Tracking Accuracies with Position and Rate Measurements

Tracking accuracies for the radial component of motion are computed for a track-while-scan radar system which obtains position and rate data during the dwell time on a target These results will be of interest to persons developing trackers for pulse Doppler surveillance radars. The normalized accuracies, computed for a two state Kalman tracking filter with white noise maneuver capability, are shown to depend upon two parameters, r = 4?0/?aT2 and s = ?dT/?0. The symbols ?0 and ?d are the position and rate measurement accuracies, respectively, ?a is the standard deviation of the white noise maneuver process and T is the antenna scan time. The scalar tracking filter equations are derived and numerical results are presented. Lower steady state tracking errors plus the earlier attainment of steady state accuracies are the direct consequence of incorporating the rate measurements into the tracking filter.     

Tracking a maneuvering target using input estimation versus theinteracting multiple model algorithm

Two maneuvering-target tracking techniques are compared. The first, called input estimation, models the maneuver as constant unknown input, estimates its magnitude and onset time, and then corrects the state estimate accordingly. The second models the maneuver as a switching of the target state model, where the various state models can be of different dimension and driven by process noises of different intensities, and estimates the state according to the interacting multiple model (IMM) algorithm. While the first requires around twenty parallel filters, it is shown that the latter, implemented in the form of the IMM, performs equally well or better with two or three filters     

有向拓扑条件下针对机动目标的分布式协同制导律设计

研究了在有向拓扑条件下针对机动目标的分布式协同制导律的设计问题。首先，根据飞行器与目标之间追击过程的几何关系建立制导过程系统模型，针对该模型的非线性问题采用动态反馈线性化方法进行处理。将目标未知机动视为干扰，通过扩张状态观测器进行观测，同时将该估计值用于制导律的设计中，通过直接补偿的方式剔除目标机动对飞行器剩余飞行时间的影响。然后，将所设计的制导律代入到制导模型中，利用一致性分析方法将多飞行器协同制导问题转化为一致性问题，利用极点分析的方法对非一致性子空间的收敛性进行分析，得到协同制导律收敛的充要条件。最后，通过仿真分析的方式对所设计的协同制导律以及制导律的参数选取方法进行分析。     

交互作用的双自适应模型估计器

 通过对目标的不确定机动分析和对不确定机动的模式分类(非机动、临界机动、弱机动、强机动),建立了一种新的目标状态自适应估计器——交互作用的双自适应模型估计器。它通过具有机动识别特性的二阶自适应模型和具有机动水平特性的三阶自适应模型,以及它们之间交互作用自适应组合方式的结合,达到了跟踪估计目标各种运动的“全面”自适应能力。应用新估计器对目标的5种基本运动进行了Monto-carlo仿真。仿真表明,它具有所期望的良好性能。     

An online ensemble semi-supervised classification framework for air combat target maneuver recognition

Online target maneuver recognition is an important prerequisite for air combat situation recognition and maneuver decision-making. Conventional target maneuver recognition methods adopt mainly supervised learning methods and assume that many sample labels are available. However, in real-world applications, manual sample labeling is often time-consuming and laborious. In addition, airborne sensors collecting target maneuver trajectory information in data streams often cannot process information in real time. To solve these problems, in this paper, an air combat target maneuver recognition model based on an online ensemble semi-supervised classification framework based on online learning, ensemble learning, semi-supervised learning, and Tri-training algorithm, abbreviated as Online Ensemble Semi-supervised Classification Framework (OESCF), is proposed. The framework is divided into four parts: basic classifier offline training stage, online recognition model initialization stage, target maneuver online recognition stage, and online model update stage. Firstly, based on the improved Tri-training algorithm and the fusion decision filtering strategy combined with disagreement, basic classifiers are trained offline by making full use of labeled and unlabeled sample data. Secondly, the dynamic density clustering algorithm of the target maneuver is performed, statistical information of each cluster is calculated, and a set of micro-clusters is obtained to initialize the online recognition model. Thirdly, the ensemble K-Nearest Neighbor (KNN)-based learning method is used to recognize the incoming target maneuver trajectory instances. Finally, to further improve the accuracy and adaptability of the model under the condition of high dynamic air combat, the parameters of the model are updated online using error-driven representation learning, exponential decay function and basic classifier obtained in the offline training stage. The experimental results on several University of California Irvine (UCI) datasets and real air combat target maneuver trajectory data validate the effectiveness of the proposed method in comparison with other semi-supervised models and supervised models, and the results show that the proposed model achieves higher classification accuracy.     

Position and Velocity Estimation Via Bearing Observations

The problem of performing target motion analysis using noisy bearing measurements derived from multiple observation platforms or from a single moving observer is addressed. For the latter case, the properties of an estimator based on a Cartesian model of the process are detailed. Methods of providing estimates both before an observer maneuver, when the process is unobservable, and following an observer maneuver are developed. The results of an experimental study are presented.     

