PDAF with multiple clutter regions and target models

This paper presents the theory of a new multiple model probabilistic data association filter (PDAF). The analysis is generalized for the case of multiple nonuniform clutter regions within the measurement data that updates each model of the filter. To reduce the possibility of clutter measurements forming established tracks, the solution includes a model for a visible target. That is, a target that gives sensor measurements that satisfy one of the target models. Other features included in the algorithm are the selection of a fixed number of nearest measurements and the addition of signal amplitude to the target state vector. The nonuniform clutter model developed here is applicable to tracking signal amplitude. Performance of this algorithm is illustrated using experimentally recorded over-the-horizon radar (OTHR) data.     

Novel data association schemes for the probability hypothesis density filter

The probability hypothesis density (PHD) filter is a practical alternative to the optimal Bayesian multi-target Alter based on finite set statistics. It propagates the PHD function, a first-order moment of the full multi-target posterior density. The peaks of the PHD function give estimates of target states. However, the PHD filter keeps no record of target identities and hence does not produce track-valued estimates of individual targets. We propose two different schemes according to which PHD filter can provide track-valued estimates of individual targets. Both schemes use the probabilistic data-association functionality albeit in different ways. In the first scheme, the outputs of the PHD filter are partitioned into tracks by performing track-to-estimate association. The second scheme uses the PHD filter as a clutter filter to eliminate some of the clutter from the measurement set before it is subjected to existing data association techniques. In both schemes, the PHD filter effectively reduces the size of the data that would be subject to data association. We consider the use of multiple hypothesis tracking (MHT) for the purpose of data association. The performance of the proposed schemes are discussed and compared with that of MHT.     

Manoeuvring target tracking in clutter using particle filters

A particle filter (PF) is a recursive numerical technique which uses random sampling to approximate the optimal solution to target tracking problems involving nonlinearities and/or non-Gaussianity. A set of particle filtering methods for tracking and manoeuvering target in clutter from angle-only measurements is presented and evaluated. The aim is to compare PFs to a well-established tracking algorithm, the IMM-PDA-EKF (interacting multiple model, probabilistic data association, extended Kalman filter), and to provide an insight into which aspects of PF design are of most importance under given conditions. Monte Carlo simulations show that the use of a resampling scheme which produces particles with distinct values offers significant improvements under almost all conditions. Interestingly, under all conditions considered here,using this resampling scheme with blind particle proposals is shown to be superior, in the sense of providing improved performance for a fixed computational expense, to measurement-directed particle proposals with the same resampling scheme. This occurs even under conditions favourable to the use of measurement-directed proposals. The IMM-PDA-EKF performs poorly compared with the PFs for large clutter densities but is more effective when the measurements are precise.     

Active sonar application of a U-D square root PDAF

The probabilistic data association filter (PDAF) is a suboptimal approach to tracking a target in the presence of clutter. In the PDAF implementation, the Kalman measurement update is performed over the set of validated measurements and the Kalman time update is used to propagate the PDAF measurement update. A popular approach to obtaining a numerically stable set of Kalman update equations is to propagate the U-D factors of the covariance in the measurement and time updates. The PDAF measurement update equation is obtained in U-D factored form by applying the modified weighted Gram-Schmidt (MWG-S) algorithm to the three factored terms. The factors of the first two terms are determined from the U-D factors of the a priori and conditional a posteriori covariances. The third term is factored analytically using the Agee-Turner factorization. The resulting U-D square-root PDAF is then applied to the problem of active tracking of a submarine in reverberation using polar coordinates     

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.     

基于最近邻的集中式多传感器多目标跟踪算法

经典的集中式多传感器多目标跟踪算法通常计算量较大,经常难以满足系统的实时性要求,工程上实现起来比较困难,为进一步扩大集中式多传感器的应用范围,使其在对算法实时性要求较高、跟踪精度要求较小的实际场合中广泛应用。文章基于最近邻域思想,研究了并行处理结构的集中式多传感器最近邻域算法,并从算法跟踪精度、实时性、有效跟踪率3个方面对其与经典的顺序多传感器联合概率数据互联算法进行了仿真比较。经仿真验证,并行处理结构的集中式多传感器最近邻域算法实时性提高了60%以上,且在跟踪背景杂波适中的情况下能够有效跟踪目标。     

