Bayesian Approach to Extended Object and Cluster Tracking using Random Matrices

In algorithms for tracking and sensor data fusion the targets to be observed are usually considered as point source objects; i.e., compared with the sensor resolution their extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, this assumption is often no longer valid as different scattering centers of an object can cause distinct detections when passing the signal processing chain. Examples of extended targets are found in short-range applications (littoral surveillance, autonomous weapons, or robotics). A collectively moving target group can also be considered as an extended target. This point of view is the more appropriate, the smaller the mutual distances between the individual targets are. Due to the resulting data association and resolution conflicts any attempt of tracking the individual objects within the group seems to be no longer reasonable. With simulated sensor data produced by a partly unresolvable aircraft formation the addressed phenomena are illustrated and an approximate Bayesian solution to the resulting tracking problem is proposed. Ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated or tracked. We expect that the resulting tracking algorithms are also relevant for tracking large, collectively moving target swarms.     

基于庞加莱映射的多站数据融合算法

针对目前单目标跟踪数据融合中存在的伪数据问题，研究了基于庞加莱映射的补充条件定位引导算法和多站抗野值数据融合算法，建立了适应实际传感器数量变化的数据融合体系。理论分析和仿真结果均证明，该方法可行有效。     

Maximum likelihood track-before-detect with fluctuating targetamplitude

An important problem in target tracking is the detection and tracking of targets in very low signal-to-noise ratio (SNR) environments. In the past, several approaches have been used, including maximum likelihood. The major novelty of this work is the incorporation of a model for fluctuating target amplitude into the maximum likelihood approach for tracking of constant velocity targets. Coupled with a realistic sensor model, this allows the exploitation of signal correlation between resolution cells in the same frame, and also from one frame to the next. The fluctuating amplitude model is a first order model to reflect the inter-frame correlation. The amplitude estimates are obtained using a Kalman filter, from which the likelihood function is derived. A numerical maximization technique avoids problems previously encountered in “velocity filtering” approaches due to mismatch between assumed and actual target velocity, at the cost of additional computation. The Cramer-Rao lower bound (CRLB) is derived for a constant, known amplitude case. Estimation errors are close to this CRLB even when the amplitude is unknown. Results show track detection performance for unknown signal amplitude is nearly the same as that obtained when the correct signal model is used     

Tracking considerations in selection of radar waveform for rangeand range-rate measurements

The conventional approach for tracking system design is to treat the detection and tracking subsystems as completely independent units. However, the two subsystems can be designed jointly to improve system (tracking) performance. It is known that different radar signal waveforms result in very different resolution cell shapes (for example, a rectangle versus an eccentric parallelogram) in the range/range-rate space, and that there are corresponding differences in overall tracking performance. We develop a framework for the analysis of this performance. An imperfect detection process, false alarms, target dynamics, and the matched filter sampling grid are all accounted for, using the Markov chain approach of Li and Bar-Shalom. The role of the grid is stressed, and it is seen that the measurement-extraction process from contiguous radar "hits" is very important. A number of conclusions are given, perhaps the most interesting of which is the corroboration in the new measurement space of Fitzgerald's result for delay-only (i.e., range) measurements, that a linear FM upsweep offers very good tracking performance     

Joint sensor registration and track-to-track fusion for distributed trackers

Sensor registration deals with the correction of registration errors and is an inherent problem in all multisensor tracking systems. Traditionally, it is viewed as a least squares or a maximum likelihood problem independent of the fusion problem. We formulate it as a Bayesian estimation problem where sensor registration and track-to-track fusion are treated as joint problems and provide solutions in cases 1) when sensor outputs (i.e., raw data) are available, and 2) when tracker outputs (i.e., tracks) are available. The solution to the latter problem is of particular significance in practical systems as band limited communication links render the transmission of raw data impractical and most of the practical fusion systems have to depend on tracker outputs rather than sensor outputs for fusion. We then show that, under linear Gaussian assumptions, the Bayesian approach leads to a registration solution based on equivalent measurements generated by geographically separated radar trackers. In addition, we show that equivalent measurements are a very effective way of handling sensor registration problem in clutter. Simulation results show that the proposed algorithm adequately estimates the biases, and the resulting central-level trucks are free of registration errors.     