Optimal Tracking of Maneuvering Targets

Maneuvering target motion is modeled by introducing a binary random variable in the target state equation. The optimal estimate is shown to be a weighted combination of two Kalman filter estimates with weights depending on the likelihood ratio for the detection of a maneuver. A tracking scheme is proposed for maneuvering target tracking and illustrated in an example.     

高超声速滑翔目标自适应跟踪方法

针对机动模式复杂多变的高超声速滑翔目标跟踪问题，提出了一种机动频率自适应跟踪方法。采用介于常速度和常加速度模型之间的Singer模型来表征目标气动力加速度的变化，从而建立跟踪系统的状态方程。根据地基雷达量测量获得系统的量测方程，鉴于距离和角度信息的量级相差较大将其由球形量测量转换为位置量测量。为了适应高超声速滑翔目标灵活多样的机动模式，基于正交性原理和无迹卡尔曼滤波算法实现了Singer模型中机动频率参数的自适应。利用滤波信息计算得到能够反映状态模型误差大小的调整因子，用于放大Singer模型中的机动频率，进而调整状态方程的过程噪声以降低模型误差。通过对2种典型机动轨迹的跟踪仿真，并与交互式多模型等方法进行比较，结果表明所提方法的跟踪精度高、计算量小，能够较好地适应阶跃机动和连续幅值变化的机动。     

螺旋俯冲机动突防的制导律设计

针对识别和拦截技术高度发展所带来的突防难题，提出高超声速滑翔飞行器（HGV）螺旋俯冲机动突防的概念，并为此设计了一种基于虚拟滑动目标的自适应比例导引律。首先，通过分析HGV绕目标飞行的运动学特性，建立对数型的螺旋运动模型，以该模型为基础利用曲线渐伸线原理设计虚拟目标的滑动轨迹。然后，采用包含时变附加项的比例导引律追踪虚拟目标，从而实现引导HGV进行螺旋俯冲机动以及对真实目标的打击。接着，为提高虚拟目标的跟踪精度以及抵抗外部干扰的能力，设计了制导参数的闭环非线性自适应律，能根据当前偏差在线选择制导参数值。此外，还分析了满足收敛条件的制导参数的取值范围以及其进入闭环更新的策略。最后，分别针对静止目标和低速移动目标进行数值仿真验证，结果表明所设计的制导律不但能够引导HGV实施螺旋俯冲机动，还能够准确地命中目标。     

Detection of Target Maneuver Onset

A classical maneuvering target tracking (MTT) problem (detection of the onset of a target maneuver) is presented in two parts. The first part reviews most traditional maneuver onset detectors and presents results from a comprehensive simulation study and comparison of their performance. Six algorithms for maneuver onset detection are examined: measurement residual chi-square, input estimate chi-square, input estimate significance test, generalized likelihood ratio (GLR), cumulative sum, and marginalized likelihood ratio (MLR) detectors. The second part proposes two novel maneuver onset detectors based on sequential statistical tests. Cumulative sums (CUSUM) type and Shiryayev sequential probability ratio (SSPRT) maneuver onset detectors are developed by using a likelihood marginalization technique to cope with the difficulty that the target maneuver accelerations are unknown. The proposed technique gives explicit solutions for Gaussian-mixture prior distributions, and can be applied to arbitrary prior distributions through Gaussian-mixture approximations. The approach essentially utilizes a~priori information about the maneuver accelerations in typical tracking engagements and thus allows to improve detection performance as compared with traditional maneuver detectors. Simulation results demonstrating the improved capabilities of the proposed onset maneuver detectors are presented.     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

Optimization of observer trajectories for bearings-only targetlocalization

The problem of bearings-only target localization is to estimate the location of a fixed target from a sequence of noisy bearing measurements. Although, in theory, this process is observable even without an observer maneuver, estimation performance (i.e., accuracy, stability and convergence rate) can be greatly enhanced by properly exploiting observer motion to increase observability. This work addresses the optimization of observer trajectories for bearings-only fixed-target localization. The approach presented herein is based on maximizing the determinant of the Fisher information matrix (FIM), subject to state constraints imposed on the observer trajectory (e.g., by the target defense system). Direct optimal control numerical schemes, including the recently introduced differential inclusion (DI) method, are used to solve the resulting optimal control problem. Computer simulations, utilizing the familiar Stansfield and maximum likelihood (ML) estimators, demonstrate the enhancement to target position estimability using the optimal observer trajectories     

