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.     

基于决策不确定性的多目标跟踪传感器管理

针对高杂波、电子干扰环境,在量测驱动的多目标滤波框架下提出了一种基于决策不确定性的传感器管理方法。首先,根据部分可观测马尔科夫决策过程的理论,给出了基于Rényi信息增量的传感器管理一般方法。其次,综合考虑决策过程的信息完整性、信息质量、信息的内涵等因素,在量测驱动的自适应滤波框架下,基于目标运动态势评估多目标决策不确定性水平,并选取最大决策不确定性目标。最后,以最大决策不确定性目标的信息增量最大化为准则进行传感器分配方案的求解。仿真实验表明所提方法能够有效抑制电子干扰、杂波对多目标跟踪及传感器分配的影响,与基于威胁的传感器管理方法相比,所提方法的平均最优子模式分配（OSPA）距离及平均计算时长均显著降低,且在高杂波、电子干扰情形下具有较高的可靠性。     

Shifted Rayleigh filter: a new algorithm for bearings-only tracking

A new algorithm, the "shifted Rayleigh filter," is introduced for two- or three-dimensional bearings-only tracking problems. In common with other "moment matching" tracking algorithms such as the extended Kalman filter and its modern refinements, it approximates the prior conditional density of the target state by a normal density; the novel feature is that an exact calculation is then performed to update the conditional density in the light of the new measurement. The paper provides the theoretical justification of the algorithm. It also reports on simulations involving variants on two scenarios, which have been the basis of earlier comparative studies. The first is a "benign" scenario where the measurements are comparatively rich in range-related information; here the shifted Rayleigh filter is competitive with standard algorithms. The second is a more "extreme" scenario, involving multiple sensor platforms, high-dimensional models and noisy measurements; here the performance of the shifted Rayleigh filter matches the performance of a high-order bootstrap particle filter, while reducing the computational overhead by an order of magnitude.     

Information space of sensor networks: Lagrangian,energy-momentum tensor,and applications

It is a challenge to investigate the interrelationship between the geometric structure and performance of sensor networks due to the increasingly complex and diverse architecture of them. This paper presents two new formulations for the information space of sensor networks, including Lagrangian and energy–momentum tensor, which are expected to integrate sensor networks target tracking and performance evaluation from a unified perspective. The proposed method presents two geometric objects to represent the dynamic state and manifold structure of the information space of sensor networks. Based on that, the authors conduct the property analysis and target tracking of sensor networks. To the best of our knowledge, it is the first time to investigate and analyze the information energy–momentum tensor of sensor networks and evaluate the performance of sensor networks in the context of target tracking. Simulations and examples confirm the competitive performance of the proposed method.     

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 using infrared measurements and laser illumination

A missile target tracker is designed using a filter/correlator (with adaptive target shape identification) based on forward-looking infrared (FLIR) sensor measurements to track the center-of-intensity of the hardbody/plume combination, and another filter using Doppler and/or speckle information in the return from a low-power laser illuminator to estimate the offset between the intensity centroid and the hardbody center-of-mass. The Doppler information is shown to yield smaller bias and error variance from the tracker than the speckle information. Performance of trackers based on just Doppler or both Doppler and speckle information from the laser return is portrayed as a function of important parameters in the tracking environment     

The Tracking Index: A Generalized Parameter for ? ? ? and ? ? ? ? Target Trackers

A generalized, optimal filtering solution is presented for the target tracking problem. Applying optimal filtering theory to the target tracking problem, the tracking index, a generalized parameter proportional to the ratio of the position uncertainty due to the target maneuverability to that due to the sensor measurement, is found to have a fundamental role not only in the optimal steady-state solution of the stochastic regulation tracking problem, but also in the track initiation process. Depending on the order of the tracking model, the tracking index solution yields a closed form, consistent set of generalized tracking gains, relationships, and performances. Using the tracking index parameter, an initializing and tracking procedure in recursive form, realizes the accuracy of the Kalman filter with an algorithm as simple as the well-known ? ? ? filter or ? ? ? ? ? filter depending on the tracking order.     

