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     

幅度及多普勒信息辅助的多目标跟踪算法

针对现有的多目标跟踪（MTT）算法在强杂波环境下会出现严重的性能衰退,利用目标的幅度及多普勒特征,基于随机有限集（RFS）理论,提出了一种幅度及多普勒信息辅助的δ广义标签多伯努利（ADI-δ-GLMB）滤波器。首先,利用幅度及多普勒信息对目标状态进行扩展,在此基础上建立了新的量测似然函数。然后,基于δ-GLMB滤波器框架推导了新的更新方程。最后,进行仿真验证,结果表明：强杂波下,ADI-δ-GLMB滤波器跟踪性能明显优于δ-GLMB滤波器,估计精度及稳定性更高,且计算量更低;同信息辅助的概率假设密度（PHD）、多目标多伯努利（MeMBer）滤波器相比,ADI-δ-GLMB滤波器状态估计精度更高。     

Uniform versus nonuniform sampling when tracking in clutter

Many target tracking subsystems have the ability to schedule their own data rates; essentially they can "order" new information whenever they need it, and the cost is in terms of the sensor resource. But among the unmanaged schemes, uniform sampling, in which a new measurement is requested periodically and regularly, is the most commonly-used sampling scheme; deliberately nonuniform schemes are seldom given serious consideration. In this paper, however, we show that such schemes may have been discarded prematurely: a nonuniform sampling can have its benefits. Specifically, the nonuniform and uniform sampling schemes are compared for two kind of trackers: the probabilistic data association filter (PDAF), which updates its track based on a single scan of information at a time; and N-D assignment (an optimization-based implementation of the multi-hypothesis tracker (MHT)), in which the sliding window involves many scans of observations. We find that given the ground rule of maintenance of the same overall scan rate (i.e., the same sensor effort) uniform sampling is always optimal for the single-scan tracker in the sense of track life. However, nonuniform sampling can outperform uniform sampling if a more sophisticated multi-scan tracker is used, particularly when 1) the target has a high process noise, and/or 2) the false alarm density is high, and/or 3) the probability of detection is high.     

Doppler Compensation & Single Pulse Imaging using Adaptive Pulse Compression

The effects of target Doppler are addressed in relation to adaptive receive processing for radar pulse compression. To correct for Doppler-induced filter mismatch over a single pulse, the Doppler-compensated adaptive pulse compression (DC-APC) algorithm is presented whereby the respective Doppler shifts for large target returns are jointly estimated with the illuminated range profile and subsequently incorporated into the original APC adaptive receive filter formulation. As a result, the Doppler-mismatch-induced range sidelobes can be suppressed thereby regaining a significant portion of the sensitivity improvement that is possible when applying adaptive pulse compression (APC) without the existence of significant Doppler mismatch. In contrast, instead of compensating for Doppler mismatch, the single pulse imaging (SPI) algorithm generalizes the APC formulation for a bank of Doppler-shifted matched filters thereby producing a sidelobe-suppressed range-Doppler image from the return signal of a single radar pulse which is applicable for targets with substantial variation in Doppler. Both techniques are based on the recently proposed APC algorithm and its generalization, the multistatic adaptive pulse compression (MAPC) algorithm, which have been shown to be effective for the suppression of pulse compression range sidelobes thus dramatically increasing the sensitivity of pulse compression radar.     

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     

Multiframe detector/tracker: optimal performance

We develop the optimal Bayes multiframe detector/tracker for rigid extended targets that move randomly in clutter. The performance of this optimal algorithm provides a bound on the performance of any other suboptimal detector/tracker. We determine by Monte Carlo simulations the optimal performance under a variety of scenarios including spatially correlated Gaussian clutter and non-Gaussian (K and Weibull) clutter. We show that, for similar tracking performance, the optimal Bayes tracker can achieve peak signal-to-noise ratio gains possibly larger than 10 dB over the commonly used combination of a spatial matched filter (spatial correlator) and a linearized Kalman-Bucy tracker. Simulations using real clutter data with a simulated target suggest similar performance gains when the clutter model parameters are unknown and estimated from the measurements     

