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For the problem that the standard probability hypothesis density is unable to correctly estimate the states of targets and their number when tracking multiple targets in possible missed detection environments, an improved probability hypothesis density filter based multi-target tracking algorithm is proposed under the linear Gaussian conditions. Two assisted parameters, namely label and probability of existence, are introduced to expand the standard target state in the proposed algorithm which includes three robust schemes compared with the Gaussian mixture probability hypothesis density filter. Firstly, the extended component set of target states representing the target intensity can be correctly updated in the proposed target intensity update scheme. Secondly, by optimizing the component set that approximates the target posterior intensity, the excess and invalid components are effectively reduced in the improved component fusion scheme. Lastly, a new target state extraction scheme is able to accurately estimate the states of targets by comprehensively utilizing both the weight and existent probability of the target. Simulation results show that the proposed algorithm not only provides relatively accurate multi-target estimates, but also has a relatively low computational burden.

Probability hypothesis density (PHD) filter is a suboptimal Bayesian multi-target filter based on random finite set. The Gaussian mixture PHD filter is an analytic solution to the PHD filter for linear Gaussian multi-target models. However, when targets move near each other, the GM-PHD filter cannot correctly estimate the number of targets and their states. To solve the problem, a novel reweighting scheme for closely spaced targets is proposed under the framework of the GM-PHD filter, which can be able to correctly redistribute the weights of closely spaced targets, and effectively improve the multiple target state estimation precision. Simulation results demonstrate that the proposed algorithm can accurately estimate the number of targets and their states, and effectively improve the performance of multi-target tracking algorithm.

Probability hypothesis density (PHD) filter is an effective means to track multiple targets in that it avoids explicit data association between measurements and tracks. The Gaussian mixture (GM) implementation of the PHD filter is a closed-form solution to the PHD filter for linear Gaussian model. However, the Gaussian mixture PHD filter suffers from filtering performance degradation problem in multi-target tracking scenarios with low probability of detection, especially when it comes to tracking nearby targets in the imperfect probability of detection conditions. Aiming at the problem, a robust Gaussian mixture PHD algorithm for tracking multiple targets is proposed. First, a novel nearby target tracking method is introduced to reallocate the possible incorrect weights of the nearby targets. Then, a novel target state estimation scheme, making full use of the multiple previous weights of the targets, is adopted to extract the estimates of the target states. Simulation experiments have demonstrated that the proposed approach can achieve better performance in terms of target states and their number than the other related algorithms when tracking multiple nearby targets in the low probability of detection scenarios.

The Gaussian inverse Wishart probability hypothesis density (GIW-PHD) filter is a promising approach for tracking an unknown number of extended targets. However, it does not achieve satisfactory performance if targets in different sizes are spatially close and manoeuvring because the partitioning methods are sensitive to manoeuvres. To solve this problem, the authors propose the shape selection partitioning (SSP) measurement partitioning algorithm. The proposed algorithm first calculates potential centres and shapes of targets. It then combines each centre with different shapes to divide measurements into subcells. Accordingly, some candidate partitions can be obtained. Finally, it selects the most likely candidate partition and outputs the corresponding subcells. Simulation results show that the application of SSP to the GIW-PHD filter can achieve better performance when targets are spatially close and manoeuvring, which leads to a lower optimal subpattern assignment distance and a higher accuracy of the sum of weights.

The probability hypothesis density (PHD) filter is an effective means to track multiple targets in that it avoids explicit data associations between the measurements and targets. However, the target birth intensity as a prior is assumed to be known before tracking in a traditional target-tracking algorithm; otherwise, the performance of a conventional PHD filter will decline sharply. Aiming at this problem, a novel target birth intensity scheme and an improved measurement-driven scheme are incorporated into the PHD filter. The target birth intensity estimation scheme, composed of both PHD pre-filter technology and a target velocity extent method, is introduced to recursively estimate the target birth intensity by using the latest measurements at each time step. Second, based on the improved measurement-driven scheme, the measurement set at each time step is divided into the survival target measurement set, birth target measurement set, and clutter set, and meanwhile, the survival and birth target measurement sets are used to update the survival and birth targets, respectively. Lastly, a Gaussian mixture implementation of the PHD filter is presented under a linear Gaussian model assumption. The results of numerical experiments demonstrate that the proposed approach can achieve a better performance in tracking systems with an unknown newborn target intensity.

As one suboptimal but tractable alternative to the Bayes filter within the random finite set (RFS) framework, the probability hypothesis density (PHD) filter has attracted considerable attention because of its low computational load and ease of implementation. However, the standard PHD filter is unable to estimate the tracks of targets in clutter circumstances. Although some PHD-based trackers are proposed to estimate the tracks of targets, the track maintenance performances of these trackers suffer from significant declines in closely spaced target environments. In this paper, with the help of the track label and an association-update factor matrix, a closely spaced target track maintenance algorithm based on the Gaussian mixture PHD filter is proposed to identify and provide the trajectories of close targets over times. Numerical simulations demonstrate that the proposed algorithm is capable of correctly estimating the tracks of closely spaced targets in clutter environments, and is superior to the related multi-target trackers in terms of target states, computational load, and association accuracy of tracks.

