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.     

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。     

Bayesian tracking of two possibly unresolved maneuvering targets

The paper studies the problem of maintaining tracks of two targets that may maneuver in and out formation flight, whereas the sensor and measurement extraction chain produces false and possibly unresolved or missing measurements. If the possibility of unresolved measurements is not modelled then it is quite likely that either the two tracks coalesce or that one of the two tracks diverges on false measurements. In literature a robust measurement resolution model has been incorporated within an interacting multiple model/multiple hypothesis tracking (IMM/MHT) track maintenance setting. A straightforward incorporation of the same model within an IMM and probabilistic data association (PDA)-like hypothesis merging approach suffers from track coalescence. In order to improve this situation, the paper develops a track-coalescence avoiding hypotheses merging version for the two target problem considered. Through Monte Carlo simulations, the novel filters are compared with applying hypotheses merging approaches that ignore the possibility of unresolved measurements or track-coalescence.     

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 of multiple maneuvering targets using multiscan JPDA and IMM filtering

The paper considers the problem of tracking multiple maneuvering targets in the presence of clutter using switching multiple target motion models. A novel suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach and the joint probabilistic data association (JPDA) technique. Unlike the standard single-scan JPDA approach, the authors exploit a multiscan joint probabilistic data association (mscan-JPDA) approach to solve the data association problem. The algorithm is illustrated via a simulation example involving tracking of four maneuvering targets and a multiscan data window of length two     

Fixed-interval retrodiction approach to Bayesian IMM-MHT formaneuvering multiple targets

In a Bayesian framework, we propose a hierarchy of suboptimal retrodiction algorithms that generalize Rauch-Tung-Striebel (RTS) fixed-interval smoothing to multiple hypothesis tracking (MHT) applications employing interacting multiple model (IMM) methods (IMM-MHT). As a limiting case we obtain new simple formulae for suboptimal fixed-interval smoothing applied to Markovian switching systems. Retrodiction techniques provide uniquely interpretable and accurate trajectories from ambiguous MHT output if a certain (small) time delay is tolerated. By a simulated example with two maneuvering targets that operate closely spaced under relatively hard conditions we demonstrate the potential gain by fixed-interval retrodiction and provide a quantitative idea of the achievable track accuracy and mean time delay involved     

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.     

A formulation of multitarget tracking as an incomplete data problem

Traditional multihypothesis tracking methods rely upon an enumeration of all the assignments of measurements to tracks. Pruning and gating are used to retain only the most likely hypotheses in order to drastically limit the set of feasible associations. The main risk is to eliminate correct measurement sequences. The probabilistic multiple hypothesis tracking (PMHT) method has been developed by Streit and Luginbuhl in order to reduce the drawbacks of "strong" assignments. The PMHT method is presented in a general mixture densities perspective. The Expectation-Maximization (EM) algorithm is the basic ingredient for estimating mixture parameters. This approach is then extended and applied to multitarget tracking for nonlinear measurement models in the passive sonar perspective.     

IMMPDAF for radar management and tracking benchmark with ECM

A framework is presented for controlling a phased array radar for tracking highly maneuvering targets in the presence of false alarms (FAs) and electronic countermeasures (ECMs). Algorithms are presented for track formation and maintenance; adaptive selection of target revisit interval, waveform and detection threshold; and neutralizing techniques for ECM, namely, against a standoff jammer (SOJ) and range gate pull off (RGPO). The interacting multiple model (IMM) estimator in combination with the probabilistic data association (PDA) technique is used for tracking. A constant false alarm rate (CFAR) approach is used to adaptively select the detection threshold and radar waveform, countering the effect of jammer-induced false measurements. The revisit interval is selected adaptively, based on the predicted angular innovation standard deviations. This tracker/radar-resource-allocator provides a complete solution to the benchmark problem for target tracking and radar control. Simulation results show an average sampling interval of about 2.5 s while maintaining a track loss less than the maximum allowed 4%     