A Novel Speckle Filter for SAR Images Based on Informationtheoretic Heterogeneity Measurements

Most adaptive speckle filters are based on the local coefficient of variation, which serves to measure the heterogeneity of synthetic aperture radar (SAR) images. However, the sensitivity of the measurements to speckle and noise of SAR images would greatly deteriorate the speckle reduction. This article, based upon the information theory, presents a novel parameter for the heterogeneity measurement as a general index to quantitate the SAR image heterogeneity. Further, as a new speckle reduction algorithm based on the aforesaid quantitative heterogeneity measurements, it puts forward a heterogeneity-based speckle reduction filter (HBSRF), which uses the information-theoretic heterogeneity measurements as a criterion to classify the SAR images as belonging to homogeneous or heterogeneous regions. Then the finite iteration procedure and edge detection algorithms are adopted to strike the best balance between speckle reduction and edge preservation. The results from the computer simulation have demonstrated that the proposed effective method is superior to the conventional speckle filters based on the local coefficient of variation both in textural preservation and speckle reduction.     

Radar detection in clutter

Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.     

一类新型机动目标跟踪算法

阐述了当跟踪非机动目标时,传统的Kalman滤波可以得到很好的跟踪精度。但是当日标机动时,传统的Kalman滤波不能对目标的突然变化做出及时的改正和预测,因此跟踪精度很差,甚至出现丢失目标的情况。文中采用的基于截断正态概率模型的改进自适应目标跟踪算法, 其结构和计算简单,鲁棒性好,较好地解决了使用Kalman滤波带来的不足。     

FRS技术对瞬态高速喷流的可视化研究

为了诊断瞬态高速喷流的结构特征,开展了基于分子滤波瑞利散射(FRS)技术的可视化研究.介绍了FRS技术的基本原理,分析了散射光的多普勒频移对诊断的影响.针对瞬态高速喷流特点,建立了FRS诊断系统,设计了两种不同的激光入射方式.采用与流场方向垂直的激光入射方式,获得了喷流与空气作用的湍流结构.而采用与流场轴向平行的激光入射方式,则获得了喷流自身的结构.FRS技术对瞬态高速喷流的可视化研究,对研究超声速湍流混合层流场具有重要指导意义.      

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.     

调频连续波激光雷达目标相对距离及径向速度信息提取方法

利用线性调频连续波（LFM/CW）激光雷达进行测量时,相对运动引起的多普勒效应和信息输出延迟都会造成测量结果偏差。分析了多普勒效应和信息输出延迟对测量的影响,提出了基于偏差抵消原理的相对距离及径向速度信息提取方法,根据测量任务需求对该方法和基于二维傅里叶变换的信息提取方法进行了仿真比较。结果表明：基于偏差抵消的信息提取方法不仅可以在相对径向速度未知的情况下准确提取目标相对距离信息,更可在每个调频周期结束后给出测距结果从而提高测距实时性;相比基于二维傅里叶变换的信息提取方法,当相对径向速度小于750 m/s时,基于偏差抵消的信息提取方法可使得测速偏差减小一个数量级。     

Second-order acceleration models for an MMAE target tracker

The performance of a multiple model adaptive estimator (MMAE) for an enhanced correlator/forward-looking-infrared tracker for airborne targets is analyzed in order to improve its performance. Performance evaluation is based on elemental filter selection and MMAE estimation error sizes and trends. The elemental filters are based on either first or second-order acceleration models. Improved filter selection is achieved by using acceleration models that separate the frequency content of acceleration power spectral densities into non-overlapping regions with second-order models versus the more traditional overlapping regions with first-order models. A revised tuning method is presented. The maximum a posteriori (MAP) versus the Bayesian MMAE is investigated. The calculation of the hypothesis probability calculation is altered to see how performance is affected. The impact of the ad hoc selection of a lower bound on the elemental filter probability calculation to prevent filter lockout is evaluated. Parameter space discretization is investigated     

