A Kalman Filter Based Tracking Scheme with Input Estimation

Beginning with the derivation of a least squares estimator that yields an estimate of the acceleration input vector, this paper first develops a detector for sensing target maneuvers and then develops the combination of the estimator, detector, and a "simple" Kalman filter to form a tracker for maneuvering targets. Finally, some simulation results are presented. A relationship between the actual residuals, assuming target maneuvers, and the theoretical residuals of the "simple" Kalman filter that assumes no maneuvers, is first formulated. The estimator then computes a constant acceleration input vector that best fits that relationship. The result is a least squares estimator of the input vector which can be used to update the "simple" Kalman filter. Since typical targets spend considerable periods of time in the constant course and speed mode, a detector is used to guard against automatic updating of the "simple" Kalman filter. A maneuver is declared, and updating performed, only if the norm of the estimated input vector exceeds a threshold. The tracking sclheme is easy to implement and its capability is illustrated in three tracking examples.     

Interacting acceleration compensation algorithm for trackingmaneuvering targets

The two-stage Kalman estimator has been studied for state estimation in the presence of random bias and applied to the tracking of maneuvering targets by treating the target acceleration as a bias vector. Since the target acceleration is considered a bias, the first stage contains a constant velocity motion model and estimates the target position and velocity, while the second stage estimates the target acceleration when a maneuver is detected, the acceleration estimate is used to correct the estimates of the first stage. The interacting acceleration compensation (IAC) algorithm is proposed to overcome the requirement of explicit maneuver detection of the two-stage estimator. The IAC algorithm is viewed as a two-stage estimator having two acceleration models: the zero acceleration of the constant velocity model and a constant acceleration model. The interacting multiple model (IMM) algorithm is used to compute the acceleration estimates that compensate the estimate of the constant velocity filter. Simulation results indicate the tracking performance of the IAC algorithm approaches that of a comparative IMM algorithm while requiring approximately 50% of the computations     

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。     

Target tracking in maneuver-centered coordinates

Aircraft targets normally maneuver on circular paths, which has led to tracking filters based on circular turns. A coordinate system to track circular maneuvers with a simple Kalman filter is introduced. This system is a polar coordinate system located at the center of the maneuver. It leads to a tracking filter with range, angle, and angular velocity in the state vector. Simulation results are presented, showing that the algorithm displays improved performance over methods based on constant x-y acceleration when tracking circular turns     

机动多目标跟踪问题中关联区域的研究

 本文研究了跟踪多个机动目标时,由滤波算法所获得的新息向量范数的统计性质,关联区域的大小以及接收正确回波的概率。借助拉蒙特卡洛方法,考察了不同的目标状态模型、目标机动加速度及状态噪声方差等因素对所研究的问题的影响。研究表明,文献[1]所提出的机动目标状态模型及相应的自适应算法具有较好的适应目标机动的能力,关联区域的大小及接收正确回波的概率均较为稳定。     

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     

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“当前”统计模型与自适应跟踪算法

本文提出机动目标“当前”统计模型的概念并建议用修正的瑞利-马尔科夫过程描述目标随机加速机动的统计特性。文中指出了在机动目标运动模型中状态（机动加速度）估值与状态噪声之间的内在联系。在此基础上提出了具有机动加速度均值及方差自适应的卡尔曼滤波算法。对一维和三维的情形进行了计算机模拟。计算结果表明,在仅对目标位置进行观测的情况下,这类自适应估值算法无论对高度机动或无机动的目标均可绘出较好的位置、速度及加速度估值。     

基于直升机/涡轴发动机综合仿真平台的发动机非线性模型预测控制

 基于具有可靠置信度的直升机/涡轴发动机综合仿真平台,研究了涡轴发动机带约束优化的非线性模型预测控制(NMPC)技术。首先通过设计多输出迭代约简最小二乘支持向量回归机(RRLSSVR),训练具有较好实时性、精度及泛化能力的内嵌式预测模型,在高度0~5 km、前飞速度0~75 m/s范围内模型精度达5‰。其次,考虑了扭矩、燃油流量、动力涡轮转速、燃气涡轮转速等综合信息及相关约束对控制效果的影响,利用在线序列二次规划(SQP)算法实现滚动优化控制,而后加入目标转速偏差的积分项以消除静差,保证输出恒定。最后,通过对直升机进行机动飞行大扰动仿真验证了该预测控制器对扰动的抑制能力,相比传统串级PID控制,能够显著降低动力涡轮转速下垂/超调量,达到更好的控制品质。     

