Integrated track maintenance for the PMHT via the hysteresis model

Unlike other tracking algorithms the probabilistic multi-hypothesis tracker (PMHT) assumes that the true source of each measurement is an independent realisation of a random process. Given knowledge of the prior probability of this assignment variable, data association is performed independently for each measurement. When the assignment prior is unknown, it can be estimated provided that it is either time independent, or fixed over the batch. This paper presents a new extension of the PMHT, which incorporates a randomly evolving Bayesian hyperparameter for the assignment process. This extension is referred to as the PMHT with hysteresis. The state of the hyperparameter reflects each model's contribution to the mixture, and thus can be used to quantify the significance of mixture components. The paper demonstrates how this can be used as a method for automated track maintenance in clutter. The performance benefit gained over the standard PMHT is demonstrated using simulations and real sensor data     

PMHT: problems and some solutions

The probabilistic multihypothesis tracker (PMHT) is a target tracking algorithm of considerable theoretical elegance. In practice, its performance turns out to be at best similar to that of the probabilistic data association filter (PDAF); and since the implementation of the PDAF is less intense numerically the PMHT has been having a hard time finding acceptance. The PMHT's problems of nonadaptivity, narcissism, and over-hospitality to clutter are elicited in this work. The PMHT's main selling-point is its flexible and easily modifiable model, which we use to develop the "homothetic" PMHT; maneuver-based PMHTs, including those with separate and joint homothetic measurement models; a modified PMHT whose measurement/target association model is more similar to that of the PDAF; and PMHTs with eccentric and/or estimated measurement models. Ideally, "bottom line" would be a version of the PMHT with clear advantages over existing trackers. If the goal is of an accurate (in terms of mean square error (MSE)) track, then there are a number of versions for which this is available.     

Multiple model PMHT and its application to the benchmark radar tracking problem

The probabilistic multiple hypothesis tracker (PMHT) uses the expectation-maximization (EM) algorithm to solve the measurement-origin uncertainty problem. Here, we explore some of its variants for maneuvering targets and in particular discuss the multiple model PMHT. We apply this PMHT to the six "typical" tracking scenarios given in the second benchmark problem from W. D. Blair and G. A. Watson (1998). The manner in which the PMHT is used to track the targets and to manage radar allocation is discussed, and the results compared with those of the interacting multiple model probabilistic data association filter (IMM/PDAF) and IMM/MHT (multiple hypothesis tracker). The PMHT works well: its performance lies between those of the IMM/PDAF and IMM/MHT both in terms of tracking performance and computational load.     

面向目标的概率多假设跟踪算法

 概率多假设跟踪(PMHT)算法由于其计算量与目标和量测的个数成线性关系而成为一种重要的数据关联方法,但该算法采用的是一种面向量测的参数模型,容易受到杂波的干扰。针对这个问题,提出一种面向目标的PMHT（TO/PMHT）算法,将量测与目标的距离作为权重,使计算出的后验关联概率能够真实地反映量测和目标的关联可能性。通过多种典型环境的仿真计算表明：TO/PMHT算法和面向量测的PMHT算法相比,跟踪性能有了明显的提高;与多假设跟踪(MHT)算法相比,在保持跟踪性能的同时,极大地提高了计算效率。     

The turbo PMHT

The PMHT (probabilistic multihypothesis tracker) uses "soft" a posteriori probability associations between measurements and targets. Its implementation is a straightforward iterative application of a Kalman smoother operating on "synthetic" (i.e., modified) measurements, and of recalculation of these synthetic measurements based on the current track estimate. In this correspondence, we first discuss the basic PMHT and some of the older PMHT variants that have been used to enhance convergence. We then introduce the new turbo PMHT, which is informed by the recent success of turbo decoding in the digital communication context. This new PMHT has performance substantially improved versus any of the previous versions.     

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.     

