Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

Track formation with bearing and frequency measurements in clutter

Target motion analysis from a narrowband passive sonar that yields bearing and frequency measurements in the presence of false detections (clutter) in a low-SNR (low signal-to-noise ratio) environment is discussed. The likelihood function used to compute the maximum likelihood estimation of the track parameters (localization and frequency) incorporates the false alarms via the probabilistic data association technique. The Cramer-Rao lower bound is calculated and results obtained from simulations are shown to be compatible with it. A test of track acceptance is also presented     

Performance analysis of a dynamic programming track before detectalgorithm

We analyze a dynamic programming (DP)-based track before detect (TBD) algorithm. By using extreme value theory we obtain explicit expressions for various performance measures of the algorithm such as probability of detection and false alarm. Our analysis has two advantages. First the unrealistic Gaussian and independence assumptions used in previous works are not required. Second, the probability of detection and false alarm curves obtained fit computer simulated performance results significantly more accurately than previously proposed analyses of the TBD algorithm     

Interacting multiple model tracking with target amplitude feature

A recursive tracking algorithm is presented which uses the strength of target returns to improve track formation performance and track maintenance through target maneuvers in a cluttered environment. This technique combines the interacting multiple model (IMM) approach with a generalized probabilistic data association (PDA), which uses the measured return amplitude in conjunction with probabilistic models for the target and clutter returns. Key tracking decisions can be made automatically by assessing the probabilities of target models to provide rapid and accurate decisions for both true track acceptance and false track dismissal in track formation. It also provides the ability to accurately continue tracking through coordinated turn target maneuvers     

Evaluating a multiple-hypothesis multitarget tracking algorithm

The performance evaluation of multiple-hypothesis, multitarget tracking algorithm is presented. We are primarily interested in target-detection/track-initiation capabilities as measures of performance. Through Monte Carlo simulations, a multiple-hypothesis tracking algorithm was evaluated in terms of 1) probability of establishing a track from target returns and 2) false track density. A radar was chosen as the sensor, and a general multiple-hypothesis, multitarget tracking algorithm was used in the Monte Carlo simulations. The simulation results predict the probability of establishing a track from returns of a target as well as the false track density per scan volume per unit time. The effects of the target radar cross section and the radar power, measured through the mean signal-to-noise ratio (SNR) were studied, as were the effects of detection threshold and track quality threshold. Computational requirements were also investigated     

Effectiveness of track monitoring with multiple 2D passive sensors

An analytical technique is presented which can be used to evaluate the effectiveness of the track monitoring scheme presented by J.A. Roecker (see ibid., vol.27, no.6, p.872-6, Nov. 1991) in detecting false track-to-track (ghost track) assignments without the use of simulations. It is shown that when two tracks are traveling in parallel and in the direction of the inclination angle, it is impossible to determine which tracks to associate. However, track monitoring is effective under all other circumstances. A tracking algorithm designer can use this technique to determine the length of time before track-to-track initiation for good ghost track rejection. This technique also determines the probability of accepting ghost tracks during mature track monitoring.<>     

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.     

Joint integrated probabilistic data association: JIPDA

A new recursive filter for multi-target tracking in clutter is presented. Multiple tracks may share the same measurement(s). Joint events are formed by creating all possible combinations of track-measurement assignments and the probabilities for these joint events are calculated. The expressions for the joint event probabilities incorporate the probabilities of target existence of individual tracks, an efficient approximation for the cluster volume and a priori probability of the number of clutter measurements in each cluster. From these probabilities the data association and target existence probabilities of individual tracks are obtained, which allows track state update and false track discrimination. A simulation study is presented to show the effectiveness of this approach.     

Optimization of waveform and detection threshold for range and range-rate tracking in clutter

We address an optimization problem to obtain the combined sequence of waveform parameters (pulse amplitudes and lengths, and FM sweep rates) and detection thresholds for optimal range and range-rate tracking in clutter. The optimal combined sequence minimizes a tracking performance index under a set of parameter constraints. The performance index includes the probability of track loss and a function of estimation error covariances. The track loss probability and the error covariances are predicted using a hybrid conditional average algorithm. The effect of the false alarms and clutter interference is taken into account in the prediction. A measurement model in explicit form is also presented which is developed based on the resolution cell in the delay-Doppler plane for a single Gaussian pulse. Numerical experiments were performed to solve the optimization problem for several examples.     