一种基于径向加速度的Singer-EKF机动目标跟踪算法

针对雷达均不能提供目标加速度信息,在目标机动时会出现跟踪精度差甚至跟踪发散的问题,提出一种基于径向加速度的Singer-EKF算法。该算法在信号处理阶段利用Radon-Ambiguity变换（RAT）估计出目标的径向加速度,并通过坐标转换将其引入量测向量中,然后采用基于Singer模型的扩展卡尔曼滤波（EKF）算法实现机动目标的跟踪。仿真验证了该方法的有效性,并与传统的不带径向加速度的扩展卡尔曼滤波（EKF）方法进行了比较,结果表明该方法在径向距离、位置、加速度和速度估计精度方面都有所提高。     

Modeling and Estimation for Tracking Maneuvering Targets

A new approach to the three-dimensional airborne maneuvering target tracking problem is presented. The method, which combines the correlated acceleration target model of Singer [3] with the adaptive semi-Markov maneuver model of Gholson and Moose [8], leads to a practical real-time tracking algorithm that can be easily implemented on a modern fire-control computer. Preliminary testing with actual radar measurements indicates both improved tracking accuracy and increased filter stability in response to rapid target accelerations in elevation, bearing, and range.     

A Kalman Tracker with a Simple Input Estimator

Two Kalman filter based schemes are proposed for tracking maneuvering targets. Both schemes use least squares to estimate a target's acceleration input vector and to update the tracker by this estimate. The first scheme is simpler and by an approximation to its input estimator the computation can be considerably reduced with insignificant performance degradation. The second scheme requires two Kalman filters and hence is more complex. However, since one of its two filters assumes input noise, it may outperform the first scheme when input noise is indeed present. A detector that compares the weighted norm of the estimated input vector to a threshold is used in each scheme. Its function is to guard against false updating of the trackers and to keep the error covariance small during constant velocity tracks. Simulation results for various target profiles are included. They show that in terms of tracking performance, both schemes are comparable. However, because of its computation simplicity, the first scheme is far superior.     

Validation and comparison of coordinated turn aircraft maneuvermodels

A major challenge posed by aircraft tracking problems is the nondeterministic nature of an aircraft flight, due to the difficulty of predicting the pilot's actions. Accurate aircraft maneuver models are however highly desirable, particularly in air defense applications, to achieve accurate tracking and prediction. Through analysis of actual fighter aircraft trajectories and comparison with the Singer maneuver model, particularly in terms of prediction performance, coordinated turn (CT) aircraft maneuver models are presented, compared, and validated. A more general CT model is shown to better model actual trajectories than the classical CT model used in the literature     

Incremental maneuver estimation model for target tracking

An incremental model for maneuver detection and estimation for use in target tracking with the Kalman filter is described. The approach is similar to the multiple Kalman filter bank, but with a memory for the maneuver status for the track under consideration. The advantage of this approach is that the target acceleration can be more accurately estimated. The maneuver-detection model has shown good maneuver-following capability. Moreover, it needs only a finite number of Kalman filters to handle all possible maneuver values and it responds quickly as maneuver occurs. When there is an abrupt maneuver change the model can still track the targets in short time     

Observability of an integrated GPS/INS during maneuvers

An observability analysis of a GPS/INS system during manoeuvers is presented based upon a perturbation model with respect to the Earth-centered-Earth-fixed (ECEF) coordinate system. Analysis is performed on two types of manoeuvers, linear acceleration and steady turn. These manoeuvers could be used for in-flight INS alignment using GPS. During the constant linear acceleration without rotation relative to the Earth, the linear system model is shown to be time-invariant. The observability analysis for the time invariant linear system model shows that linear acceleration does not change the number of observable modes but rather the structure of the observable space. For a nonconstant linear acceleration or a steady turn, the perturbation linear system becomes time varying. For this time-varying system, three types of observability are considered, complete, differential, and instantaneous observability. Instantaneous observability is the strongest properties and means that the state of the system at any time may be determined instantaneously from observation of the output and its derivatives. Instantaneous observability is important for fast in-flight INS alignment. It is shown that the number of instantaneously observable moded is increased by at least 2 during a maneuver. Hence, some linear combinations of the attitude angles become instantaneously observable.     