Multiassignment for tracking a large number of overlapping objects[and application to fibroblast cells]

In this paper we present a new technique for data association using multiassignment for tracking a large number of closely spaced (and overlapping) objects. The algorithm is illustrated on a biomedical problem, namely the tracking of a group of fibroblast (tissue) cells from an image sequence, which motivated this work. Because of their proximity to one another and due to the difficulties in segmenting the images accurately from a poor-quality image sequence, the cells are effectively closely spaced objects (CSOs). The algorithm presents a novel dichotomous, iterated approach to multiassignment using successive one-to-one assignments of decreasing size with modified costs. The cost functions, which are adjusted depending on the “depth” of the current assignment level and on the tracking results, are derived. The resulting assignments are used to form, maintain and terminate tracks with a modified version of the probabilistic data association (PDA) filter, which can handle the contention for a single measurement among multiple tracks in addition to the association of multiple measurements to a single track. Estimation results are given and compared with those of the standard 2D one-to-one assignment algorithm. It is shown that iterated multiassignment results in superior measurement-to-track association. The algorithms presented can be used for other general tracking problems, including dense air traffic surveillance and control     

Mixture Reduction Algorithms for Point and Extended Object Tracking in Clutter

The Bayesian solution to the problem of tracking a target with measurement association uncertainty gives rise to mixture distributions, which are composed of an ever increasing number of components. To produce a practical tracking filter, the growth of components must be controlled by approximating the mixture distribution. Two mixture reduction schemes (a joining algorithm and a clustering algorithm) have been derived for this purpose. If significant well spaced mixture components are present, these techniques can provide a useful improvement over the probabilistic data association filter (PDAF) approach, which reduces the mixture to a single Gaussian component at each time step. For the standard problem of tracking a point target in uniform random clutter, a Monte Carlo simulation study has been employed to identify the region of the problem parameter space where significant performance improvement is obtained over the PDAF. In the second part of this paper, the formal Bayesian filter is derived for an extended target consisting of an array of measurement sources with association uncertainty. A practical multiple hypothesis filter is implemented using mixture reduction and simulation results are presented.     

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。     

一种基于三维到达角的无偏伪线性卡尔曼滤波

为了解决大场景下基于三维到达角的目标跟踪问题，提出了一种具有无偏性的伪线性卡尔曼滤波。首先，基于三维到达角信息对目标运动模型与量测模型进行建模；之后，对量测模型进行了伪线性化处理，得到了线性形式的目标量测模型。为了解决伪线性卡尔曼滤波存在的有偏性问题，提出了一种结合EKF（extend Kalman filter）的三维伪线性无偏卡尔曼滤波。仿真实验表明，该模型能够对非机动目标与机动目标有效跟踪，对于百公里级别的目标，当角测量误差从0.1°变化到0.5°，算法在仿真时间结束时均能将绝对位置误差降低至10 km以内，且算法的运行速度与EKF为同一个量级，同时兼顾了抗干扰能力、定位跟踪精度、运行效率的要求，能够为大场景下的目标跟踪提供有效方法。     

Multi-Target Tracking in Clutter without Measurement Assignment

When tracking targets using radars and sonars, the number of targets and the origin of data is uncertain. Data may be false measurements or clutter, or they may be detections from an unknown number of targets whose possible trajectories and detection processes can only be described in a statistical manner. Optimal all-neighbor multi-target tracking (MTT) in clutter enumerates all possible joint measurement-to-track assignments and calculates the a posteriori probabilities of each of these joint assignments. The numerical complexity of this process is combinatorial in the number of tracks and the number of measurements. One of the key differences between most MTT algorithms is the manner in which they reduce the computational complexity of the joint measurement-to-track assignment process. We propose an alternative approach, using a form of soft assignment, that enables us to bypass this step entirely. Specifically, our approach treats possible detections of targets followed by other tracks as additional clutter measurements. It starts by approximating the a~priori probabilities of measurement origin. These probabilities are then used to modify the clutter spatial density at the location of the measurements. A suitable single target tracking (STT) filter then uses the modified clutter intensity for updating the track state. In effect, the STT filter is transformed into an MTT filter with a numerical complexity that is linear in the number of tracks and the number of measurements. Simulations show the effectiveness of this approach in a number of different multi-target scenarios.     

均方意义下三维雷达无偏转换测量误差协方差阵的推导

在以前的研究中,无偏转测量误差协方差阵是基于当前测量值得到的.为了能利用所有历史数据以得到更精确的转换测量误差协方差阵估计,文中在均方意义下,推导了三维雷达的最优无偏转换测量误差协方差阵.     

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.     

