Observability Requirements for Three-Dimensional Tracking via Angle Measurements

Observability requirements previously established for bearings-only tracking in two dimensions are extended to a class of three-dimensional estimation algorithms capable of processing any pairwise combination of azimuth bearing, conical bearing, and depth/elevation angle measurements. Although these algorithms are intrinsically nonlinear, it is shown that they can be analyzed in a linear framework without sacrificing mathematical rigor. A simplified observability criterion, applicable to both autonomous and nonautonomous linear systems, is presented and utilized to specify conditions on own-ship motion which are both necessary and sufficient for a unique tracking solution. Further analysis reveals that observability dependence on own-ship maneuvers for the three-dimensional algorithms considered here parallels the concomitant two-dimensional requirements. An interesting difference, however, is that under certain conditions, a unique tracking solution can be obtained in three dimensions for unaccelerated own-ship motion.     

Observability Criteria for Bearings-Only Target Motion Analysis

The observability requirements for bearings-only target motion analysis (TMA) are rigorously established by solving a third-order nonlinear differential equation. Closed form expressions are developed and subsequently used to specify necessary and sufficient conditions on own-ship motion that insure a uniquetracking solution. It is shown that for certain types of maneuvers the estimation process remains unobservable, even when the associated bearing rate is nonzero. Such maneuvers are frequently overlooked in heuristic discussions of TMA observability, which may account for some common misconceptions regarding the characteristics of acceptable own-ship motion.     

Multi-objective approach in GNSS code discriminator design

In spread spectrum ranging system receivers such as the Global Navigation Satellite System (GNSS) receivers, a discriminator is used in the code tracking loop to provide an error signal for the tracking of incoming signals. Typically, the discriminator manipulates several correlator outputs to form the correction signal. A multi-objective approach is adopted here to design the coefficients associated with a multi-correlator-based discriminator to lead to a better performance tradeoff in large tracking range, acceptable multipath-induced bias, high sensitivity, free of ambiguity, and small variance. It is shown that the multiple-objective problem can be tackled via a quadratic/linear programming method, rendering the optimal coefficient vector for the implementation of the discriminator. In addition, as the discriminator design is often subject to conflicting requirements, it is shown that the proposed design approach is capable of establishing bounds on achievable performance. Examples with respect to BPSK (binary phase-shift keying) NRZ (nonreturn-to-zero), and BOC (binary-offset carrier) signals are given to illustrate the design approach.     

增广误差模型算法在目标跟踪中的应用

针对目标机动运行过程中,滤波模型与机动状态模型失配的问题,提出了一种新的增广状态误差滤波模型。不同于现有增广方案,该模型从模型失配所致状态滤波误差的角度出发,将状态估计误差增广为一状态量,通过滤波估计后用其校正原状态量。算法分析表明,该增广滤波模型具有自适应调节多重渐消因子的等效特性,增强了对目标的跟踪能力。基于该增广状态误差滤波模型,给出了滤波算法设计并进行了仿真实验。实验结果表明,基于该模型的滤波算法在对机动目标进行跟踪时具有更强的鲁棒性。     

地球静止卫星精密测定轨技术的现状及发展

介绍并分析了针对地球静止卫星的各种高精度测定轨跟踪技术.指出测距系统的校正误差是常规测距跟踪网定轨在沿迹方向和法向的主要误差源,为保证一致的卫星三维位置解算精度,应利用高分辨率的角度观测约束信息来有效地降低测距偏差对轨道确定的影响,或者利用天地基联合定轨的低轨卫星运动几何在轨道改进的同时精化测距偏差.     

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     

Adaptive Correlation Regions for Alpha-Beta Tracking Filters

The design of correlation regions for track-while-scan systems is examined, assuming the requirement to maintain a constant probability of successful correlation. Starting with the assumption of independent and Gaussian-distributed range and azimuth errors in the sensor and assuming a constant-coefficient isotropic ?-? tracking filter, it is shown how the correlation region design must include such factors as sensor errors, timing jitter, tracking errors, and the asynchronous operation of the tracking function with respect to the sensor measurements. For a maneuvering target, it is shown that the size of the correlation region must be equal to the sum of the radius used for the straight-line case plus the magnitude of any tracking bias which results from deviation from the straight-line trajectory assumed in the tracking filter. An upper bound is derived for the magnitude of the bias which could reasonably be expected in typical maneuvers. By specifying the size of the correlation region on a constant probability basis, it is possible to obtain better discrimination against false targets and improved detection of maneuvers by sensing the development of tracking biases.     

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     

基于I、Q信号的北斗接收机跟踪环路设计

传统的北斗接收机一般采用标量跟踪环,每个通道的卫星相互独立,在此 基础上,又发展起来了基于矢量跟踪的接收机,使每个通道的卫星跟踪不再相互独立。 提出的基于I、Q 信号观测的接收机跟踪环路,保留矢量跟踪的特点,并且采用EKF 作 为跟踪环路预处理滤波器,代替传统跟踪环路的鉴别器,可以在高动态的环境下对卫星 信号进行跟踪,提高环路的稳定性,从而可以有效地提高BDS/INS 深组合导航滤波器观 测量的估计精度。主要对高动态信号跟踪进行仿真,并与传统的标量跟踪方法和矢量跟 踪方法的跟踪能力进行比较。实验表明, 改进的矢量跟踪环能够在高动态的环境下运 行,比起传统环路有更小的跟踪误差。     

Optical Calibration of Geostationary Satellite Tracking Systems

A precise calibration method for range and angle observation has been developed for eliminating the systematic error of tracking systems, thus improving the accuracy of orbit determination for geostationary satellites. The principle of calibration is based on an orbit determination employing a point of optical angle observation in addition to radio tracking observation, in which we estimate observation bias parameters simultaneously with orbital elements, including the effects of geodetic mismodelings. As shown by an actual calibration experiment in our ground station, orbit determinations is sufficiently accurate that the error of predicting satellite range falls within a few meters at four days after the day of orbit determination.     

