Gaussian Mixture Probability Hypothesis Density Filter Research Articles

Refined GM-PHD tracker for tracking targets in possible subsequent missed detections

Gaussian mixture probability hypothesis density (GM-PHD) filter is proposed as an alternative of PHD filter to estimate the first-order moment of the multi-target posterior density. Theoretically, the GM-PHD filter handles missed detection in its filtering recursion. However, in practice, the performance of this filter might be degraded in subsequent miss-detection, when all factors that affect miss-detection cannot be appropriately incorporated in the filtering recursions. In this paper, we propose a heuristic method called Refined GM-PHD (RGM-PHD) tracker which aims at improving the performance of GM-PHD filter in subsequent missed detections. To accomplish this purpose, we define a survival model and introduce probability of confirm for each Gaussian component and each track which are adaptively calculated in time. Accordingly, we propose a state refinement step and a novel state extraction step to improve the tracking performance of the filter. Comprehensive Monte Carlo simulations in terms of various probabilities of detection, false alarm rates and subsequent miss-detection rates are performed to investigate the effectiveness of the method.

Maintaining Track Continuity for Extended Targets Using Gaussian-Mixture Probability Hypothesis Density Filter

A multiextended-target tracker based on the extended target Gaussian-mixture probability hypothesis density (ET-GMPHD) filter, which can provide the tracks of the extended targets, is proposed to maintain the track continuity for the extended targets. To identify the extended targets, each individual Gaussian term of the mixture representing the posterior intensity function will be assigned a label, which is evolved through time. Then a track management scheme, including track initiation, track confirmation, track propagation, and termination, is developed to form the tracks for the extended targets. Furthermore, to improve the performance of the extended target tracker we also propose a mixture partitioning algorithm for resolving the identities of the extended targets in close proximity. The simulation results show that our proposed tracker achieves the less error of the position estimates and decreases the probability of incorrect label assignments from 0.6 to 0.25.

GM-PHD Filter Combined with Track-Estimate Association and Numerical Interpolation

For the standard Gaussian mixture probability hypothesis density (GM-PHD) filter, the number of targets can be overestimated if the clutter rate is too high or underestimated if the detection rate is too low. These problems seriously affect the accuracy of multitarget tracking for the number and the value of measurements and clutters cannot be distinguished and recognized. Therefore, we proposed an improved GM-PHD filter to tackle these problems. Firstly, a track-estimate association was implemented in the filtering process to detect and remove false-alarm targets. Secondly, a numerical interpolation technique was used to compensate the missing targets caused by low detection rate. At the end of this paper, simulation results were presented to demonstrate the proposed GM-PHD algorithm is more effective in estimating the number and state of targets than the previous ones.

Extended emitter target tracking using GM-PHD filter.

If equipped with several radar emitters, a target will produce more than one measurement per time step and is denoted as an extended target. However, due to the requirement of all possible measurement set partitions, the exact probability hypothesis density filter for extended target tracking is computationally intractable. To reduce the computational burden, a fast partitioning algorithm based on hierarchy clustering is proposed in this paper. It combines the two most similar cells to obtain new partitions step by step. The pseudo-likelihoods in the Gaussian-mixture probability hypothesis density filter can then be computed iteratively. Furthermore, considering the additional measurement information from the emitter target, the signal feature is also used in partitioning the measurement set to improve the tracking performance. The simulation results show that the proposed method can perform better with lower computational complexity in scenarios with different clutter densities.

Multiple extended target tracking algorithm based on GM-PHD filter and spectral clustering

With the increase of the resolution of modern radars and other detection equipments, one target may produce more than one measurement. Such targets are referred to as extended targets. Recently, multiple extended target tracking (METT) has drawn a considerable attention. However, one crucial problem is how to partition the measurement sets accurately and rapidly. In this paper, an improved METT algorithm is proposed based on the Gaussian mixture probability hypothesis density (GM-PHD) filter and an effective partition method using spectral clustering technique. First, the density analysis technique is introduced to eliminate the disturbance of clutter, and then the spectral clustering technique based on neighbor propagation is used to partition the measurements. Finally, the GM-PHD filter is implemented to achieve the METT. Simulation results show that the proposed algorithm has a better performance, especially a better real-time performance, than the conventional distance partition and K-means++ methods.

