Two-step optimal estimator for three dimensional target tracking

This study presents an adaptation of a novel estimation methodology to the general nonlinear three-dimensional problem of tracking a maneuvering target. The two-step optimal estimator (TSE) suggests an attractive alternative to the standard extended Kalman filter (EKF). A superior performance is accomplished by dividing the estimation problem into two steps: a linear first step and a nonlinear second step. The target tracking performance of the TSE is shown to be better than an EKF implemented in either inertial or modified spherical coordinates. In the passive case, where bearing/elevation angles only are measured, the TSE yields excellent range and target acceleration estimates. In the active case, where range measurement is available as well, a homing missile employing closed-loop optimal guidance based on the TSE state estimates obtains smaller miss distances than with either versions of the EKF.     

TMA from bearings and multipath time delays

A novel approach for target motion analysis (TMA), which uses conventional passive bearing together with multipath time-delay measurements is examined. This so-called "Multipath TMA" offers two tactical advantages over the classical bearings-only TMA: no requirement for any ownship maneuver, and a good performance in terms of estimation error achieved in a shorter time. Both known and unknown multipath cases are addressed. Finally, Monte-Carlo simulations and at-sea trials demonstrate the practical efficiency of such a multipath TMA.     

基于倾斜角的多目标测向无源定位技术

对多目标测向无源定位问题进行了研究。虽然无源观测站不同,针对同一目标的方位角和俯仰角数据也不同,但它们有共同的倾斜角。基于此,提出了基于倾斜角的多目标测向无源定位算法。该算法分别计算一组与多个目标对应的倾斜角,然后利用倾斜角最接近原则对这2组数据进行关联判断,解决多目标测向数据的关联和定位问题,并通过仿真实验,对算法的有效性和可行性进行了验证。     

Data fusion and tracking using HMMs in a distributed sensor network

This work deals with the problem of multiple target tracking, from the measurements made on a field of passive sonars activated by an active sonar (multistatic network). The difficulties encountered then are of two kinds: each sensor alone does not provide full observability of a target, and multiple, possibly maneuvering targets moving in a cluttered environment must be dealt with. The algorithm presented here is based on a discrete Markovian modelization of the targets evolution in time. It starts with a fusion of the detections obtained at each measurement time. Tracking and target motion analysis (TMA) are next achieved thanks to dynamic programming (DP). This approach leads to multiple and maneuvering target tracking, with few assumptions; for instance, the use of deterministic target state models are avoided. Simulation results are presented and discussed.     

基于超短基线声传感器阵的高速目标轨迹估计

针对低空高速飞行目标跟踪问题，首先研究了某典型目标噪声信号的时频特性，发现其信号呈现宽带低频特征，难以从频域对目标轨迹进行估计。在此基础上，从各路接收信号的到达时延量入手，考虑到声基阵只能布设于有限空间内的制约，提出了一种基于超短基线阵时延估计的目标跟踪方法。该方法利用各个超短基线阵接收声强极值点分别估计目标运动轨迹垂线方向，计算多个垂线的叉乘向量实现对目标运动方向的估计，再利用多面交汇的方式获估计得到目标运动轨迹。分别对目标俯仰角、方位角及运动轨迹估计的理论误差进行了推导，根据理论估计误差，为能够实现对目标运动轨迹的估计，各个超短基线阵应尽量保证与目标运动轨迹不在同一平面上。根据仿真结果，在采用4个传感器基阵时，角度估计平均误差在4°以内，位置估计相对误差在5%左右。仿真结果验证了该方法的有效性。     

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。     

Bearings-only target motion analysis with acoustic propagation models of uncertain fidelity

The augmented bearings-only target motion analysis (TMA) problem arises when the bearing measurements of the classical bearings-only TMA problem are augmented with received signal-to-noise ratio (SNR) measurements. A combined acoustic propagation and sensor (CAPS) performance prediction model specifying the conditional density of the SNR measurements is assumed given; however, mismatch may exist between the CAPS model and the real world. We present a novel "missing data" formulation of the augmented bearings-only TMA problem using an empirical maximum a posteriori (EMAP) method for target parameter estimation, and show that it provides a natural and straightforward technique for mitigating CAPS model mismatch. The EMAP approach leads to an iteratively reweighted, linear least-squares algorithm for solving both the augmented bearings-only TMA problem and the classical (nonaugmented) bearings-only TMA problem. Examples are provided.     