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。     

末制导雷达虚警概率检验方法

针对只有10^-8～10^-9量级的末制导雷达虚警概率难以检验的问题,研究虚警概率与发现概率、虚警时间的关系,论证了将虚警概率转化为虚警时间的检验方法,利用定时截尾统计检验理论,研究了不同鉴别比、不同试验时间、不同接收故障数时研制方与使用方的风险,提出了新型末制导雷达虚警概率的检验方法,解决了该项指标检验的难题。     

Sequential track extraction

Sensors like radar or sonar usually produce data on the basis of a single frame of observation: target detections. The detection performance is described by quantities like detection probability Pd and false alarm density f. A different task of detection is formation of tracks of targets unknown in number from data of multiple consecutive frames of observation. This leads to quantities which are of a higher level of abstraction: extracted tracks. This again is a detection process. Under benign conditions (high Pd, low f and well separated targets) conventional methods of track initiation are recommended to solve a simple task. However, under hard conditions the process of track extraction is known to be difficult. We here concentrate on the case of well separated targets and derive an optimal combinatorial method which can be used under hard operating conditions. The method relates to MHT (multiple hypothesis tracking), uses a sequential likelihood ratio test and derives benefit from processing signal strength information. The performance of the track extraction method is described by parameters such as detection probability and false detection rate on track level, while Pd and f are input parameters which relate to the signal-to-noise interference ratio (SNIR), the clutter density, and the threshold set for target detection. In particular the average test lengths are analyzed parametrically as they are relevant for a user to estimate the time delay for track formation under hard conditions     

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。     

巡航导弹飞行撞地概率的一种计算方法

研究了巡航导弹飞行高度控制系统对应的高度控制误差和地形起伏误差,在综合这两种误差的基础上,提供了一种飞行撞地概率的计算方法,并给出了飞行高度与之对应的撞地概率计算实例。计算和分析得出,参考航迹高度取现行标准值的某型巡航导弹撞地概率太大,需通过减小高度探测控制系统的误差或者增大参考航迹的规划高度来降低撞地概率。     

EM-ML algorithm for track initialization using possibly noninformative data

Initializing and maintaining a track for a low observable (LO) (low SNR, low target detection probability and high false alarm rate) target can be very challenging because of the low information content of measurements. In addition, in some scenarios, target-originated measurements might not be present in many consecutive scans because of mispointing, target maneuvers, or erroneous preprocessing. That is, one might have a set of noninformative scans that could result in poor track initialization and maintenance. In this paper an algorithm based on the expectation-maximization (EM) algorithm combined with maximum likelihood (ML) estimation is presented for tracking slowly maneuvering targets in heavy clutter and possibly noninformative scans. The adaptive sliding-window EM-ML approach, which operates in batch mode, tries to reject or weight down noninformative scans using the Q-function in the M-step of the EM algorithm. It is shown that target features in the form of, for example, amplitude information (AI), can also be used to improve the estimates. In addition, performance bounds based on the supplemented EM (SEM) technique are also presented. The effectiveness of new algorithm is first demonstrated on a 78-frame long wave infrared (LWIR) data sequence consisting of an Fl Mirage fighter jet in heavy clutter. Previously, this scenario has been used as a benchmark for evaluating the performance of other track initialization algorithms. The new EM-ML estimator confirms the track by frame 20 while the ML-PDA (maximum likelihood estimator combined with probabilistic data association) algorithm, the IMM-MHT (interacting multiple model estimator combined with multiple hypothesis tracking) and the EVIM-PDA estimator previously required 28, 38, and 39 frames, respectively. The benefits of the new algorithm in terms of accuracy, early detection, and computational load are illustrated using simulated scenarios as well.     

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%     

某型涡喷发动机的可靠性增长分析

针对某型涡喷发动机的一组含零故障的多台不同步截尾故障数据。给出了趋势检验、AMSAA模型的拟合优度检验及模型参数的极大似然估计方法。分析表明，该型发动机有显著的可靠性增长，且可用AMSAA模型拟合其故障数据，在考虑零故障后，其参数及MTBF的极大似然估计（MLE）更为可信。     

一种全自动的检测方法用于SAR-ATI的GMTI

针对星载SAR-ATI处理的中间结果,提出了一种称为"两步-类高斯拟合"完全自适应的检测方法。该方法可以完全自动地实现杂波和噪声中的运动目标检测,避免了传统方法作联合高斯数据的假定,无须推导SAR-ATI干涉图的理论概率密度函数。此外,该方法还可以大大降低系统的虚警概率并用仿真研究了最小可检测速度。     

基于运动状态的航迹起始算法研究

 针对传统的基于逻辑的航迹起始方法在量测扩展过程中存在的弊端,提出了基于目标运动状态的航迹起始算法,并给出了更为精确的起始波门构造方法。利用目标的位置信息形成候选目标航迹,在候选目标航迹扩展过程中,采用提出的修正Hough变换提取目标状态信息,并根据目标〖JP2〗的状态信息对候选航迹进行检验。仿真结果表明,该算法比其他基于逻辑的方法有更低的虚警概率,并且对存储空间要求低,适于工程应用。