Detection and range/Doppler estimation for colocated sensors

The problem of multisensor detection and high resolution signal state estimation using joint maximum a posteriori detection and high order nonlinear filtering techniques is addressed. The model-based fusion approach offers the potential for increased target resolution in range/Doppler/azimuth space. The approach employs joint detection/estimation filters (JDEF) for target detection and localization. The JDEF approach segments the aggregate nonlinear model over the entire target resolution space into a number of localized nonlinear models by partitioning the resolution space into a number of resolution subcells. This partitioning leads to extremely accurate state estimation. The proposed JDEF approach has a built-in capability for automatic data alignment from multiple sensors, and can be used for centralized, decentralized, and distributed data fusion.     

Local SNR considerations in decentralized CFAR detection

We consider the decentralized detection problem, involving N sensors and a central processor, in which the sensors transmit unquantized data to the fusion center. Assuming a homogeneous background for constant false-alarm rate (CFAR) analysis, we obtain the performances of the system for the Swerling I and Swerling III target models. We demonstrate that a simple nonparametric fusion rule at the central processor is sufficient for nearly optimum performance. The effect of the local signal-to-noise ratios (SNRs) on the performances of the optimum detector and two suboptimum detectors is also examined. Finally, we obtain a set of conditions, related to the SNRs, under which better performance may be obtained by using decentralized detection as compared with centralized detection     

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     

Distributed decision fusion using empirical estimation

The problem of optimal data fusion in multiple detection systems is studied in the case where training examples are available, but no a priori information is available about the probability distributions of errors committed by the individual detectors. Earlier solutions to this problem require some knowledge of the error distributions of the detectors, for example, either in a parametric form or in a closed analytical form. Here we show that, given a sufficiently large training sample, an optimal fusion rule can be implemented with an arbitrary level of confidence. We first consider the classical cases of Bayesian rule and Neyman-Pearson test for a system of independent detectors. Then we show a general result that any test function with a suitable Lipschitz property can be implemented with arbitrary precision, based on a training sample whose size is a function of the Lipschitz constant, number of parameters, and empirical measures. The general case subsumes the cases of nonindependent and correlated detectors.     

Optimization of waveform and detection threshold for range and range-rate tracking in clutter

We address an optimization problem to obtain the combined sequence of waveform parameters (pulse amplitudes and lengths, and FM sweep rates) and detection thresholds for optimal range and range-rate tracking in clutter. The optimal combined sequence minimizes a tracking performance index under a set of parameter constraints. The performance index includes the probability of track loss and a function of estimation error covariances. The track loss probability and the error covariances are predicted using a hybrid conditional average algorithm. The effect of the false alarms and clutter interference is taken into account in the prediction. A measurement model in explicit form is also presented which is developed based on the resolution cell in the delay-Doppler plane for a single Gaussian pulse. Numerical experiments were performed to solve the optimization problem for several examples.     

OS-CFAR thresholding in decentralized radar systems

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization     

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     

Monte Carlo filtering for multi target tracking and data association

We present Monte Carlo methods for multi-target tracking and data association. The methods are applicable to general nonlinear and non-Gaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data association problem that arises due to unlabelled measurements in the presence of clutter, and the curse of dimensionality that arises due to the increased size of the state-space associated with multiple targets. We develop a number of algorithms to achieve this. The first, which we refer to as the Monte Carlo joint probabilistic data association filter (MC-JPDAF), is a generalisation of the strategy proposed by Schulz et al. (2001) and Schulz et al. (2003). As is the case for the JPDAF, the distributions of interest are the marginal filtering distributions for each of the targets, but these are approximated with particles rather than Gaussians. We also develop two extensions to the standard particle filtering methodology for tracking multiple targets. The first, which we refer to as the sequential sampling particle filter (SSPF), samples the individual targets sequentially by utilising a factorisation of the importance weights. The second, which we refer to as the independent partition particle filter (IPPF), assumes the associations to be independent over the individual targets, leading to an efficient component-wise sampling strategy to construct new particles. We evaluate and compare the proposed methods on a challenging synthetic tracking problem.     

