Extended Target Probability Hypothesis Density Research Articles

Network Flow Labeling for Extended Target Tracking PHD Filters

The probability hypothesis density (PHD) filter is a method for tracking multiple target objects based on unlabeled detections. However, as the PHD filter employs a first-order approximation of random finite sets, it does not provide track labels, i.e., targets of consecutive time steps are not associated with each other. In this paper, an intuitive and efficient labeling strategy on top of the extended target PHD filter is proposed. The approach is based on solving a network flow problem and makes use of the Wasserstein metric to account for the spatial extent of the objects. The resulting tracker is evaluated with laser scanner data from two traffic scenarios.

Fast density peak-based clustering algorithm for multiple extended target tracking

The key challenge of the extended target probability hypothesis density (ET-PHD) filter is to reduce the computational complexity by using a subset to approximate the full set of partitions. In this paper, the influence for the tracking results of different partitions is analyzed, and the form of the most informative partition is obtained. Then, a fast density peak-based clustering (FDPC) partitioning algorithm is applied to the measurement set partitioning. Since only one partition of the measurement set is used, the ET-PHD filter based on FDPC partitioning has lower computational complexity than the other ET-PHD filters. As FDPC partitioning is able to remove the spatially close clutter-generated measurements, the ET-PHD filter based on FDPC partitioning has good tracking performance in the scenario with more clutter-generated measurements. The simulation results show that the proposed algorithm can get the most informative partition and obviously reduce computational burden without losing tracking performance. As the number of clutter-generated measurements increased, the ET-PHD filter based on FDPC partitioning has better tracking performance than other ET-PHD filters. The FDPC algorithm will play an important role in the engineering realization of the multiple extended target tracking filter.

Two Measurement Set Partitioning Algorithms for the Extended Target Probability Hypothesis Density Filter.

The extended target probability hypothesis density (ET-PHD) filter cannot work well if the density of measurements varies from target to target, which is based on the measurement set partitioning algorithms employing the Mahalanobis distance between measurements. To tackle the problem, two measurement set partitioning approaches, the shared nearest neighbors similarity partitioning (SNNSP) and SNN density partitioning (SNNDP), are proposed in this paper. In SNNSP, the shared nearest neighbors (SNN) similarity, which incorporates the neighboring measurement information, is introduced to DP instead of the Mahalanobis distance between measurements. Furthermore, the SNNDP is developed by combining the DBSCAN algorithm with the SNN similarity together to enhance the reliability of partitions. Simulation results show that the ET-PHD filters based on the two proposed partitioning algorithms can achieve better tracking performance with less computation than the compared algorithms.

Labeled box-particle CPHD filter for multiple extended targets tracking

In multiple extended targets tracking, replacing traditional multiple measurements with a rectangular region of the nonzero volume in the state space inspired by the box-particle idea is exactly suitable to deal with extended targets, without distinguishing the measurements originating from the true targets or clutter. Based on our recent work on extended box-particle probability hypothesis density (ET-BP-PHD) filter, we propose the extended labeled box-particle cardinalized probability hypothesis density (ET-LBP-CPHD) filter, which relaxes the Poisson assumptions of the extended target probability hypothesis density (PHD) filter in target numbers, and propagates not only the intensity function but also cardinality distribution. Moreover, it provides the identity of individual target by adding labels to box-particles. The proposed filter can improve the precision of estimating target number meanwhile achieve targets' tracks. The effectiveness and reliability of the proposed algorithm are verified by the simulation results.

Detection of Multiple Maneuvering Extended Targets by Three-Dimensional Hough Transform and Multiple Hypothesis Tracking

Existing extended target probability hypothesis density (ET-PHD) filters are insufficient in tracking weak extended targets. Hough transform-based track-before-detect methods are designed to detect the weak targets in a straight-line constant-velocity model. Therefore, this paper presents a novel method for detecting and tracking multiple maneuvering weak extended targets by a 3-dimensional Hough transform (3DHT) and multiple hypothesis tracking (MHT). The proposed method consists of two stages. In stage 1, the measurements in multiple scans are partitioned into overlapped time windows. The tracklets in each window can be detected by the 3DHT. In stage 2, the tracklets are associated to get the entire trajectories by the MHT. The tracklets of weak targets can be detected by the 3DHT in stage 1. Association in stage 2 is designed to detect maneuvering targets. Some false alarm tracklets could be built in stage 1. However, the false alarm tracklets are independent and unlikely to form a sequential trajectory in stage 2. Merely, the trajectories whose target likelihood ratio larger than a detection threshold can be confirmed as a target. Both the real data and the synthetic data are performed with the proposed approach and several existing algorithms. The result infers that the proposed approach is superior to the others with much less prior information that is necessary.