Waveform selective probabilistic data association

An adaptive, waveform selective probabilistic data association (WSPDA) algorithm for tracking a single target in clutter is presented. The assumption of an optimal receiver allows the inclusion of transmitted waveform specification parameters in the tracking subsystem equations, leading to a waveform selection scheme where the next transmitted waveform parameters are selected so as to minimize the average total mean-square tracking error at the next time step. Semiclosed form solutions are given to the local (one-step-ahead) adaptive waveform selection problem for the case of one-dimensional target motion. A simple simulation example is given to compare the performance of a tracking system using a WSFDA based tracking filter with that of a conventional system with a fixed waveform shape and probabilistic data association (PDA) tracking filter.     

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.     

密集杂波环境下的数据关联快速算法

基于联合概率数据互联（JPDA）的思想,提出了一种新的数据关联快速算法（Fast Al-gorithm for Data Association,简称FAFDA算法）.该方法不需象在最优JPDA算法中那样生成所有可能的联合互联假设,因而具有计算量小,易于工程实现的特点。仿真结果表明,与最优JPDA算法相比,FAFDA算法的跟踪性能令人满意,并且在密集杂波环境下可实时、有效地跟踪100批次以上的目标。     

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.     

A class of near optimal JPDA algorithms

The crucial problem in multiple target tracking is the hit-to-track data association. A hit is a received signal from a target or background clutter which provides positional information If an incorrect hit is associated with a track, that track could diverge and prematurely terminate or cause other tracks to also diverge. Most methods for hit-to-track data association fall into two categories: multiple hypothesis tracking (MHT) and joint probabilistic data association (JPDA). Versions of MHT use all or some reasonable hits to update a track and delay the decision on which hit was correct. JPDA uses a weighted sum of the reasonable hits to update a track. These weights are the probability that the hit originated from the target in track. The computational load for the joint probabilities increases exponentially as the number of targets increases and therefore, is not an attractive algorithm when expecting to track many targets. Reviewed here is the JPDA filter and two simple approximations of the joint probabilities which increase linearly in computational load as the number of targets increase. Then a new class of near optimal JPDA algorithms is introduced which run in polynomial time. The power of the polynomial is an input to the algorithm. This algorithm bridges the gap in computational load and accuracy between the very fast simple approximations and the efficient optimal algorithms     

Tracking in Clutter using IMM-IPDA?Based Algorithms

We describe three single-scan probabilistic data association (PDA) based algorithms for tracking manoeuvering targets in clutter. These algorithms are derived by integrating the interacting multiple model (IMM) estimation algorithm with the PDA approximation. Each IMM model a posteriori state estimate probability density function (pdf) is approximated by a single Gaussian pdf. Each algorithm recursively updates the probability of target existence, in the manner of integrated PDA (IPDA). The probability of target existence is a track quality measure, which can be used for false track discrimination. The first algorithm presented, IMM-IPDA, is a single target tracking algorithm. Two multitarget tracking algorithms are also presented. The IMM-JIPDA algorithm calculates a posteriori probabilities of all measurement to track allocations, in the manner of the joint IPDA (JIPDA). The number of measurement to track allocations grows exponentially with the number of shared measurements and the number of tracks which share the measurements. Therefore, IMM-JIPDA can only be used in situations with a small number of crossing targets and low clutter measurement density. The linear multitarget IMM-IPDA (IMM-LMIPDA) is also a multitarget tracking algorithm, which achieves the multitarget capabilities by integrating linear multitarget (LM) method with IMM-IPDA. When updating one track using the LM method, the other tracks modulate the clutter measurement density and are subsequently ignored. In this fashion, LM achieves multitarget capabilities using the number of operations which are linear in the: number of measurements and the number of tracks, and can be used in complex scenarios, with dense clutter and a large number of targets.     

