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.     

A Tracking Filter in Spherical Coordinates Enhanced by De-noising of Converted Doppler Measurements

Tracking problem in spherical coordinates with range rate (Doppler) measurements, which would have errors correlated to the range measurement errors, is investigated in this paper. The converted Doppler measurements, constructed by the product of the Doppler measurements and range measurements, are used to replace the original Doppler measurements. A de-noising method based on an unbiased Kalman filter (KF) is proposed to reduce the converted Doppler measurement errors before updating the target states for the constant velocity (CV) model. The states from the de-noising filter are then combined with the Cartesian states from the converted measurement Kalman filter (CMKF) to produce final state estimates. The nonlinearity of the de-noising filter states are handled by expanding them around the Cartesian states from the CMKF in a Taylor series up to the second order term. In the mean time, the correlation between the two filters caused by the common range measurements is handled by a minimum mean squared error (MMSE) estimation-based method. These result in a new tracking filter, CMDN-EKF2. Monte Carlo simulations demonstrate that the proposed tracking filter can provide efficient and robust performance with a modest computational cost.     

Use of measurements from an imaging sensor for precision targettracking

The extraction of measurements for precision tracking of the centroid of a target from a forward-looking infrared imaging sensor is presented. The size of the image of the target is assumed to be small, i.e. around 10 pixels. The statistical characterization of the centroid of the target is obtained. Similarly, the statistical properties of the image correlation of two frames, which measures the target offset, are derived. Explicit expressions that map the video noise statistics into measurement noise statistics are obtained. The offset measurement noise is shown to be autocorrelated. State variable models for tracking the target centroid with these measurements are then presented. Simulation results and quantitative conclusions about achievable subpixel tracking accuracy are given. It is shown that the filter that models the autocorrelated measurement noise provides the best performance     

A Comparison of Binary Delay-Lock Tracking-Loop Implementations

The delay-lock loop is a device for tracking the delay difference between two correlated waveforms. It is used as a synchronizing loop for binary communications and tracking. The delay tracking performance is derived for various radio-frequency implementations of the binary delay-lock loop. Amplitude and biphase modulation by pseudorandom sequences are considered. Three types of receivers are analyzed for each modulation: envelope correlation, phase-coherent correlation, and phase-lock demodulation followed by video correlation.     

Analytical solution for continuous-time Kalman tracking filterswith colored measurement noise in frequency domain

New expressions are given for analytical solutions to the steady-state Kalman gains of the two-state exponentially correlated velocity (ECV) and the three-state exponentially correlated acceleration (ECA) tracking filters with position measurements by using spectral factorization method. The measurement colored noise model is characterized by a correlation time 1/λ. The vehicle oscillations such as wind-induced-bending is also considered in the modeling of the system which leads to the most generalized state transition matrix     

Tracking multiple targets with correlated measurements andmaneuvers

The problem of tracking N targets with correlation in both measurement and maneuver statistics is solved by transforming to a coordinate frame in which the N targets are decoupled. For the case of N identical targets, the decoupling is shown to coincide with a transformation to a set of nested center-of-mass coordinates. Absolute and differential tracking accuracies are compared with suboptimal results to show the improvement that is achieved by properly exploiting the correlation between targets     

Digital tracking filters with high order correlated measurement noise

The existing algorithms for the design of digital filters with colored measurement noise involve a restriction on the dimension of the measurement error model. Kalman filter equations and state space partition are used to formulate an optimal tracking filter without such restrictions. The input to the new filter are two consecutive measurements, and it is initialized by using the first available measurements and the error model correlation matrix. Several examples illustrate the filter formulation and initialization.     