航空拖曳诱饵系统机动过程缆绳张力仿真

为解决航空拖曳诱饵系统研制过程中拖曳缆绳强度设计问题,对拖曳诱饵系统机动过程缆绳张力进行了仿真研究。仿真中建立了缆绳的质量弹簧阻尼模型和诱饵弹的六自由度动力学模型,研究了直线加速和机动转弯2个典型飞行动作中缆绳受力情况,分析了载机加速度、飞行高度、缆绳弹性模量、缆绳直径等因素对缆绳张力的影响。结果表明：缆绳中张力大小不仅与诱饵弹、缆绳的气动阻力、重力有关,还与它们的惯性力有关;由于张力在缆绳中传递存在时滞性,机动过程中缆绳张力存在波动现象,波动的剧烈程度与载机加速度、缆绳弹性模量、缆绳直径有关;机动转弯过程中,缆绳会承受一个较大的峰值应力,该应力随着转弯角速度的增大而增大。     

A Decision?Directed Adaptive Tracker

In the design of a tracking filter for air traffic control (ATC) applications, a maneuvering aircraft can be modelled by a linear system with random noise accelerations. A Kalman filter tracker, designed on the basis of a variance chosen according to the distribution of the potential maneuver accelerations, will maintain track during maneuvers and provide some improvement in position accuracy. However, during those portions of the flight path where the aircraft is not maneuvering, the tracking accuracy will not be as good as if no acceleration noise had been allowed in the tracking filter. In this paper, statistical decision theory is used to derive an optimal test for detecting the aircraft maneuver; a more practical suboptimal test is then deduced from the optimal test. As long as no maneuver is declared, a simpler filter, based on a constant-velocity model, is used to track the aircraft. When a maneuver is detected, the tracker is reinitialized using stored data, up-dated to the present time, and then normal tracking is resumed as new data arrives. In essence, the tracker performs on the basis of a piecewise linear model in which the breakpoints are defined on-line using the maneuver detector. Simulation results show that there is a significant improvement in tracking capability using the decision-directed adaptive tracker.     

True proportional navigation with maneuvering target

We analytically obtain the capture regions for the true proportional navigation (TPN) missile guidance law against an intelligently maneuvering target. Two versions of TPN are considered. The first is the original TPN which assumes the commanded lateral acceleration to be directly proportional to the line-of-sight (LOS) rate only, the proportionality factor being an arbitrary constant or dependent only on the initial closing velocity. The other, known as RTPN (realistic TPN), assumes the commanded lateral acceleration to be directly proportional to the LOS rate and also the current closing velocity. The target is assumed to maneuver in such a way as to increase the LOS rate and thus directly oppose the proportional navigation (PN) philosophy of annulling the LOS rate. A necessary and sufficient condition for capture is derived for the original TPN, and using it, the exact capture region is obtained. A sufficient condition for capture is derived for RTPN and is used to obtain its capture region partially. Some necessary conditions for capture are also derived for RTPN and are used to obtain an upper bound on its complete capture region. Using these conditions some important results on the existence of capture regions and a comparative study of capturability of TPN laws are also presented     

机动飞行飞行器内具有初始弯曲和刚度不对称的转子运动模型

本文建立了位于机动飞行飞行器内且同时具有初始弯曲、不对称刚度和质量不平衡的单盘Jeffcott转子的动力学模型。当飞行器静止时,设相关参数为零后该模型与相应地面转子系统的数学模型完全相同。应用该模型可数值仿真研究飞行器运动时位于飞行器内的等转速、等加速、等减速运行转子的动态特性,研究飞行器不同飞行速度和加速度对转子动力学特性的影响,分析飞行器飞行时转子出现故障时的响应特性,从而为机动飞行器内转子的动力学分析和故障诊断提供依据。     

考虑空间机动飞行的直升机尾传动轴建模与临界转速分析

建立了具有普遍性的考虑直升机空间机动飞行的尾传动轴动力学模型.分析了机动飞行对尾传动轴临界转速的影响,发现只有俯仰角速度、偏航角速度、横滚角速度和角加速度4个转动运动分量会影响尾传动轴的临界转速.通过算例着重分析了俯仰、偏航和横滚角速度对尾传动轴前3阶临界转速的影响规律.结果表明:俯仰角速度使尾传动轴的临界转速降低,但只对反进动第1阶临界转速有较大影响;偏航角速度对尾传动轴临界转速的影响效果与俯仰角速度完全相同;正向横滚角速度使尾传动轴的正进动临界转速提高,而使反进动临界转速降低;但对于反向横滚,在以横滚角速度等于某值的分界线之前,横滚角速度对尾传动轴临界转速的影响规律与正向横滚相反,前3阶临界转速变化曲线的分界线对应的横滚角速度分别为1.86,27.41,124.5rad/s.