A multipath data association tracker for over-the-horizon radar

A new algorithm, multipath probabilistic data association (MPDA), for initiation and tracking in over-the-horizon radar (OTHR) is described. MPDA is capable of exploiting multipath target signatures arising from discrete propagation modes that are resolvable by the radar. Nonlinear measurement models exhibiting multipath target signatures in azimuth, slant range, and Doppler are used. Tracking is performed in ground coordinates and therefore depends on the provision of estimates of virtual ionospheric heights to achieve coordinate registration. Although the propagation mode characteristics are assumed to be known, their correspondence with the detections is not required to be known. A target existence model is included for automatic track maintenance. Numerical simulations for four resolvable propagation modes are presented that demonstrate the ability of the technique to initiate and maintain track at probabilities of detection of 0.4 per mode in clutter densities for which conventional probabilistic data association (PDA) has a high probability of track loss, and suffers from track bias. A nearest neighbor version of MPDA is also presented     

基于先验门限优化准则的探测阈值自适应选择

针对 2维测量和 4 -sigma确认门 ,把先验检测门限优化准则和修正 Riccati方程的解析近似表示相结合 ,得到了在瑞利起伏环境下使跟踪性能优化的信号探测阈值解析表示式 ,从而使在线求解自适应信号探测阈值能比较容易地实现。通过研究和仿真发现 :在滤波稳定阶段 ,本文给出的自适应信号检测门限方法的跟踪性能优于固定虚警率方法的跟踪性能 ;基于先验检测门限优化准则实现检测 -跟踪的联合优化要求信噪比要大于一定的门限 ,在瑞利起伏环境下 ,对 2维测量和 4 -sigma确认门 ,该门限为 1 .57     

修正的概率数据互联算法

阐明了概率数据互联(PDA)算法能很好地解决密集环境下的目标跟踪问题,在该算法基础上,人们又提出了联合概率数据互联(JPDA)算法和一些基于 PDA 的修正算法。在概率数据互联算法中,有一个很重要的参数就是杂波数密度(或波门内虚假量测期望数)。然而在许多实际情况中,这个参数是很难获取的。针对这一问题,文中提出了一种修正的概率数据互联算法,该算法通过实时地调整这一参数来获得对目标较为准确的估计结果。最后,给出了算法的仿真分析。     

An improved multiple model GM-PHD filter for maneuvering target tracking

In this paper, an improved implementation of multiple model Gaussian mixture probability hypothesis density (MM-GM-PHD) filter is proposed. For maneuvering target tracking, based on joint distribution, the existing MM-GM-PHD filter is relatively complex. To simplify the filter, model conditioned distribution and model probability are used in the improved MM-GM-PHD filter. In the algorithm, every Gaussian components describing existing, birth and spawned targets are estimated by multiple model method. The final results of the Gaussian components are the fusion of multiple model estimations. The algorithm does not need to compute the joint PHD distribution and has a simpler computation procedure. Compared with single model GM-PHD, the algorithm gives more accurate estimation on the number and state of the targets. Compared with the existing MM-GM-PHD algorithm, it saves computation time by more than 30%. Moreover, it also outperforms the interacting multiple model joint probabilistic data association (IMMJPDA) filter in a relatively dense clutter environment.     

Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

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.     

Neural solution to the multitarget tracking data associationproblem

The problem of tracking multiple targets in the presence of clutter is addressed. The joint probabilistic data association (JPDA) algorithm has been previously reported to be suitable for this problem in that it makes few assumptions and can handle many targets as long as the clutter density is not very high. However, the complexity of this algorithm increases rapidly with the number of targets and returns. An approximation of the JPDA that uses an analog computational network to solve the data association problem is suggested. The problem is viewed as that of optimizing a suitably chosen energy function. Simple neural-network structures for the approximate minimization of such functions have been proposed by other researchers. The analog network used offers a significant degree of parallelism and thus can compute the association probabilities more rapidly. Computer simulations indicate the ability of the algorithm to track many targets simultaneously in the presence of moderately dense clutter     

Track formation with bearing and frequency measurements in clutter

Target motion analysis from a narrowband passive sonar that yields bearing and frequency measurements in the presence of false detections (clutter) in a low-SNR (low signal-to-noise ratio) environment is discussed. The likelihood function used to compute the maximum likelihood estimation of the track parameters (localization and frequency) incorporates the false alarms via the probabilistic data association technique. The Cramer-Rao lower bound is calculated and results obtained from simulations are shown to be compatible with it. A test of track acceptance is also presented