over a varying grid of IMMs to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.     

Maneuvering target tracking using IMM method at high measurementfrequency

The problem of tracking a maneuvering target with a high measurement frequency is considered. The measurement noise is significantly correlated when the measurement frequency is high. A simple decorrelation process is proposed to enhance the interacting multiple model (IMM) algorithm to track a maneuvering target with correlated measurement noise. It is found that the decorrelation process may improve system performance significantly, especially in velocity and acceleration estimations     

非合作目标动态RCS仿真方法

针对非合作目标难以开展动态测量的问题,根据空气动力学原理提出了一种非合作目标动态雷达散射截面（RCS）仿真方法。该方法首先建立测量背景下典型飞行航路模型,然后计算雷达视线在机体坐标系上的时变姿态角。根据姿态角开展电磁计算,获得F-117A隐身攻击机在侧站平飞、背站拉起、对站俯冲、侧站盘旋4种航路下的动态RCS数据。着重分析了动、静态RCS特性在起伏目标检测性能评估上的差异。结果表明：静态RCS特性难以反映目标运动时真实的雷达特性,利用静态数据描述目标特性可能导致错误结论,而文中方法获取的动态RCS数据可以提高结论的完整性和可信度。     

Multi-Target Tracking in Clutter without Measurement Assignment

When tracking targets using radars and sonars, the number of targets and the origin of data is uncertain. Data may be false measurements or clutter, or they may be detections from an unknown number of targets whose possible trajectories and detection processes can only be described in a statistical manner. Optimal all-neighbor multi-target tracking (MTT) in clutter enumerates all possible joint measurement-to-track assignments and calculates the a posteriori probabilities of each of these joint assignments. The numerical complexity of this process is combinatorial in the number of tracks and the number of measurements. One of the key differences between most MTT algorithms is the manner in which they reduce the computational complexity of the joint measurement-to-track assignment process. We propose an alternative approach, using a form of soft assignment, that enables us to bypass this step entirely. Specifically, our approach treats possible detections of targets followed by other tracks as additional clutter measurements. It starts by approximating the a~priori probabilities of measurement origin. These probabilities are then used to modify the clutter spatial density at the location of the measurements. A suitable single target tracking (STT) filter then uses the modified clutter intensity for updating the track state. In effect, the STT filter is transformed into an MTT filter with a numerical complexity that is linear in the number of tracks and the number of measurements. Simulations show the effectiveness of this approach in a number of different multi-target scenarios.     

IMM estimator with out-of-sequence measurements

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.     

Application of the Kalman-Levy Filter for Tracking Maneuvering Targets

Among target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an interacting multiple model (IMM) estimator). The oversimplification resulting from the above assumptions can cause degradation in tracking performance. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy-tailed noise distribution known as the Levy distribution. Due to the heavy-tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of the Kalman-Levy filter in the nonmaneuvering portion of track is worse than that of a Kalman filter. For this reason, an IMM with one Kalman and one Kalman-Levy module is developed here. Also, the superiority of the IMM with Kalman-Levy module over only Kalman-filter-based IMM for realistic maneuvers is shown by simulation results.     

海上低空突防群目标跟踪的IMM-Bayesian实现

由于海上低空突防编队目标存在低检测和高机动的特点,采用传统跟踪算法对编队内目标逐个跟踪存在航迹连续性差、关联混乱等问题。针对上述问题,基于对编队群整体跟踪的思想,将交互式多模型(IMM)与Bayesian算法相结合,采用IMM-Bayesian算法完成典型机动场景下(拐弯、合并、分裂)海上低空编队群目标整体的跟踪,同时利用随机矩阵作为群的扩展状态完成对群形状信息的估计。其中,对海上低空突防编队群目标运动过程中出现的分裂与合并现象,在IMM-Bayesian算法的基础上采用最近邻分类的思想对其进行有效跟踪。仿真结果表明了算法的有效性。     

Finding the best set of K paths through a trellis withapplication to multitarget tracking

A solution is presented to the problem of finding the best set of K completely unmerged paths through a trellis with M _i⩾K states at depth i in the trellis, i=0, 1, 2, . . ., N. Here, `best set' means that the sum of the metrics of all K paths in the set is minimized, and `completely unmerged' means that no two paths pass through a common state. The solution involves using the Viterbi algorithm on an expanded trellis. This result is then used to separate the tracks of K targets optimally in a simplified model of a multitarget radar system. The model includes measurement errors and false alarms, but it does not include the effects of missing detections or merged measurements