Multi-target Bayesian filter for propagating marginal distribution

The Bayesian filter and its approximation, the probability hypothesis density (PHD) filter, propagate joint distribution of the multi-target state and the first-order moment of the joint distribution, respectively. However, these two filters fail to distinguish multiple distinct targets when these targets are closely spaced. To efficiently distinguish closely spaced targets according to a sequence of measurements, we (1) use the individual state distributions to model the uncertainties of individual target states caused by the target dynamic uncertainty and measurement uncertainty, (2) use the existence probabilities of individual targets to characterize the randomness of target appearance and disappearance, and (3) propose a novel multi-target Bayesian filter. Instead of maintaining the joint state distribution, the proposed filter jointly propagates the marginal distributions and existence probabilities of each target. An implementation of the proposed filter for linear and Gaussian models is also presented to deal with an unknown and variable number of targets. The simulation results demonstrate that the proposed filter is better at distinguishing distinct targets and tracking multiple targets than the Gaussian mixture PHD filter.

Fast Gaussian Mixture Probability Hypothesis Density Filter

Although the Gaussian mixture probability hypothesis density (GMPHD) filter is a multi-target tracker that can alleviate the computational intractability of the optimal multi-target Bayes filter and its computational complex is lower than that of sequential Monte Carlo probability hypothesis density (SMCPHD), its computational burden can be reduced further. In the standard GMPHD filter, each observation should be matched with each component when the PHD is updated. In practice, time cost of evaluating many unlikely measurements-to-components parings is wasteful, because their contribution is very limited. As a result, a substantial reduction in complexity could be obtained by directly setting relative value associated with these parings. A fast GMPHD algorithm is proposed in the paper based on gating strategy. Simulation results show that the fast GMPHD can save computational time by 60%~70% without any degradation in performance compared with standard GMPHD.

GM-PHD-Based Multi-Target Visual Tracking Using Entropy Distribution and Game Theory

Tracking multiple moving targets in a video is a challenge because of several factors, including noisy video data, varying number of targets, and mutual occlusion problems. The Gaussian mixture probability hypothesis density (GM-PHD) filter, which aims to recursively propagate the intensity associated with the multi-target posterior density, can overcome the difficulty caused by the data association. This paper develops a multi-target visual tracking system that combines the GM-PHD filter with object detection. First, a new birth intensity estimation algorithm based on entropy distribution and coverage rate is proposed to automatically and accurately track the newborn targets in a noisy video. Then, a robust game-theoretical mutual occlusion handling algorithm with an improved spatial color appearance model is proposed to effectively track the targets in mutual occlusion. The spatial color appearance model is improved by incorporating interferences of other targets within the occlusion region. Finally, the experiments conducted on publicly available videos demonstrate the good performance of the proposed visual tracking system.

Collaborative penalized Gaussian mixture PHD tracker for close target tracking

Gaussian mixture probability hypothesis density (GM-PHD) recursion is a promising, computationally tractable implementation for the probability hypothesis density (PHD) filter. The competitive GM-PHD (CGM-PHD) and penalized GM-PHD (PGM-PHD) filters employ renormalization schemes to refine the weights assigned to each target and improve the estimation performance of the GM-PHD filter for closely spaced targets. However, these methods do not provide target trajectories over time, and the problem of wrongly identifying close targets is not still solved for the GM-PHD tracker. In this paper, we propose a collaborative penalized scheme to overcome the drawbacks of the GM-PHD tracker using the track label of each Gaussian component in the GM-PHD recursion. The simulation results show that the collaborative penalized GM-PHD (CPGM-PHD) tracker not only improves the estimation accuracy of the number of target and states but also provides the correct identities of targets in close proximity.

Multi-target tracking with PHD filter using Doppler-only measurements

In this paper, we address the problem of multi-target detection and tracking over a network of separately located Doppler-shift measuring sensors. For this challenging problem, we propose to use the probability hypothesis density (PHD) filter and present two implementations of the PHD filter, namely the sequential Monte Carlo PHD (SMC-PHD) and the Gaussian mixture PHD (GM-PHD) filters. Performances of both filters are carefully studied and compared for the considered challenging tracking problem. Simulation results show that both PHD filter implementations successfully track multiple targets using only Doppler shift measurements. Moreover, as a proof-of-concept, an experimental setup consisting of a network of microphones and a loudspeaker was prepared. Experimental study results reveal that it is possible to track multiple ground targets using acoustic Doppler shift measurements in a passive multi-static scenario. We observed that the GM-PHD is more effective, efficient and easy to implement than the SMC-PHD filter.