The probability hypothesis density (PHD) filter is a promising method for multi-target tracking problem. The Gaussian mixture PHD filter is an analytic solution to the PHD filter for linear Gaussian multi-target models. However, the PHD filter is inapplicable to the multi-target tracking scenario with unknown newborn target intensity. To overcome the problem, an adaptive Gaussian mixture probability hypothesis density algorithm for multiple target tracking is proposed, where the Dirichlet distribution with negative exponent parameters and target maximum velocity constraint-based schemes are introduced to recursively estimate the newborn target intensity at each time step. The simulation results illustrate that the proposed algorithm has better performance under the unknown newborn target intensity in the multi-target tracking systems.

Probability hypothesis density (PHD) filter is a suboptimal Bayesian multi-target filter based on random finite set. Gaussian mixture is an approximation scheme to obtain the closed solution of the PHD filter, which is only suitable for linear Gaussian case. However, when targets are moving closely to each other, GM-PHD filter cannot correctly estimate the number of targets and their states. Especially, the estimation accuracy of both target number and their states is rather difficult when targets born and disappear in closely spaced target tracking scenarios. To solve these problems, a novel multiple target tracking algorithm is proposed in this paper. For one hand, when the targets are close, a novel weight redistribution scheme of targets is proposed, which can appropriately modify the weights of the closely spaced targets so that the higher precision of state estimates can be obtained. On the other hand, we propose a false alarm detection method by using an irregular window, in which the multi-scan measurement information is considered to reduce the disturbance of clutter. In numerical experiments, the results demonstrate that the proposed approach can achieve better performance compared to the other existing methods. A GM-PHD algorithm based on false alarm detection with irregular window is proposed.The weight correction of closely spaced targets can be solved by the novel weight redistribution scheme.An irregular window scheme is adopted to solve the false alarm problem in closely spaced target tracking scenario.An improved pruning and merging scheme of Gaussian components can avoid the phenomenon of merging erroneously of different targets.Simulation results show that the proposed algorithm can effectively estimate the number of targets and their states.

The random finite set (RFS)-based Gaussian mixture probability hypothesis density (GM-PHD) filter is a promising and efficient suboptimal approximation for the multi-target Bayes filter. However, the GM-PHD filter is unable to track nearby targets caused by the improper position distribution of target-originated measurements. Aiming at the problem, a multi-target GM-PHD filter with an improved component merging method is proposed. Based on a proposed adaptive threshold-based component similarity measure scheme, the improved component merging method is able to avoid incorrect fusion of the components of targets in close proximity and optimize the target components within the target posterior intensity. Experimental results illustrate that the proposed algorithm not only can achieve better estimation accuracy in terms of the target states and its number but also has high computation efficiency when compared against the related GM-PHD-based filters.

For the problem that the standard probability hypothesis density is unable to estimate the states of targets when tracking multiple targets in possible missed detection environments, a Gaussian mixture probability hypothesis density filter based multi-target tracking algorithm is proposed. Two assisted parameters, namely label and existence probability, are introduced to expand the standard target state in the proposed algorithm which includes three robust schemes compared with the Gaussian mixture probability hypothesis density filter. Firstly, the extended parameter set of target states representing the target intensity can be correctly updated in the proposed target intensity update scheme. Secondly, by optimizing the component set that approximates the target posterior intensity, the invalid components are effectively reduced in the improved component fusion scheme. Lastly, the new target state extraction scheme can accurately estimate the states of targets by extracting the components that can better represent the real targets by comprehensively utilizing both the weight and existence probability of the target. Simulation results show that the proposed algorithm not only provides relatively accurate multi-target estimates, but also has a relatively low computational burden.

The probability hypothesis density (PHD) filter is a promising tool for tracking the time-varying number of targets in real time. The Gaussian mixture PHD filter is an analytic solution to the PHD filter for linear Gaussian multi-target models. By using Gaussian component labels in GM-PHD filter, the identities of individual target can be obtained. However, the labeling GM-PHD filter cannot correctly discriminate tracks of individual targets when targets are moving closely to each other. To solve this problem, an improved GM-PHD tracker is proposed, which is able to identify and manage the track of individual target effectively. First, a detection-guided dynamic reweight scheme is employed in the GM-PHD filter to alleviate the weight error of closely spaced targets. Then, a novel track management scheme is introduced to form and maintain the tracks of individual targets. The simulation results demonstrate the better performance of the proposed algorithm in comparison with the labeling GM-PHD filter.

Gaussian inverse Wishart probability hypothesis density (GIW-PHD) filter has proven to be a promising algorithm for multiple extended target tracking with shape estimation. However, as far as I know, this method only can be used in the single sensor tracking system, which cannot obtain the accurate state estimates for the complex tracking scenario. To solve this problem, we propose a multi-sensor GIW-PHD method by using the multiple sensor infusion technique, which is suitable to the multi-sensor tracking system for multiple extended target tracking. First, a novel measurement model of the extended target is constructed for multi-sensor in three-dimensional scenario, and then the fusion formulas of state update are derived. Simulation results show that the proposed algorithm has a better performance than that of the conventional GIW-PHD with a single sensor.

Probability hypothesis density (PHD) filter is an optimal Bayesian multi-target filter based on random finite set. Gaussian mixture is an approximation scheme of PHD filter, which is suitable for linear Gaussian case. In multi-target tracking, when targets are moving closely to each other, GM-PHD filter cannot correctly estimate the number of targets and target states in complex tracking environment. To solve the problem, we propose an improved algorithm in this paper. The improved algorithm uses a novel method for the redistribution of target weights. The simulation results demonstrate that the proposed approach can achieve better performance compared to the other existing methods.