Multiresolutional multiple-model target tracking

A multiresolutional multiple-model target tracking algorithm is developed which uses the wavelet transform as a means for mapping data between different resolution levels. The algorithm is effective for tracking maneuvering targets given measurements with a low S/N ratio     

脉冲干扰对软件接收机的影响分析

卫星信号经过长距离传播,信号能量损耗严重,到达地面的功率很弱,容易受到各种干扰的影响。脉冲干扰为常见的干扰类型,所以针对不同功率、不同周期,以及不同占空比的脉冲干扰信号,通过接收前端采集受脉冲干扰的GPS L1信号,利用软件接收机及多相关器生成技术,详细分析了脉冲干扰对接收机信号捕获与跟踪性能的影响。分析结果表明,周期为1ms的脉冲干扰信号,能对接收机产生强烈的干扰效果,捕获图中的噪声明显增大;跟踪过程中,载噪比和相关值突发性减小,造成跟踪数据异常。而长周期的脉冲信号仅在脉冲到达时影响接收机的捕获和跟踪,但由于信号跟踪不能连续进行,导致伪距观测量的不连续与导航数据不能正常解码,从而干扰接收机。     

Correlation of Multiple-Site Track Data

Tactical air defense systems often require the interchange of target tracking data between two radar sites. This paper presents a systematic and effective procedure, employing correlation gates, for associating , or correlating, track information from one site with that from the other. Using the correlation equation, gate sizes are selected, based on remote and local tracking accuracies, target separation, the number of track coordinates investigated, and the number of successive correlation attempts made, to maximize the selected measure of correlation accuracy. The modeling of physical encounters is discussed and a representative situation is selected for analysis. A variety of correlation procedures are compared in terms of correlation accuracy and ease of implementation.     

Architectures and algorithms for track association and fusion

Target tracking using multiple sensors can provide better performance than using a single sensor. One approach to multiple target tracking with multiple sensors is to first perform single sensor tracking and then fuse the tracks from the different sensors. Two processing architectures for track fusion are presented: sensor to sensor track fusion, and sensor to system track fusion. Technical issues related to the statistical correlation between track estimation errors are discussed. Approaches for associating the tracks and combining the track state estimates of associated tracks that account for this correlation are described and compared by both theoretical analysis and Monte Carlo simulations     

Event-triggered cooperative target tracking in wireless sensor networks

Since the issues of low communication bandwidth supply and limited battery capacity are very crucial for wireless sensor networks, this paper focuses on the problem of event-triggered cooperative target tracking based on set-membership information filtering. We study some fundamental properties of the set-membership information filter with multiple sensor measure-ments. First, a sufficient condition is derived for the set-membership information filter, under which the boundedness of the outer ellipsoidal approximation set of the estimation means is guaranteed. Second, the equivalence property between the parallel and sequential versions of the set-membership information filter is presented. Finally, the results are applied to a 1D event-triggered target tracking scenario in which the negative information is exploited in the sense that the measurements that do not satisfy the triggering conditions are modelled as set-membership mea-surements. The tracking performance of the proposed method is validated with extensive Monte Carlo simulations.     

Tracking multitarget in cluttered environment

A method for multitarget tracking and initiating tracking in a cluttered environment is proposed. The algorithm uses a sliding window of length uT (T is the sampling time) to keep the measurement sequence at time k. Instead of solving a large problem, the entire set of targets and measurements is divided into several clusters so that a number of smaller problems are solved independently. When a set of measurements is received, a new set of data-association hypotheses is formed for all the measurements lying in the validation gates within each cluster from time K-u+1 to K. The probability of each track history is computed, and, choosing the largest of these histories, the target measurement is updated with an adaptive state estimator. A covariance-matching technique is used to improve the accuracy of the adaptive state estimator. In several examples, the algorithm successfully tracks targets over a wide range of conditions     

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。     

MULTISENSOR TRACKING SYSTEM WITH ATTITUDE MEASUREMENTS

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双星编队对空间非合作目标的仅测角跟踪方法

针对单星仅测角对目标跟踪误差较大和不良测量条件下跟踪精度下降的问题,提出利用编队卫星对非合作目标进行联合跟踪的方法。采用考虑地球非球形J2引力摄动的轨道动力学模型,建立多视线测量模型,融合编队卫星对目标的观测数据。然后,基于新息设计增益调节矩阵提高滤波器在测量故障条件下的鲁棒性。最后,建立仿真模型进行验证。仿真结果表明,相比单星跟踪,该方法的位置误差和速度误差分别减少了27.06%和26.96%。在系统存在异常量测时,相比常规滤波,该方法也具有更高的精确性和更好的鲁棒性。     