Update with out-of-sequence measurements in tracking: exact solution

In target tracking systems measurements are typically collected in "scans" or "frames" and then they are transmitted to a processing center. In multisensor tracking systems that operate in a centralized manner, there are usually different time delays in transmitting the scans or frames from the various sensors to the center. This can lead to situations where measurements from the same target arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting "negative-time measurement update" problem, which is quite common in real multisensor systems, was solved previously only approximately in the literature. The exact state update equation for such a problem is presented. The optimal and two suboptimal algorithms are compared on a number of realistic examples, including a GMTI (ground moving target indicator) radar case.     

Tracking in clutter with nearest neighbor filters: analysis andperformance

The measurement that is “closest” to the predicted target measurement is known as the “nearest neighbor” (NN) measurement in tracking. A common method currently in wide use for tracking in clutter is the so-called NN filter, which uses only the NN measurement as if it were the true one. The purpose of this work is two fold. First, the following theoretical results are derived: the a priori probabilities of all three data association events (updates with correct measurement, with incorrect measurement, and no update), the probability density functions (pdfs) of the NN measurement conditioned on the association events, and the one-step-ahead prediction of the matrix mean square error (MSE) conditioned on the association events. Secondly, a technique for prediction without recourse to expensive Monte Carlo simulations of the performance of tracking in clutter with the NN filter is presented. It can quantify the dynamic process of tracking divergence as well as the steady-state performance. The technique is a new development along the line of the recently developed general approach to the performance prediction of algorithm with both continuous and discrete uncertainties     

Bernoulli particle flter with observer altitude for maritime radiation source tracking in the presence of measurement uncertainty

For maritime radiation source target tracking in particular electronic counter measures（ECM）environment,there exists two main problems which can deteriorate the tracking performance of traditional approaches.The frst problem is the poor observability of the radiation source.The second one is the measurement uncertainty which includes the uncertainty of the target appearing/disappearing and the detection uncertainty（false and missed detections）.A novel approach is proposed in this paper for tracking maritime radiation source in the presence of measurement uncertainty.To solve the poor observability of maritime radiation source target,using the radiation source motion restriction,the observer altitude information is incorporated into the bearings-only tracking（BOT）method to obtain the unique target localization.Then the two uncertainties in the ECM environment are modeled by the random fnite set（RFS）theory and the Bernoulli fltering method with the observer altitude is adopted to solve the tracking problem of maritime radiation source in such context.Simulation experiments verify the validity of the proposed approach for tracking maritime radiation source,and also demonstrate the superiority of the method compared with the traditional integrated probabilistic data association（IPDA）method.The tracking performance under different conditions,particularly those involving different duration of radiation source opening and switching-off,indicates that the method to solve our problem is robust and effective.     

Rao-blackwellised particle filtering in random set multitarget tracking

This article introduces a Rao-Blackwellised particle filtering (RBPF) approach in the finite set statistics (FISST) multitarget tracking framework. The RBPF approach is proposed in such a case, where each sensor is assumed to produce a sequence of detection reports each containing either one single-target measurement, or a "no detection" report. The tests cover two different measurement models: a linear-Gaussian measurement model, and a nonlinear model linearised in the extended Kalman filter (EKF) scheme. In the tests, Rao-Blackwellisation resulted in a significant reduction of the errors of the FISST estimators when compared with a previously proposed direct particle implementation. In addition, the RBPF approach was shown to be applicable in nonlinear bearings-only multitarget tracking.     

Joint integrated probabilistic data association: JIPDA

A new recursive filter for multi-target tracking in clutter is presented. Multiple tracks may share the same measurement(s). Joint events are formed by creating all possible combinations of track-measurement assignments and the probabilities for these joint events are calculated. The expressions for the joint event probabilities incorporate the probabilities of target existence of individual tracks, an efficient approximation for the cluster volume and a priori probability of the number of clutter measurements in each cluster. From these probabilities the data association and target existence probabilities of individual tracks are obtained, which allows track state update and false track discrimination. A simulation study is presented to show the effectiveness of this approach.     

星体标定技术在光电跟踪系统计量确认中的应用

测角精度是光电跟踪系统计量确认中最重要的技术指标，通常是以校准塔和方位标为基准进行单项误差标定的，其过程繁琐、周期长。为了提高测量及校准精度，缩短确认周期，本文在实践的基础上，研究了一种应用星体标定技术开展光电跟踪系统计量确认的原理、方法、程序；讨论分析了误差来源、数学模型的建立及其解算方法。     

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.