Passive sonar fusion for submarine C2 systems

The most important sensors for gathering target information onboard a submarine are passive sonars. Problems concerning fusion of these passive sonars are discussed. Three typical passive sonars-passive noise sonar, passive ranging sonar and acoustic pulse surveillance sonar-constitute a passive sonar system for data fusion. This paper is concerned mainly with problems of significance in system development, such as tactical application background, special fusion techniques and own-ship maneuver considerations     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

应用卡尔曼滤波的机载雷达跟踪系统

本文论述将滤波理论应用于机载雷达中对单个目标进行距离、速度、方位角和高低角跟踪的多环反馈系统。首先根据目标和天线的相对运动建立控制四坐标跟踪环所需的状态矢量微分方程,然后推导相应的非线性滤波算法。最后给出计算机的模拟结果。计算机模拟的结果清晰地说明采用最佳滤波的系统性能比通常的有很大改善,并且这种瞄准轴坐标系的最佳系统对目标的随机机动是不灵敏的。 本文所讨论的方法和得出的结论可以延用到地面雷达、舰载雷达以及其他有源和无源的跟踪系统。     

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。     

空基多雷达航迹抗差关联算法

基于高斯随机矢量统计特性,推导出一种适用于探测距离较远、系统误差时变、雷达上报目标不一致等复杂环境的空基多雷达航迹抗差关联算法。分解航迹距离矢量,对消系统误差矢量得出适用于3个及3个以上雷达的航迹抗差关联条件和流程。分别设置了目标密集程度、随机误差和系统误差适应性实验验证算法性能。仿真结果表明所提算法的关联准确性和复杂环境适应性相比现有的基于参照拓扑特征的航迹关联算法（RET算法）和基于距离检测的可信关联算法（confidential算法）有较大幅度的提升。     

基于鉴相器的矢量跟踪环设计

基于鉴相器的矢量跟踪环是锁定导航卫星码和载波的一种跟踪算法,这种算法适合于在弱信号环境下进行跟踪。矢量环不仅充分利用信号跟踪和导航状态解算之间的内在耦合关系,而且每一通道中采用鉴相器和锁频环结合的方式,系统一步内完成信号跟踪和导航解算任务。反馈控制量NCO是由导航滤波器和环路内部滤波器共同产生。实验表明,矢量跟踪环具有快速重捕获特性,能够在弱信号的环境下运行,比起传统环路有更小的跟踪误差。     

Codes cross-correlation analysis and data/pilot code pairs optimization for Galileo E1 OS and GPS L1C

The Galileo E1 open service (OS) and the global positioning system (GPS) L1C are intending to use the multiplexed binary offset carrier (MBOC) modulation in E1/L1 band, including both pilot and data components. The impact of data and pilot codes cross-correlation on the distortion of the discriminator function (i.e., the S-curve) is investigated, when only the pilot (or data) components of MBOC signals are tracked. It is shown that the modulation schemes and the receiver configuration (e.g., the correlator spacing) strongly affect the S-curve bias. In this paper, two methods are proposed to optimize the data/pilot code pairs of Galileo E1 OS and GPS L1C. The optimization goal is to obtain the minimum average S-curve bias when tracking only the pilot components a the specific correlator spacing. Figures of merit, such as S-curve bias, correlation loss and code tracking variance have been adopted for analyzing and comparing the un-optimized and optimized code pairs. Simulation results show that the optimized data/pilot code pairs could significantly mitigate the intra-channel codes cross-correlation, and then improve the code tracking performance of MBOC signals.     

Kalman Filter Behavior in Bearings-Only Tracking Applications

The extended Kalman filter applied to bearings-only target tracking is theoretically analyzed. Closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability (i.e., premature covariance collapse and divergence). Further investigation reveals that conventional initialization techniques often precipitate such anomalous behavior. These results have important practical implications and are not presently being exploited to full advantage. In particular, they suggest that substantial improvements in filter stability can be realized by employing alternative initialization and relinearization procedures. Some candidate methods are proposed and discussed.     

Multiple model particle flter track-before-detect for range ambiguous radar

The middle pulse repetition frequency（MPRF）and high pulse repetition frequency（HPRF）modes are widely adopted in airborne pulse Doppler（PD）radar systems,which results in the problem that the range measurement of targets is ambiguous.The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio（SNR）is high enough.In this paper,a multiple model particle flter（MMPF）based track-beforedetect（TBD）method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment.By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number（PIN）as components of the target state vector,and modeling the incremental variable of the PIN as a three-state Markov chain,the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state fltering problem.At last,the hybrid fltering problem is implemented by a MMPF-based TBD method in the Bayesian framework.Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously,and succeeds in detecting and tracking weak targets with the range ambiguous radar.Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis（MH）method in low-SNR environment.