Time-matching extended target probability hypothesis density filter for multi-target tracking of high resolution radar

Abstract Extended target probability hypothesis density (ET-PHD) filters have recently become popular owing to their relatively simple recursion processes, which makes them suitable for use in applications requiring real-time results, such as radar multi-target tracking. However, in the classic ET-PHD filters, the measurements of different targets are generally considered to be generated at the end of each scan. With this assumption, the measurement time diversity in radar applications cannot be modeled. To address this shortcoming, a novel time-matching ET-PHD filter in which a multi-prediction filtering framework is applied, and the true measurement times are used in the PHD propagation of each cell, i.e., prediction and correction, is proposed in this paper. In addition, a pre-partitioning strategy is employed to reduce the computational complexity of the proposed filter. The results of simulations conducted using the gamma Gaussian inverse Wishart PHD filter indicate that the proposed pre-partitioning-based time-matching ET-PHD filter is superior to standard filters in terms of both estimation accuracy and real-time performance.

Augmented state PHD filter for extended target tracking with bias compensation

The extended target probability hypothesis density (ET-PHD) filter developed recently is an elegant algorithm for tracking an unknown number of extended targets based on the random finite set (RFS) theory. However, the standard ET-PHD filter can not be straightforwardly applied to track multiple extended targets in the scenarios with sensor biases. Otherwise, different levels of performance degradation can be easily produced due to the presence of biases in sensor measurements. To solve such a problem, an augmented state ET-PHD filter, in which the joint intensity function of target state and sensor bias is recursively estimated, is proposed in this paper. Under linear Gaussian assumptions on the system models and with the joint intensity function represented by the Gaussian mixtures, a closed-form solution to the augmented state ET-PHD filter is also presented. The simulated results for various clutter rates and Poisson rates of measurements demonstrate that the proposed algorithm has satisfactory tracking performance in the situations where the sensor measurements are biased.

Adaptive Target Birth Intensity for ET-PHD Filter

An adaptive tracking algorithm based on Extended target Probability Hypothesis Density (ETPHD) filter is proposed for extended target tracking problem with priori unknown target birth intensity.The algorithm is implemented by gaussian mixture, where the target birth intensity is generated by measurement-driven, and the persistent and the newborn targets intensity are respectively predicted and updated. The simulation results show that the proposed algorithm improves the performance of the probability hypothesis density filter in the extended target tracking.

RFS‐based extended target multipath tracking algorithm

The issue of extended target multipath tracking has been studied. Based on the geometry model on the sea surface, a novel extended target multipath tracking algorithm is proposed under the random finite sets (RFS) framework. In the algorithm, extended target probability hypothesis density (ET-PHD) filter is used as a pre-processor, and multipath Bernoulli filter (MPBF) is used as main processor. The outputs of the ET-PHD filter are treated as pseudo-measurements and fed into the MPBF. At last, probability of existence and target state are estimated from the outputs of MPBF. In contrast with the existing extended target filter and multipath filter, the proposed algorithm does not attempt to get the rigorous solution and avoids the high computational complexity. In order to get the solution of the algorithm, its particle filter implementation has been proposed. Results of simulation show that the proposed algorithm estimates target state accurately. Comparing with extended target Bernoulli filter, the proposed algorithm has good tracking performance at the presence of multipath effect.

A fast ellipse extended target PHD filter using box-particle implementation

Abstract This paper presents a box-particle implementation of the ellipse extended target probability hypothesis density (ET-PHD) filter, called the ellipse extended target box particle PHD (EET-BP-PHD) filter, where the extended targets are described as a Poisson model developed by Gilholm et al. and the term “box” is here equivalent to the term “interval” used in interval analysis. The proposed EET-BP-PHD filter is capable of dynamically tracking multiple ellipse extended targets and estimating the target states and the number of targets, in the presence of clutter measurements, false alarms and missed detections. To derive the PHD recursion of the EET-BP-PHD filter, a suitable measurement likelihood is defined for a given partitioning cell, and the main implementation steps are presented along with the necessary box approximations and manipulations. The limitations and capabilities of the proposed EET-BP-PHD filter are illustrated by simulation examples. The simulation results show that a box-particle implementation of the ET-PHD filter can avoid the high number of particles and reduce computational burden, compared to a particle implementation of that for extended target tracking.