Estimation of Aircraft Target Motion Using Orientation Measurements

A new approach to estimating motion of a highly maneuverable aircraft target in an air-to-air tracking scenario is presented. An interactive filter system is developed that provides an improved estimate of target motion states by conditioning kinematic filter estimates on target aspect angle data. Pattern recognition techniques used with an electrooptical tracker are presumed to provide this target aspect information. A target orientation filter processes the aspect angle measurements by statistically weighting measured aspect angles with the current best estimate of target kinematics. The aerodynamic lift equation is used to relate approximate angle of attack to target velocity and acceleration. A novel statistical model for aircraft target normal acceleration is also developed to represent better the unknown target accelerations. Simulation results of realistic three-dimensional scenarios are presented to evaluate the performance of the interactive filter system.     

IMM estimator with out-of-sequence measurements

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.     

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.     

Adaptive Tracker Field-of-View Variation Via Multiple Model Filtering

Adaptive estimation using multiple model filtering is investigated as a means of changing the field of view as well as the bandwidth of an infrared image tracker when target acceleration can vary over a wide range. The multiple models are created by tuning filters for best performance at differing conditions of exhibited target behavior and differing physical size of their respective fields of view. Probabilistically weighted averaging provides the adaptation mechanism. Each filter involves online identification of the target shape function, so that this algorithm can be used against ill-defined and/or multiple-hot-spot targets. When each individual filter has the form of an enhanced correlator/linear Kalman filter, computational loading is very low. In contrast, an extended Kalman filter processing the raw infrared data directly and assuming a nonlinear constant turn-rate dynamics model provides superior tracking capability, especially for harsh maneuvers, at the cost of a larger computational burden.     

An Adaptive Two-Dimensional Kalman Tracking Filter

A continuously adaptive two-dimensional Kalman tracking filter for a low data rate track-while-scan (TWS) operation is introduced which enhances the tracking of maneuvering targets. The track residuals in each coordinate, which are a measure of track quality, are sensed, normalized to unity variance, and then filtered in a single-pole filter. The magnitude Z of the output of this single-pole filter, when it exceeds a threshold Z1 is used to vary the maneuver noise spectral density q in the Kalman filter model in a continuous manner. This has the effect of increasing the tracking filter gains and containing the bias developed by the tracker due to the maneuvering target. The probability of maintaining track, with reasonably sized target gates, is thus increased, The operational characteristic of q versus Z assures that the tracker gains do not change unless there is high confidence that a maneuver is in progress.     

Improved tracking with mode-S data-linked velocity measurements

The use of downlinked airspeed and magnetic heading data to enhance tracking in mode-S equipped air traffic control (ATC) systems is examined. A tracker performing satisfactorily during straight line flight as well as during steep maneuvers is discussed. The filter copes easily with longitudinally accelerating targets and is suitable for tracking low-velocity targets like helicopters in all phases of flight. The filter assumes that the target flies in a circular path from sample to sample, which results in nonlinear system equations. The filter is suitable for implementation in three-dimensional tracking systems, particularly on the vertical axis, where target velocities are usually small     

Data Association and Track Management for the Gaussian Mixture Probability Hypothesis Density Filter

The Gaussian mixture probability hypothesis density (GM-PHD) recursion is a closed-form solution to the probability hypothesis density (PHD) recursion, which was proposed for jointly estimating the time-varying number of targets and their states from a sequence of noisy measurement sets in the presence of data association uncertainty, clutter, and miss-detection. However the GM-PHD filter does not provide identities of individual target state estimates, that are needed to construct tracks of individual targets. In this paper, we propose a new multi-target tracker based on the GM-PHD filter, which gives the association amongst state estimates of targets over time and provides track labels. Various issues regarding initiating, propagating and terminating tracks are discussed. Furthermore, we also propose a technique for resolving identities of targets in close proximity, which the PHD filter is unable to do on its own.