不完全量测下一类非线性光电跟踪系统滤波器设计

 随着不完全量测条件下探测概率的下降,传统光电跟踪系统的跟踪性能显著降低。为此,本文考虑将俯仰和偏航两个方向的角速度量测引入传统光电跟踪系统,并设计了不完全量测下基于置信度融合的目标跟踪滤波器。首先针对这类新型的光电跟踪系统建立了系统的量测模型,利用嵌套条件方法推导了转换量测误差前两阶矩的一致性估计;然后针对位置探测通道与角速度探测通道的4种数据探测情形设计了4个子滤波器,并根据探测通道的探测情况计算出各子滤波器的置信度,进而对各子滤波器的输出按置信度进行加权融合,得到了跟踪滤波器的全局输出;最后给出了非线性跟踪系统统计意义下的Cramer-Rao下界(CRLB)。Monte-Carlo仿真表明：在不完全量测下,相比传统光电跟踪系统,附加角速度量测的光电跟踪系统的跟踪性能有了显著提高,并且滤波器估计误差均方差(RMSE)已逼近非线性跟踪系统统计意义下的CRLB。     

Heading and Speed Errors for x, y Tracking Filters

Heading and speed errors are analytically determined for noneumavering targets at the output of an x, y tracking filter which processes range and bearing measurements from a radar sensor in a track-while-scan (TWS) operation. These errors are shown to depend upon target range and speed, the angle between the radius and velocity vectors, sensor accuracies, and tracking filter parameters. eters. Depending upon the tracking filter implementation, these errors may also be a function of target bearing.     

Efficient multisensor fusion using multidimensional dataassociation

We present the development of a multisensor fusion algorithm using multidimensional data association for multitarget tracking. The work is motivated by a large scale surveillance problem, where observations from multiple asynchronous sensors with time-varying sampling intervals (electronically scanned array (ESA) radars) are used for centralized fusion. The combination of multisensor fusion with multidimensional assignment is done so as to maximize the “time-depth” in addition to “sensor-width” for the number S of lists handled by the assignment algorithm. The standard procedure, which associates measurements from the most recently arrived S-1 frames to established tracks, can have, in the case of S sensors, a time-depth of zero. A new technique, which guarantees maximum effectiveness for an S-dimensional data association (S⩾3), i.e., maximum time-depth (S-1) for each sensor without sacrificing the fusion across sensors, is presented. Using a sliding window technique (of length S), the estimates are updated after each frame of measurements. The algorithm provides a systematic approach to automatic track formation, maintenance, and termination for multitarget tracking using multisensor fusion with multidimensional assignment for data association. Estimation results are presented for simulated data for a large scale air-to-ground target tracking problem     

Removal of Out-of-Sequence Measurements from Tracks

In multisensor tracking systems that operate in a centralized or distributed information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence due to system latencies. In order to avoid either a delay in the output or the need for reordering and reprocessing entire sequences of measurements, such latent measurements have to be processed by the tracking filter as out-of-sequence measurements (OOSM). Recent work developed a "one-step" procedure for incorporating OOSM with multiple-time-step latency into the tracking filter, which, while suboptimal, was shown to yield results very close to those obtained by reordering and reprocessing an entire sequence of measurements. The counterpart of this problem is the need to remove (revocate) measurements that have already been used to update a track state. This can happen in real-world systems when such measurements are reassigned to another track. Similarly to the problem of update with an OOSM, it is desired to carry out the removal of an earlier measurement without recomputing the track estimate (and the data association) using possibly a long sequence of subsequent measurements one at a time. A one-step algorithm is presented for this problem of removing a multistep OOSM.