Estimation of Aircraft Target Motion Using Orientation Measurements

A new approach to estimating motion of a highly maneuverable aircraft target in an air-to-air tracking scenario is presented. An interactive filter system is developed that provides an improved estimate of target motion states by conditioning kinematic filter estimates on target aspect angle data. Pattern recognition techniques used with an electrooptical tracker are presumed to provide this target aspect information. A target orientation filter processes the aspect angle measurements by statistically weighting measured aspect angles with the current best estimate of target kinematics. The aerodynamic lift equation is used to relate approximate angle of attack to target velocity and acceleration. A novel statistical model for aircraft target normal acceleration is also developed to represent better the unknown target accelerations. Simulation results of realistic three-dimensional scenarios are presented to evaluate the performance of the interactive filter system.     

Maneuvering Target Tracking Using Adaptive State Estimation

Two approaches to a nonlinear state estimation problem are presented. The particular problem addressed is that of tracking a maneuvering target in three-dimensional space using spherical observations (radar data). Both approaches rely on semi-Markov modeling of target maneuvers and result in effective algorithms that prevent the loss of track that often occurs when a target makes a sudden, radical change in its trajectory. Both techniques are compared using real and simulated radar measurements with emphasis on performance and computational burden.     

改善三元子阵测距精度方法研究

在水声领域,三元子阵测距、目标运动分析(TMA)和匹配场处理(MFP)是被动噪声测距的3种主要技术。文中以三元子阵测距声呐为研究对象,从波束形成、相关系数处理、测向精度改进等方面讨论提高时延估计精度的方法,对工程应用具有一定的参考价值。     

被动式寻的导弹的运动跟踪变结构制导

应用运动跟踪变结构控制理论设计被动式寻的导弹的制导律。这种运动跟踪变结构制导律（ＭＴＶＳＧ）可以令导弹－目标相对视线角速度按照给定的运动规律变化,从而增强被动跟踪问题（等价于一个非线性系统）的可观性,同时保证导弹有很高的命中精度。仿真研究表明,在ＭＴＶＳＧ下,系统的可观性明显增强,因此系统状态的估计精度较高。进一步的研究表明,ＭＴＶＳＧ对系统状态估计误差有很强的鲁棒性。ＭＴＶＳＧ的上述各种优点使得导弹有很高的命中精度。     

Stap using knowledge-aided covariance estimation and the fracta algorithm

In the airborne space-time adaptive processing (STAP) setting, a priori information via knowledge-aided covariance estimation (KACE) is employed in order to reduce the required sample support for application to heterogeneous clutter scenarios. The enhanced FRACTA (FRACTA.E) algorithm with KACE as well as Doppler-sensitive adaptive coherence estimation (DS-ACE) is applied to the KASSPER I & II data sets where it is shown via simulation that near-clairvoyant detection performance is maintained with as little as 1/3 of the normally required number of training data samples. The KASSPER I & II data sets are simulated high-fidelity heterogeneous clutter scenarios which possess several groups of dense targets. KACE provides a priori information about the clutter covariance matrix by exploiting approximately known operating parameters about the radar platform such as pulse repetition frequency (PRF), crab angle, and platform velocity. In addition, the DS-ACE detector is presented which provides greater robustness for low sample support by mitigating false alarms from undernulled clutter near the clutter ridge while maintaining sufficient sensitivity away from the clutter ridge to enable effective target detection performance     

基于序贯关联算法的多目标无源跟踪

基于序贯关联算法,对多目标无源跟踪问题进行了研究。在只有角度信息可以利用的情况下,首先,利用波门技术对各个无源传感器角度测量数据进行关联和滤波,形成参数航迹;然后,将各个无源传感器的参数航迹送到融合中心进行关联配对,并在关联过程中通过构造关联质量函数对参数航迹的关联历史情况进行度量,解决参数航迹关联模糊问题;最后,通过对关联成功的参数航迹进行交叉定位,给出多个不同目标的位置信息,实现分布式无源系统对多目标的数据关联和跟踪,并通过仿真分析,对算法的有效性和可行性进行验证。     

Passive localization of frequency-agile radars from angle andfrequency measurements

It is well known that the position of a stationary radar can be estimated by a single moving observer from angle and/or frequency measurements taken passively at different points in its trajectory. Depending on the measurement set different localization methods result: the bearing method (BM), the frequency method (FM), and the combined method (CM). Previous studies analyze the three methods on the basis of constant emitter frequencies. However, radars with constant emitter frequencies are not realistic. Frequency drift and frequency hopping have to be taken into account. Therefore, to include radars the emitter model has been extended by drift and frequency hopping in this study, and the estimation methods have been reanalyzed. The effects of the model extensions become transparent in a parametric Cramer-Rao (CR) analysis. The results obtained in this way are confirmed by Monte Carlo simulations taking maximum likelihood (ML) as estimation procedure     