Efficient L-D factorization algorithms for PDA, IMM, and IMMPDAfilters

Efficient algorithms exist for the square-root probabilistic data association filter (PDAF). The same approach is extended to develop square-root versions of the interacting multiple model (IMM) Kalman filter and the IMMPDAF algorithms. The computational efficiency of the method stems from the fact that the terms needed in the overall covariance updates of PDAF, IMM, and IMMPDAF can be obtained as part of the square-root covariance update of an ordinary Kalman filter. In addition, a new square-root covariance prediction algorithm that is substantially faster than the usual modified weighted Gram-Schmidt (MWG-S) algorithm, whenever the process noise covariance matrix is time invariant, is proposed     

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     

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     

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.     

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.     

Multiple hypothesis track confirmation for infrared surveillancesystems

An overall methodology is described for the application of a multiple hypothesis tracking (MHT) algorithm to the infrared (IR) surveillance system problem of establishing tracks on dim targets in a heavy clutter or false alarm background. The authors discuss the manner in which the detection and tracking systems are jointly designed to optimize performance. They present approximate methods that can conveniently be used for preliminary system design and performance prediction. They discuss the use of a detailed Monte Carlo simulation for final system evaluation and present results illustrating the proposed methods and comparing predicted and simulation performance     

一种密集多回波环境下的机动多目标跟踪起始算法

 本文研究密集多回波环境下的机动多目标跟踪起始问题。文中首先提出主跟踪子空间和边缘跟踪子空间的定义与性质,接着修正Bayes轨迹确定方法BTC,并将其与具有残差滤波的修正概率数据关联滤波算法MPDAF-RF有机地结合起来,提出一种适合高密集多回波环境的机动多目环跟踪起始方法——“全邻”Bayes跟踪起始算法ABTI。Monte Carlo仿真表明,本文所给出的算法不仅克服了一类概率数据关联滤波方法没有跟踪起始机理的缺陷,而且辨别目标与虚警的能力很强,不失为解决高密集多回波环境下机动多目标跟踪起始的有效方法。     

Multisensor tracking of a maneuvering target in clutter

An algorithm is presented for tracking a highly maneuvering target using two different sensors, a radar and an infrared sensor, assumed to operate in a cluttered environment. The nonparametric probabilist data association filter (PDAF) has been adapted for the multisensor (MS) case, yielding the MSPDAF. To accommodate the fact that the target can be highly maneuvering, the interacting multiple model (IMM) approach is used. The results of single-model-based filters and of the IMM/MSPDAF algorithm with two and three models are presented and compared. The IMM has been shown to be able to adapt itself to the type of motion exhibited by the target in the presence of heavy clutter. It yielded high accuracy in the absence of acceleration and kept the target in track during the high acceleration periods     

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     

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.     

Ground target tracking with variable structure IMM estimator

In this paper we present the design of a Variable Structure Interacting Multiple Model (VS-IMM) estimator for tracking groups of ground targets on constrained paths using Moving Target Indicator (MTI) reports obtained from an airborne sensor. The targets are moving along a highway, with varying obscuration due to changing terrain conditions. In addition, the roads can branch, merge or cross-the scenario represents target convoys along a realistic road network with junctions, changing terrains, etc. Some of the targets may also move in an open field. This constrained motion estimation problem is handled using an IMM estimator with varying mode sets depending on the topography, The number of models in the IMM estimator, their types and their parameters are modified adaptively, in real-time, based on the estimated position of the target and the corresponding road/visibility conditions. This topography-based variable structure mechanism eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. Data association is handled using an assignment algorithm. The estimator is designed to handle a very large number of ground targets simultaneously. A simulated scenario consisting of over one hundred targets is used to illustrate the selection of design parameters and the operation of the tracker. Performance measures are presented to contrast the benefits of the VS-IMM estimator over the Kalman filter and the standard IMM estimator, The VS-IMM estimator is then combined with multidimensional assignment to gain “time-depth.” The additional benefit of using higher dimensional assignment algorithms for data association is also evaluated