A Quantitative Analysis on Two RFS-Based Filtering Methods for Multicell Tracking

Multiobject filters developed from the theory of random finite sets (RFS) have recently become well-known methods for solving multiobject tracking problem. In this paper, we present two RFS-based filtering methods, Gaussian mixture probability hypothesis density (GM-PHD) filter and multi-Bernoulli filter, to quantitatively analyze their performance on tracking multiple cells in a series of low-contrast image sequences. The GM-PHD filter, under linear Gaussian assumptions on the cell dynamics and birth process, applies the PHD recursion to propagate the posterior intensity in an analytic form, while the multi-Bernoulli filter estimates the multitarget posterior density through propagating the parameters of a multi-Bernoulli RFS that approximates the posterior density of multitarget RFS. Numerous performance comparisons between the two RFS-based methods are carried out on two real cell images sequences and demonstrate that both yield satisfactory results that are in good agreement with manual tracking method.

Joint detection, tracking and classification of multiple maneuvering targets based on the linear Gaussian jump Markov probability hypothesis density filter

This paper is to account for joint detection, tracking, and classification (JDTC) of an unknown and time-varying number of maneuvering targets in clutter. Unlike most tracking algorithms that use only the kinematic measurements, this paper proposes a recursive JDTC algorithm to exploit the coupled information between target detection, tracking and classification based on the Gaussian mixture probability hypothesis density filter (GMPHDF) in the linear Gaussian jump Markov systems (LGJMS) multitarget model. The original LGJMS-GMPHDF, devoted to joint detect and track all potential targets utilizing an identical and fixed set of models, has been modified to incorporate target class information and the class-dependent kinematic model set. The mutual dependence between target kinematics and class is exploited twice: first to construct the combined model sets, then to compute the combined measurement likelihood. The proposed algorithm is illustrated via a simulation example involving tracking of two closely spaced parallel moving targets and two crossing moving targets from different classes, where targets can appear and disappear.

Amultiplemaneuvering targets tracking algorithm based on a generalized pseudo-Bayesian estimator of first order

We describe the design of a multiple maneuvering targets tracking algorithm under the framework of Gaussian mixture probability hypothesis density (PHD) filter. First, a variation of the generalized pseudo-Bayesian estimator of first order (VGPB1) is designed to adapt to the Gaussian mixture PHD filter for jump Markov system models (JMS-PHD). The probability of each kinematic model, which is used in the JMS-PHD filter, is updated with VGPB1. The weighted sum of state, associated covariance, and weights for Gaussian components are then calculated. Pruning and merging techniques are also adopted in this algorithm to increase efficiency. Performance of the proposed algorithm is compared with that of the JMS-PHD filter. Monte-Carlo simulation results demonstrate that the optimal subpattern assignment (OSPA) distances of the proposed algorithm are lower than those of the JMS-PHD filter for maneuvering targets tracking.

Tracking of Midcourse Ballistic Target Group on Space-based Infrared Focal Plane using GM-CPHD Filter

Tracking of midcourse ballistic target group on space-based infrared focal plane plays a key role in the space-based early warning system. This paper proposes the Gaussian-mixture cardinalized probability hypothesis density (GM-CPHD) filter to solve this problem. The multi-target states and measurements on infrared focal plane are modeled by random finite set (RFS). The intensity function of RFS of multi-target states and the probability distribution of target number are jointly propagated by cardinalized probability hypothesis density (CPHD) recursion. Under the assumptions of linear Gaussian multi-target models, the Gaussian-mixture implementations of CPHD are presented, and the target number and the multi-target states on infrared focal plane are estimated. In order to enable track continuity, we propose 0-1 integer programming to associate the estimated states between frames. The simulation results show that the GM-CPHD filter can dramatically improve the accuracy of estimated target number and estimated target states compared with the Gaussian-mixture probability hypothesis density filter, and that the track continuity can be successfully achieved. Defence Science Journal, 2012, 62(6), pp.431-436 , DOI:http://dx.doi.org/10.14429/dsj.62.1199

Gaussian mixture PHD filter for multi-sensor multi-target tracking with registration errors

This paper studies the problem of multi-sensor multi-target tracking with registration errors in the formulation of random finite sets. The probability hypothesis density (PHD) recursion is applied by introducing the dynamics of the translational measurement bias into the associated intensity functions. Under the linear Gaussian assumptions on the bias dynamics, the Gaussian mixture implementation is used to give closed-form expressions. As the target state and the translational measurement bias are coupled through the likelihood in the update step, a two-stage Kalman filter is adopted to approximate the tractable form, which leads to a substantial reduction in computational complexity. Two numerical examples are provided to verify the effectiveness of the proposed filter.

