Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

Directed Subspace Search ML-PDA with Application to Active Sonar Tracking

The maximum likelihood probabilistic data association (ML-PDA) tracking algorithm is effective in tracking Very Low Observable targets (i.e., very low signal-to-noise ratio (SNR) targets in a high false alarm environment). However, the computational complexity associated with obtaining the track estimate in many cases has precluded its use in real-time scenarios. Previous ML-PDA implementations used a multi-pass grid (MPG) search to find the track estimate. Two alternate methods for finding the track estimate are presented-a genetic search and a newly developed directed subspace (DSS) search algorithm. Each algorithm is tested using active sonar scenarios in which an autonomous underwater vehicle searches for and tracks a target. Within each scenario, the problem parameters are varied to illustrate the relative performance of each search technique. Both the DSS search and the genetic algorithm are shown to be an order of magnitude more computationally efficient than the MPG search, making possible real-time implementation. In addition, the DSS search is shown to be the most effective technique at tracking a target at the lowest SNR levels-reliable tracking down to 5 dB (postprocessing SNR in a resolution cell) using a 5-frame sliding window is demonstrated, this being 6 dB better than the MPG search.     

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.     

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     

Radar power multiplier for acquisition of low observables using anESA radar

In this paper the acquisition of a low observable (LO) incoming tactical ballistic missile using the measurements from a surface based electronically scanned array (ESA) radar is presented. We present a batch maximum likelihood (ML) estimator to acquire the missile while it is exo-atmospheric. The proposed estimator, which combines ML estimation with the probabilistic data association (PDA) approach resulting in the ML-PDA algorithm to handle false alarms, also uses target features. The use of features facilitates target acquisition under low signal-to-noise ratio (SNR) conditions. Typically, ESA radars operate at 13-20 dB, whereas the new estimator is shown to be effective even at 4 dB SNR (in a resolution cell, at the end of the signal processing chain) for a Swerling III fluctuating target, which represents a significant counter-stealth capability. That is, this algorithm acts as an effective “power multiplier” for the radar by about an order of magnitude. An approximate Cramer-Rao lower bound (CRLB), quantifying the attainable estimation accuracies and shown to be met by the proposed estimator, is derived 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%     

基于傅里叶变换的航迹对准关联算法

研究了在组网雷达存在系统误差情况下的目标航迹关联问题,理论分析了雷达系统误差对目标航迹的影响,并将该影响表示为目标航迹的旋转和平移量。在此基础上,提出了一种基于傅里叶变换的系统误差配准前航迹对准关联算法,该算法将组网雷达的航迹数据看做为一种整体信息,采用傅里叶变换理论来估计和补偿组网雷达目标航迹数据到融合中心航迹数据的相对旋转量和平移量,将雷达网中雷达上报的目标航迹数据对准到融合中心,从而不依赖于估计雷达网系统误差,实现了误差配准前的航迹准确关联,能够为后端的系统误差配准提供可靠的关联目标航迹数据。     

On joint track initiation and parameter estimation under measurement origin uncertainty

The problem of joint detection and estimation for track initiation under measurement origin uncertainty is studied. The two well-known approaches, namely the maximum likelihood estimator with probabilistic data association (ML-PDA) and the multiple hypotheses tracking (MHT) via multiframe assignment, are characterized as special cases of the generalized likelihood ratio test (GLRT) and their performance limits indicated. A new detection scheme based on the optimal gating is proposed and the associated parameter estimation scheme modified within the ML-PDA framework. A simplified example shows the effectiveness of the new algorithm in detection performance under heavy clutter. Extension of the results to state estimation with measurement origin uncertainty is also discussed with emphasis on joint detection and recursive state estimation.     

基于点集合并的修正Hough变换TBD算法

在低信噪比条件下,基于Hough变换的检测前跟踪算法是进行强杂波背景下目标航迹检测的一种手段。本文针对Hough变换后一个目标产生多条可能航迹以及航迹内可能存在杂波点的问题,提出了一种基于能量最大点和点集合并的修正Hough变换检测前跟踪算法。该算法利用量测点时序、能量信息及目标速度先验信息对Hough变换后点迹进行关联和剔除,能够有效的对目标原始航迹进行回溯。针对高斯噪声背景下的飞行目标,仿真结果表明该算法能够对微弱目标进行有效检测,在目标数目、杂波密度、信噪比发生变化的条件下仍能保持较高的检测概率。     

Association of DF Bearing Measurements with Radar Tracks

The problem of associating direction finding (DF) bearingmeasurements with radar tracks is formulated as a multiplehypothesis testing problem. A simple decision rule for associating aset of DF bearing measurements with no radar track or one of mpossible radar tracks was developed using a combination of Bayesian and Neyman-Pearson approaches. The decision algorithmwas checked using both computer simulations and experimentaldata. Finally, a multiplatform algorithm was formulated and tested,using a combination of real and synthetic data.     