Real-time object tracking via least squares transformation in spatial and Fourier domains for unmanned aerial vehicles

This paper addresses the problem of real-time object tracking for unmanned aerial vehicles. We consider the task of object tracking as a classification problem. Training a good classifier always needs a huge number of samples, which is always time-consuming and not suitable for realtime applications. In this paper, we transform the large-scale least-squares problem in the spatial domain to a series of small-scale least-squares problems with constraints in the Fourier domain using the correlation filter technique. Then, this problem is efficiently solved by two stages. In the first stage, a fast method based on recursive least squares is used to solve the correlation filter problem without constraints in the Fourier domain. In the second stage, a weight matrix is constructed to prune the solution attained in the first stage to approach the constraints in the spatial domain. Then, the pruned classifier is used for tracking. To evaluate proposed tracker's performance, comprehensive experiments are conducted on challenging aerial sequences in the UAV123 dataset. Experimental results demonstrate that proposed approach achieves a state-ofthe-art tracking performance in aerial sequences and operates at a mean speed of beyond 40 frames/s. For further analysis of proposed tracker's robustness, extensive experiments are also performed on recent benchmarks OTB50, OTB100, and VOT2016.     

基于加权融合的多信源弹道数据实时野值检测方法

研究多信源弹道数据实时处理中斑点野值的检测问题.通过计算各信源数据的实时精度,给出了具有自适应加权系数的加权融合方法,实现了对目标状态参数较高精度的估计,从而实时、准确、高效地检测各信源数据野值.仿真结果表明,本方法可以快速、有效地检测多信源数据的斑点野值,解决因数据切换带来的台阶跳跃问题.     

基于CDKF的快速协方差交叉融合跟踪算法研究

随着目标抗干扰能力的增强,单一寻的制导方式很难完成对目标的稳定跟踪和精确打击,需采用多种探测器作为传感器,提供多种观测数据以实现对目标的稳定跟踪和精确打击。建立了适当的目标运动模型和观测模型,利用中心差分卡尔曼滤波（CDKF）变换处理模型的非线性问题,避免了求解复杂的雅克比矩阵。对于分布式多传感器融合,传统的方法多采用协方差交叉（CI）融合方法,但是这类方法需要寻优求解。而快速协方差交叉（FCI）则不需要进行寻优过程,且计算量小。在此基础上,提出了用于多传感器目标跟踪的CDKF-FCI融合算法。最后,对算法进行了仿真分析,并进一步验证了提出算法的有效性。     

非线性系统中多传感器目标跟踪融合算法研究

 研究了在非线性系统中 ,基于转换坐标卡尔曼滤波器的多传感器目标跟踪融合算法。通过分析得出 :在非线性系统的多传感器目标跟踪中 ,基于转换坐标卡尔曼滤波器 ( CMKF)的分布融合估计基本可以重构中心融合估计。仿真实验也证明了此结论。由此可见分布的 CMKFA是非线性系统中较优的分布融合算法     

A robust Poisson multi-Bernoulli filter for multi-target tracking based on arithmetic average fusion

The coalescence and missed detection are two key challenges in Multi-Target Tracking (MTT). To balance the tracking accuracy and real-time performance, the existing Random Finite Set (RFS) based filters are generally difficult to handle the above problems simultaneously, such as the Track-Oriented marginal Multi-Bernoulli/Poisson (TOMB/P) and Measurement-Oriented marginal Multi-Bernoulli/Poisson (MOMB/P) filters. Based on the Arithmetic Average (AA) fusion rule, this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli (PMB) filter, which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence. In order to fuse the different PMB distributions, the Bernoulli components in different Multi-Bernoulli (MB) distributions are associated with each other by Kullback-Leibler Divergence (KLD) minimization. Moreover, an adaptive AA fusion rule is designed on the basis of the exponential fusion weights, which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT. Finally, by comparing with the TOMB/P and MOMB/P filters, the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.     

主被动多传感器多目标状态信息融合

研究了主被动多传感器多目标状态信息融合问题。针对被动式跟踪的特点,借助主动跟踪的距离通道值,提出类主动的被动式跟踪。在此基础上提出主被动串联状态信息融合和并联状态信息融合算法。仿真结果表明两种状态信息融合方法都可以大大提高跟踪精度,同时还可以提高系统的可靠性。     

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。