Competitive Gaussian mixture probability hypothesis density filter for multiple target tracking in the presence of ambiguity and occlusion

The Gaussian mixture probability hypothesis density (GM-PHD) filter has recently been devised as a closed-form recursion for PHD filter for multiple target tracking. The GM-PHD filter works successfully when targets do not move near each other. However, the estimation performance of the GM-PHD filter degrades when targets are in close proximity, such as occlusion condition. In this study, the authors propose a novel approach to improve this drawback. The proposed method employs a renormalisation scheme to rearrange the weights assigned to each target in GM-PHD recursion. Simulation results achieved for different clutter rates and different probabilities of detection show that the proposed approach significantly improves the overall estimation performance compared with the original GM-PHD filter.

Penalized Gaussian mixture probability hypothesis density filter for multiple target tracking

Bayesian multi-target filter develops a theoretical framework for estimating the full multi-target posterior which is intractable in practice. The probability hypothesis density (PHD) is a practical solution for Bayesian multi-target filter which propagates the first order moment of the multi-target posterior instead of the full version. Recently, the Gaussian Mixture PHD (GM-PHD) has been proposed as an implementation of the PHD filter which provides a close form solution. The performance of this filter degrades when targets are moving near each other such as crossing targets. In this paper, we propose a novel approach called penalized GM-PHD (PGM-PHD) filter to improve this drawback. The simulation results provided for various probabilities of detection, clutter rates, targets velocities and frame rates indicate that the proposed method achieves better performance compared to the GM-PHD filter.

Joint Initialization and Tracking of Multiple Moving Objects Using Doppler Information

In this correspondence, a new multi-target tracking (MTT) algorithm based on the probability hypothesis density (PHD) filtering framework is designed in order to improve tracking performance via the proposal of two contributions. First, unlike typical existing systems, Doppler information is additionally employed to enhance the clutter rejection capability. Specifically, position and Doppler measurements are iteratively incorporated in a two-step process based on a Gaussian mixture PHD (GMPHD) filter. Second, a concrete initialization process is proposed in the birth intensity design of the GMPHD. The initialization process from consecutive measurements leads to a reliable birth intensity that improves track management performance. Both contributions are subsequently evaluated through MTT simulations, the results of which verify that the proposed algorithm is viable.

A Random-Finite-Set Approach to Bayesian SLAM

This paper proposes an integrated Bayesian frame work for feature-based simultaneous localization and map building (SLAM) in the general case of uncertain feature number and data association. By modeling the measurements and feature map as random finite sets (RFSs), a formulation of the feature-based SLAM problem is presented that jointly estimates the number and location of the features, as well as the vehicle trajectory. More concisely, the joint posterior distribution of the set-valued map and vehicle trajectory is propagated forward in time as measurements arrive, thereby incorporating both data association and feature management into a single recursion. Furthermore, the Bayes optimality of the proposed approach is established. A first-order solution, which is coined as the probability hypothesis density (PHD) SLAM filter, is derived, which jointly propagates the posterior PHD of the map and the posterior distribution of the vehicle trajectory. A Rao-Blackwellized (RB) implementation of the PHD-SLAM filter is proposed based on the Gaussian-mixture PHD filter (for the map) and a particle filter (for the vehicle trajectory). Simulated and experimental results demonstrate the merits of the proposed approach, particularly in situations of high clutter and data association ambiguity.

Convolution PHD Filtering for Nonlinear Non-Gaussian Models

A novel probability hypothesis density (PHD) filter, called the Gaussian mixture convolution PHD (GMCPHD) filter was proposed. The PHD within the filter is approximated by a Gaussian sum, as in the Gaussian mixture PHD (GMPHD) filter, but the model may be non-Gaussian and nonlinear. This is implemented by a bank of convolution filters with Gaussian approximations to the predicted and posterior densities. The analysis results show the lower complexity, more amenable for parallel implementation of the GMCPHD filter than the convolution PHD (CPHD) filter and the ability to deal with complex observation model, small observation noise and non-Gaussian noise of the proposed filter over the existing Gaussian mixture particle PHD (GMPPHD) filter. The multi-target tracking simulation results verify the effectiveness of the proposed method.