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。     

Maximum likelihood angle extractor for two closely spaced targets

In a scenario of closely spaced targets special attention has to be paid to radar signal processing. We present an advanced processing technique, which uses the maximum likelihood (ML) criterion to extract from a monopulse radar separate angle measurements for unresolved targets. This processing results in a significant improvement, in terms of measurement error standard deviations, over angle estimators using the monopulse ratio. Algorithms are developed for Swerling I as well as Swerling III models of radar cross section (RCS) fluctuations. The accuracy of the results is compared with the Cramer Rao lower bound (CRLB) and also to the monopulse ratio technique. A novel technique to detect the presence of two unresolved targets is also discussed. The performance of the ML estimator was evaluated in a benchmark scenario of closely spaced targets - closer than half power beamwidth of a monopulse radar. The interacting multiple model probabilistic data association (IMMPDA) track estimator was used in conjunction with the ML angle extractor     

Association of tracks from over the horizon radar

In Over-The-Horizon Radar (OTHR), multiple ionospheric layers cause several tracks per target to be observed. This effect causes ambiguities in target identification and track coordinate registration. A pattern classification approach is proposed for associating tracks. Neural networks and statistical methods are applied to combine track affinities and associate pairs of tracks. The proposed approach provides a practical and efficient way of dealing with multiple track association when the number of targets is large and optimal. Bayesian hypothesis testing is not practical     

海上目标雷达与 AIS航迹时空匹配方法

针对海上目标的雷达与船舶自动识别系统(Automatic Identification System,AIS)中,航迹之间存在的时空不匹配现象,提出了在空间对准之后结合海上航迹运动特点,对 AIS航迹数据进行插值对准雷达目标航迹的方法,在解决雷达与 AIS航迹之间时空不匹配问题的同时,最大程度减小插值误差。该方法根据船舶航向变化率,结合航速航向法和内插外推法的优势,针对不同航迹特点自动选择最佳的插值配准方法,实现海上目标的雷达与 AIS航迹点的自动插值和时空对齐。仿真实验结果表明,所提方法针对海上目标复杂运动,可以自动匹配选择最佳插值方法,有效降低误差,实现雷达与 AIS航迹之间的时空匹配。     

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.     

一种基于扩展模型的隐身目标检测前跟踪方法

现有的检测前跟踪算法对高分辨雷达隐身目标模型适应性不强,从而容易导致跟踪发散。针对该问题,把粒子滤波与检测前跟踪算法相结合应用于扩展隐身目标的检测跟踪,提出了一种隐身目标扩展模型检测前跟踪方法。首先,采用扩展模型对目标的扩展属性进行假设检验,从而判断目标是否为扩展目标;然后,把目标扩展长度引入状态向量,进行基于扩展模型的隐身目标检测前跟踪（Track-before-detect,TBD）,克服粒子滤波易发散的不足,实现对目标空间长度的估计。仿真结果表明,该算法能够准确判断目标的扩展属性并进行有效的检测跟踪。     

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。     

Low observable target motion analysis using amplitude information

In conventional passive and active sonar system, target amplitude information (AI) at the output of the signal processor is used only to declare detections and provide measurements. We show that the AI can be used in passive sonar system, with or without frequency measurements, in the estimation process itself to enhance the performance in the presence of clutter where the target-originated measurements cannot be identified with certainty, i.e., for “low observable” or “dim” (low signal-to-noise ratio (SNR)) targets. A probabilistic data association (PDA) based maximum likelihood (ML) estimator for target motion analysis (TMA) that uses amplitude information is derived. A track formation algorithm and the Cramer-Rao lower bound (CRLB) in the presence of false measurements, which is met by the estimator even under low SNR conditions, are also given. The CRLB is met by the proposed estimator even at 6 dB in a cell (which corresponds to 0 dB for 1 Hz bandwidth in the case of a 0.25 Hz frequency cell) whereas the estimator without AI works only down to 9 dB. Results demonstrate improved accuracy and superior global convergence when compared with the estimator without AI. The same methodology can be used for bistatic radar     

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.