Adaptive Phased-Array Tracking in ECM using Negative Information

Target tracking with adaptive phased-array radars in the presence of standoff jamming presents both challenges and opportunities to the track filter designer. A measurement likelihood function is derived for this situation which accounts for the effect of both positive and negative contact information. This likelihood function is approximated a? a weighted sum of Gaussian terms consisting of both positive and negative weights, accounting for the positive and negative contact information. Additionally, recent theoretical results have been reported which have derived an accurate measurement error covariance in the vicinity of the jammer when adaptive beamforming is used by the radar to null the effects of the jammer. We compare the impact of using a likelihood function that accounts for negative contact information and the corrected measurement error covariance by comparing five Kalman filter-based trackers in five different scenarios. We show that only those track filters which use both the negative contact information and the corrected measurement error covariance are effective in maintaining track on a maneuvering target as it passes through the jamming region. This approach can also be generalized to any target tracking problem where the sensor response is anisotropic.     

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     

Track labeling and PHD filter for multitarget tracking

Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approaches (as, e.g., MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter has been proposed and particle filtering techniques have been developed to implement the PHD filter. In the particle PHD filter, the track labeling problem is not considered, i.e., the PHD is obtained only for a frame at a time, and it is very difficult to perform the multipeak extraction, particularly in high clutter environments. A track labeling method combined with the PHD approach, as well as considering the finite resolution, is proposed here for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD in the resolution cell to get the estimated number and locations of the targets at each time step, and then perform the track labeling ("peak-to-track" association), whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard particle PHD filter. For example, in group target tracking, if we are interested in the motion of a specific target, we can track this target, which is not possible for the standard particle PHD filter, since the standard particle PHD filter does not keep track labels. Using our approach, multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging, and termination     

The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance

This note deals with the effect of the common process noise on the fusion (combination) of the state estimates of a target based on measurements obtained by two different sensors. This problem arises in a multisensor environment where each sensor has its information processing (tracking) subsystem. In the case of an ?-? tracking filter the effect of the process noise is that, over a wide range of its variance, the uncertainty area corresponding to the fused estimates is about 70 percent of the single-sensor uncertainty area as opposed to 50 percent obtained if the dependence is ignored.     

A Self-organizing Bearings-only Target Tracking Algorithm in Wireless Sensor Network

In the bearings-only target tracking, wireless sensor network (WSN) collects observations of the target direction at various nodes and uses an adaptive filter to combine them for target tracking. An efficient network management is necessary to gain an optimal tradeoff between locating accuracy and energy consumption. This article proposes a self-organizing target tracking algorithm to select the most beneficial subset of nodes to track the target at every snapshot. Compared with traditional methods, this scheme avoids the need for keeping global position information of the network as in greedy selection. Each node judges its future usefulness depending on the knowledge of its own position and using simple mathematics computation. Simulations indicate that this scheme has locating accuracy comparable to the global greedy algorithm. Also, it has good robustness against node failure and autonomous adaptability to the change of the network scale. Furthermore, this algorithm consumes limited energy because only a portion of nodes partakes in the selection at every snapshot.     

A three-state Kalman tracker using position and rate measurements

A three-state Kalman tracker is described for tracking a moving target, such as an aircraft, making use of the position and rate measurements obtained by a track-white-scan radar sensor which employs pulsed Doppler processing, such as the moving target detector providing unambiguous Doppler data. The steady-state filter parameters have been analytically obtained under the assumption of white noise maneuver capability. The numerical computations of these parameters are in excellent agreement with those obtained from the recursive Kalman filter matrix equations. The solution for the case when only the range measurements are available is obtained as a special case of this model. Graphs of normalized covariances and gains are presented to illustrate how the solution depends on different parameters     

A pure-Cartesian formulation for tracking filters

A pure-Cartesian formulation is presented for angle-only and angle-plus-range tracking filters. Unlike conventional angle-only filters, which use target elevation and bearing as measurements, the filter expresses the sensor measurements in Cartesian coordinates. Consequently, the filter performs equally well for any line-of-sight (LOS) geometry, even when target elevation approaches or is equal to ±90°     

Efficient Approximation of Kalman Filter for Target Tracking

A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.     

Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets

The majority of tactical weapons systems require that manned maneuverable vehicles, such as aircraft, ships, and submarines, be tracked accurately. An optimal Kalman filter has been derived for this purpose using a target model that is simple to implement and that represents closely the motions of maneuvering targets. Using this filter, parametric tracking accuracy data have been generated as a function of target maneuver characteristics, sensor observation noise, and data rate and that permits rapid a priori estimates of tracking performance to be made when maneuvering targets are to be tracked by sensors providing any combination of range, bearing, and elevation measurements.     

多目标跟踪的概率假设密度粒子滤波

在多目标跟踪中,当目标数很大时,目标状态的联合分布的计算量会非常大。如果目标独立运动,可用各目标分别滤波来代替,但这要求考虑数据互联问题。文章介绍一种可以解决计算量问题的方法,只需计算联合分布的一阶矩——概率假设密度(PHD),PHD在任意区域S上的积分是S内目标数的期望值。因未记录目标身份,避免了数据互联问题。仿真中,传感器为被动雷达,目标观测值为距离、角度及速度时,对上述的PHD滤波进行了粒子实现,并对观测值是否相关的不同情况进行比较。PHD粒子滤波应用在非线性模型的多目标跟踪,实验结果表明,滤波可以稳健跟踪目标数为变数的情况,得到了接近真实情况的结果。     

Track monitoring when tracking with multiple 2D passive sensors

A fast method of track monitoring is presented which determines what tracks are good and what tracks have had data association problems and should be eliminated. The philosophy of tracking in a dense target environment with limited central processing unit (CPU) time is to acquire the targets, track them with as simple a filter as will meet requirements, and monitor the tracks to determine if they are still tracking a target or are tracking incorrect returns and should be terminated. After termination the true targets are reacquired. However, it is difficult to determine from simple track monitoring the correct interpretation of a poor track. Poor tracks can be a result of a sensor failure, target maneuver, or incorrect data association. The author describes track monitoring and provides a solution to this dilemma when tracking with multiple two-dimensional passive sensors. The method is much faster than other monitoring methods.<>     

一种对多传感器异步数据的融合处理方法

在传感器异步采样时刻情况下 ,对机动目标的跟踪滤波算法进行了探讨 ,基于细分时间片的方法 ,提出了一种将多传感器数据组合成类似于单传感器数据的异步数据处理方法 ,运用于目标点迹航迹的合成。通过对多传感器数据的利用 ,增大对目标观测的数据流数据率 ,来提高跟踪精度。仿真实验显示 ,各通道的均方根误差均相对减小 ,表明了算法的可行性。     

Tracking with classification-aided multiframe data association

In most conventional tracking systems, only the target kinematic information from, for example, a radar or sonar or an electro-optical sensor, is used in measurement-to-track association. Target class information, which is typically used in postprocessing, can also be used to improve data association to give better tracking accuracy. The use of target class information in data association can improve discrimination by yielding purer tracks and preserving their continuity. In this paper, we present the simultaneous use of target classification information and target kinematic information for target tracking. The approach presented integrates target class information into the data association process using the 2-D (one track list and one measurement list) as well as multiframe (one track list and multiple measurement lists) assignments. The multiframe association likelihood is developed to include the classification results based on the "confusion matrix" that specifies the accuracy of the target classifier. The objective is to improve association results using class information when the kinematic likelihoods are similar for different targets, i.e., there is ambiguity in using kinematic information alone. Performance comparisons with and without the use of class information in data association are presented on a ground target tracking problem. Simulation results quantify the benefits of classification-aided data association for improved target tracking, especially in the presence of association uncertainty in the kinematic measurements. Also, the benefit of 5-D (or multiframe) association versus 2-D association is investigated for different quality classifiers. The main contribution of this paper is the development of the methodology to incorporate exactly the classification information into multidimensional (multiframe) association.