带异步相关噪声的战斗机蛇形机动跟踪算法

针对异步相关噪声背景下战斗机蛇形机动模式转弯角速度辨识问题,考虑到目标状态与转弯角速度之间相互耦合的特性,从联合优化的解决思路出发,基于期望最大化（EM）算法框架,提出了一种带异步相关噪声的联合估计与辨识算法。首先采用"去相关框架"解除过程噪声与量测噪声之间的相关性,从而将异步相关噪声背景下的转弯角速度辨识问题转换成具有一步状态延迟的转弯角速度辨识问题,其次通过解除目标状态与转弯角速度之间的非线性耦合关系,基于期望最大化算法实现了战斗机蛇形机动目标状态与转弯角速度的联合估计与辨识,从而获得转弯角速度闭环形式的解析解：在E-step,通过利用异步相关噪声背景下的高阶容积卡尔曼平滑器（HCKS）,获得目标状态的后验估计;在M-step,通过极大化条件似然函数,获得转弯角速度的解析解。最后通过仿真验证了所提算法的目标状态估计与角速度辨识的精度均优越于传统的扩维法。     

Analytical solution of discrete colored noise ECA tracking filter

New analytical solutions of steady-state Kalman gains are presented for a discrete-time tracking filter with correlation in both the measurement noise and the target maneuver. The measurement noise model is a first-order discrete Markov process characterized by a correlation coefficient ρ. The target motion is examined for an exponentially correlated acceleration maneuver type in which the vehicle oscillation such as wind-induced-bending is also considered. The present solution method is based on factorizing the observed spectral density matrix Ψ(z) in frequency domain. The algorithm proposed here gives the Kalman gain matrix directly. For a case when the steady-state error covariance matrix is desired, such gains can be incorporated with the algebraic Riccati equation     

一种二维耦合模型机动目标跟踪算法

针对雷达跟踪固定翼飞机的单目标跟踪问题,提出了一种新的二维耦合运动模型。该方法把切向加速度和法向加速度作为状态变量,给出了切向加速度和法向加速度为常值时解析计算状态转移的方法。该模型可以较好地一步预测目标加速度的变化,而且法向和切向加速度的过程噪声可以分别设置。利用该耦合模型的滤波方法,显著地改善了滤波效果,尤其是对加速度的估计。     

机动目标的模型与跟踪算法

 <正> 在机动目标的“当前”统计模型中,目标的加速度被描述为修正的瑞利—马尔科夫过程,对应的自适应跟踪算法呈现出较好的跟踪特性。文献[2]研究了该模型及其自适应算法在实际的机载雷达跟踪系统的应用;文献[3]进一步推广了基于“当前”模型的MPDAF算法。本文提出一个新的机动目标模型,即假定目标加速度为一高斯—马尔     

基于深度强化学习的无人机栖落机动控制策略设计

无人机栖落机动飞行是一种无需跑道的降落方法，能够提升无人机在复杂环境下执行任务的适应能力。针对具有高非线性、多约束特性的无人机栖落机动过程，提出了一种基于模仿深度强化学习的控制策略设计方法。首先，建立了固定翼无人机栖落机动的纵向非线性动力学模型，并设计了无人机栖落机动的强化学习环境。其次，针对栖落机动状态动作空间大的特点，为了提高探索效率，通过模仿专家经验的方法对系统进行预训练。然后，以模仿学习得到的权重为基础，采用近端策略优化方法学习构建无人机栖落机动的神经网络控制器。最后，通过仿真验证了上述控制策略设计方法的有效性。     

导弹靶弹弹道机动变轨通用控制指令设计

导弹进行一定强度的机动飞行,就能够提高突防能力,因而,在军事训练中需要具有末端机动变轨能力的靶弹.针对靶弹机动变轨弹道的设计问题,提出变轨通用控制指令设计形式,利用此设计可使靶弹位移与过载指令控制信号协调配合,控制靶弹实现跃升机动、蛇行机动、摆式机动和螺旋机动等变轨形式.通过仿真证明,此设计的变轨弹道通用控制指令,可以满足靶弹跃升机动、蛇行机动、摆式机动和螺旋机动等各种变轨形式的弹道设计要求.     

Adaptive nonlinear guidance law considering control loop dynamics

A new adaptive nonlinear guidance law is proposed here. The fourth order state equation for integrated guidance and control loop is formulated taking into consideration the target uncertainties and control loop dynamics. The state equation is further changed into the normal form by nonlinear coordinate transformation. Using the normal form of state equation, an adaptive nonlinear guidance law is proposed to compensate for the uncertainties in both target acceleration and control loop dynamics. The proposed law adopts the sliding mode control approach with adaptation for unknown bound of uncertainties. The present approach can effectively solve the existing guidance problem against target maneuver and the limited performance of control loop. We have provided the stability analyses and performed simulations comparing favorably our approach to the state of the art.