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     

Optimal Cooperative Sensing using a Team of UAVs

The authors investigates the joint optimal estimation of both the position and velocity of a ground moving target (GMT) using pulse Doppler radars on-board unmanned aerial vehicles (UAVs). The problem of cooperative estimation using a UAV team and the optimization of the team's configuration to achieve optimal GMT position and velocity estimates are addressed. Based on the Cramer-Rao bound, the minimum achievable error variance of the GMT position and velocity estimates is derived. The expression of the minimum achievable estimation error variance for unbiased estimation provided by the Cramer-Rao bound is minimized yielding the optimal configuration of the UAV team. Our solution is complete in that it addresses various GMT tracking scenarios and an arbitrary number of UAVs. Optimal sensor geometries for typical applications are illustrated     

Comments on “Discrete-time observability and estimabilityanalysis for bearings-only target motion analysis”

Discusses the extensive mathematical analysis carried out by the authors of the original paper [see ibid., vol. 33, no. 1, p. 178-201, 1997] and submits the following points. The authors used pseudo measurements for recasting the observability problem into a linear framework. They treated the bearings-only passive target tracking system as a deterministic system. It is already established that for deterministic systems, the pseudo measurements are linear functions of the states of the system, though the coefficient matrix is a nonlinear function of the original measurements, By using the pseudo measurements in a linear observer, global stability can be shown. However, if the pseudo measurement observer, for which the analysis is mostly carried out by the authors, is used in a noisy environment as a pseudo measurement filter (PMF), biased estimates are arrived at. Hence, though the approach of authors is quite direct and provides insights about the algebraic structure of the BOT problem, as pseudo measurements are used throughout the analysis is not of much use to the TMA community, as the nonlinear measurement equation along with measurement noise are required to be considered in the BOT problem to obtain unbiased results     

基于Leader-Follower编队的无人机协同跟踪地面目标制导律设计

对地面目标的自动跟踪是无人机在任务应用阶段需要解决的重要问题之一,多无人机协同跟踪能够提高对目标运动状态的估计精度并降低目标丢失的概率,因而具有重要研究意义。本文提出了一种基于Leader-Follower编队的无人机协同跟踪制导方法,解决了传统Standoff跟踪模式对地面目标的速度范围限制问题。首先,通过控制无人机的航向不断趋近于地面目标牵连跟踪圆切线方向的方法设计了Leader无人机自动跟踪地面目标的制导律并完成了稳定性证明;其次,通过控制Follower无人机的速度和航向角逐渐趋近于Leader无人机速度和航向的协同跟踪策略,分别设计了Follower无人机自动跟踪Leader无人机的制导律和编队相位协同制导律并完成了稳定性证明;最后,分别针对静止目标、匀速直线运动目标和变速运动目标的跟踪问题进行了仿真验证,结果表明所提出的制导方法能够实现对不同运动状态地面目标的自动协同跟踪,并且跟踪性能优于基于李雅普诺夫向量法的制导方法。     

Moving scanning emitter tracking by a single observer using time of interception: Observability analysis and algorithm

The target motion analysis (TMA) for a moving scanning emitter with known fixed scan rate by a single observer using the time of interception (TOI) measurements only is investigated in this paper.By transforming the TOI of multiple scan cycles into the direction difference of arrival (DDOA) model,the observability analysis for the TMA problem is performed.Some necessary conditions for uniquely identifying the scanning emitter trajectory are obtained.This paper also proposes a weighted instrumental variable (WIV) estimator for the scanning emitter TMA,which does not require any initial solution guess and is closed-form and computationally attractive.More importantly,simulations show that the proposed algorithm can provide estimation mean square error close to the Cramer-Rao lower bound (CRLB) at moderate noise levels with significantly lower estimation bias than the conventional pseudo-linear least square (PLS) estimator.     

Angle measurement in the presence of mainbeam interference

The problem of reducing interference impinging on an antenna array when the sources lie in the main beam is addressed. Adaptive antenna arrays are incorporated to form adapted sum and difference beams in which the interference signals are suppressed. Monopulse error curves are then obtained, providing the necessary distortion correction curves across the entire mainbeam tracking angle region. New Cramer-Rao (C-R) bounds on the angle estimation error are derived with generalized assumptions on the signal amplitude and phase. The bounds previously derived by others are valid under different conditions. With these generalized assumptions on the signal characteristics, a Monte Carlo simulation is performed, based on the estimation procedure presented, to determine the angle estimation error. These errors are compared with the C-R bounds. Good performance is shown for sufficient S/N₀ and angular separation between the target and the interference sources