A Multiple-Detection Probability Hypothesis Density Filter

Most conventional target tracking algorithms assume that one target can generate at most one detection per scan. However, in many practical target tracking applications, one target may generate multiple detections in one scan, because of multipath propagation, or high sensor resolution or some other reason. If the multiple detections from the same target can be effectively utilized, the performance of the multitarget tracking system can be improved. However, the challenge is that the uncertainty in the number of targets and the measurement set-to-target association will increase the complexity of tracking algorithms. To solve this problem, the random finite set (RFS) modeling and the random finite set statistics (FISST) are used in this paper. Without any extra approximation beyond those made in the standard probability hypothesis density (PHD) filter, a general multi-detection PHD (MD-PHD) update formulation is derived. It is also established in this paper that, with certain reasonable assumptions, the proposed MD-PHD recursion can function as a generalized extended target PHD or multisensor PHD filter. Furthermore, a Gaussian Mixture (GM) implementation of the proposed MD-PHD formulation, called the MD-GM-PHD filter, is presented. The proposed MD-GM-PHD filter is demonstrated on a simulated over-the-horizon radar (OTHR) scenario.

Extended target probability hypothesis density filter based on cubature Kalman filter

Aiming at the extended target tracking problem in a non-linear Gaussian system, we proposed an extended target probability hypothesis density (EPHD) filter based on the cubature Kalman filter (CKF). To approximate the analytical solution of the extended target tracking, a spherical radial cubature rule was applied to make it possible to numerically compute multivariate moment integrals in the non-linear Bayesian filter. Cubature points and weights were obtained to approximate the integrals in the process. The new algorithm achieved almost the same filtering accuracy as the Gaussian mixture extended Kalman EPHD (EK-EPHD) filter, when solving tracking problems in such complex conditions that the Jacobian matrix of a non-linear function does not exist or is difficult to solve. This work provides a new approach for the extended target tracking under the non-linear Gaussian system.

A new multiple extended target tracking algorithm using PHD filter

A new multiple extended target tracking algorithm using the probability hypothesis density (PHD) filter is proposed in our study, to solve problems on tracking performance degradation of the extended target PHD (ET-PHD) filter under the nonlinear conditions and its intolerable computational requirement. It is noted that with the current Gaussian mixture implement of ET-PHD filter satisfying tracking performance could only be obtained under linear and Gaussian conditions. To extend the application of ET-PHD filter for nonlinear models, our study has derived a particle implement of ET-PHD (ET-P-PHD) filter. Our study finds that the main factors influencing the computational complexity of the ET-P-PHD filter are the partition number of measurement set and the calculation of non-negative coefficients of cells in partitions. With the pretreatment of measurements and application of a new K-means clustering based measurement set partition method, we have successfully decreased the partition number. In addition, a gating method for target state space, which is based on likelihood relationship between target state and measurement, is proposed to simplify the calculation of non-negative coefficients. Simulation results show that the algorithms proposed by our study could satisfyingly deal with multiple extended target tracking issues under nonlinear conditions, and lead to significantly lower computational complexity with tiny effect on tracking performance.

An Extended Target CPHD Filter and a Gamma Gaussian Inverse Wishart Implementation

This paper presents a cardinalized probability hypothesis density (CPHD) filter for extended targets that can result in multiple measurements at each scan. The probability hypothesis density (PHD) filter for such targets has been derived by Mahler, and different implementations have been proposed recently. To achieve better estimation performance this work relaxes the Poisson assumptions of the extended target PHD filter in target and measurement numbers. A gamma Gaussian inverse Wishart mixture implementation, which is capable of estimating the target extents and measurement rates as well as the kinematic state of the target, is proposed, and it is compared to its PHD counterpart in a simulation study. The results clearly show that the CPHD filter has a more robust cardinality estimate leading to smaller OSPA errors, which confirms that the extended target CPHD filter inherits the properties of its point target counterpart.

On Spawning and Combination of Extended/Group Targets Modeled With Random Matrices

In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events.

Convergence Results for the Gaussian Mixture Implementation of the Extended-Target PHD Filter and Its Extended Kalman Filtering Approximation

The convergence of the Gaussian mixture extended-target probability hypothesis density (GM-EPHD) filter and its extended Kalman (EK) filtering approximation in mildly nonlinear condition, namely, the EK-GM-EPHD filter, is studied here. This paper proves that both the GM-EPHD filter and the EK-GM-EPHD filter converge uniformly to the true EPHD filter. The significance of this paper is in theory to present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which the two filters satisfy uniform convergence.