Probability Hypothesis Density Filter Research Articles

Robust multi-sensor generalized labeled multi-Bernoulli filter

This paper proposes an efficient and robust algorithm to estimate target trajectories with unknown target detection profiles and clutter rates using measurements from multiple sensors. In particular, we propose to combine the multi-sensor Generalized Labeled Multi-Bernoulli (MS-GLMB) filter to estimate target trajectories and robust Cardinalized Probability Hypothesis Density (CPHD) filters to estimate the clutter rates. The target detection probability is augmented to the filtering state space for joint estimation. Experimental results show that the proposed robust filter exhibits near-optimal performance in the sense that it is comparable to the optimal MS-GLMB operating with true clutter rate and detection probability. More importantly, it outperforms other studied filters when the detection profile and clutter rate are unknown and time-variant. This is attributed to the ability of the robust filter to learn the background parameters on-the-fly.

Estimations of time-varying birth cardinality distribution and birth intensity in Gaussian mixture CPHD filter for multi-target tracking

Cardinalized probability hypothesis density (CPHD) filter is a promising algorithm for multi-target tracking. However, the performance of standard CPHD is degraded when the target birth process is unknown and dynamically changing. To remove this limitation, a discrete kernel estimator in conjunction with exponential weighted moving average scheme is introduced in this study to estimate the time-varying target birth cardinality distribution (i.e., probability distribution on number of newborn targets appearing during one sampling time) at each processing step. The target birth intensity is then updated according to the resulting estimated birth cardinality distribution. The estimated birth intensity and cardinality distribution can be employed by a tracker based on Gaussian mixture CPHD (GMCPHD) to modulate its filtering strength for target tracking. The performance of the proposed framework is demonstrated by both numerical simulations and experiment on a video surveillance dataset. Results show that the proposed algorithm can reduce the delay of standard GMCPHD filter's response to the changes in the number of targets, and thus improve the accuracy of cardinality estimates. Satisfactory estimation of cardinality can be obtained even when there is a fast change in the rate of birth.

Occlusion-robust online multi-object visual tracking using a GM-PHD filter with CNN-based re-identification

We propose a novel online multi-object visual tracker using a Gaussian mixture Probability Hypothesis Density (GM-PHD) filter and deep appearance learning. The GM-PHD filter has a linear complexity with the number of objects and observations while estimating the states and cardinality of time-varying number of objects, however, it is susceptible to miss-detections and does not include the identity of objects. We use visual-spatio-temporal information obtained from object bounding boxes and deeply learned appearance representations to perform estimates-to-tracks data association for target labeling as well as formulate an augmented likelihood and then integrate into the update step of the GM-PHD filter. We also employ additional unassigned tracks prediction after the data association step to overcome the susceptibility of the GM-PHD filter towards miss-detections caused by occlusion. Extensive evaluations on MOT16, MOT17 and HiEve benchmark data sets show that our tracker significantly outperforms several state-of-the-art trackers in terms of tracking accuracy and identification.

Tracking of Multiple Maneuvering Random Hypersurface Extended Objects Using High Resolution Sensors

With the increased resolution capability of modern sensors, an object should be considered as extended if the target extent is larger than the sensor resolution. Multiple maneuvering extended object tracking (MMEOT) uses not only measurements of the target centroid but also high-resolution sensor measurements which may resolve individual features or measurement sources. MMEOT aims to jointly estimate object number, centroid states, and extension states. However, unknown and time-varying maneuvers of multiple objects produce difficulties in terms of accurate estimation. For multiple maneuvering star-convex extended objects using random hypersurface models (RHMs) in particular, their complex maneuvering behaviors are difficult to be described accurately and handled effectively. To deal with these problems, this paper proposes an interacting multiple model Gaussian mixture probability hypothesis density (IMM-GMPHD) filter for multiple maneuvering extended object tracking. In this filter, linear maneuver models derived from RHMs are utilized to describe different turn maneuvers of star-convex extended objects accurately. Based on these, an IMM-GMPHD filtering recursive form is given by deriving new update and merging formulas of model probabilities for extended objects. Gaussian mixture components of different posterior intensities are also pruned and merged accurately. More importantly, the geometrical significance of object extension states is fully considered and exploited in this filter. This contributes to the accurate estimation of object extensions. Simulation results demonstrate the effectiveness of the proposed tracking approach—it can obtain the joint estimation of object number, kinematic states, and object extensions in complex maneuvering scenarios.

A Particle PHD Filter for Dynamic Grid Map Building towards Indoor Environment

The PHD (Probability Hypothesis Density) filter is a sub-optimal multi-target Bayesian filter based on a random finite set, which is widely used in the tracking and estimation of dynamic objects in outdoor environments. Compared with the outdoor environment, the indoor environment space and the shape of dynamic objects are relatively small, which puts forward higher requirements on the estimation accuracy and response speed of the filter. This paper proposes a method for fast and high-precision estimation of the dynamic objects’ velocity for mobile robots in an indoor environment. First, the indoor environment is represented as a dynamic grid map, and the state of dynamic objects is represented by its grid cells state as random finite sets. The estimation of dynamic objects’ speed information is realized by using the measurement-driven particle-based PHD filter. Second, we bound the dynamic grid map to the robot coordinate system and derived the update equation of the state of the particles with the movement of the robot. At the same time, in order to improve the perception accuracy and speed of the filter for dynamic targets, the CS (Current Statistical) motion model is added to the CV (Constant Velocity) motion model, and interactive resampling is performed to achieve the combination of the advantages of the two. Finally, in the Gazebo simulation environment based on ROS (Robot Operating System), the speed estimation and accuracy analysis of the square and cylindrical dynamic objects were carried out respectively when the robot was stationary and in motion. The results show that the proposed method has a great improvement in effect compared with the existing methods.

Adaptive grid‐driven probability hypothesis density filter for multi‐target tracking

The probability hypothesis density (PHD) filter and its cardinalised version PHD (CPHD) have been demonstratedasa class of promising algorithms for multi-target tracking (MTT) with unknown,time-varying number of targets. However, these methods can only be used in MTT systems with some prior information of multipletargets, such asdynamic model, newborn target distribution etc.;otherwise, the tracking performance will decline greatly. To solve this problem,an adaptive Grid-driven technique is proposed based on the framework of the PHD/CPHD filter to recursively estimate the target states without knowing the dynamic model and the newborn target distribution. The grid size can be adaptively adjusted according to the grid resolution, and the dynamic tendencies of the grids can respond to the unknown dynamic models of each targets, including arbitrary manoeuvring models. The newborn targets outside the grid area can be identified by analysing the measurements, and some new grids are generated around them. The experimental results show that the proposed algorithm has a better performance than the traditional particle filter-based PHD method in terms of average optimal sub-pattern assignment distance and average target number estimation for tracking multiple targets with unknown dynamic parameters and unknown newborn target distribution.

Radiation intensity Gaussian mixture PHD filter for close target tracking

The Gaussian mixture probability hypothesis density (GM-PHD) filter has recently been devised as a suboptimal Bayesian solution for multiple target tracking. However, the performance of standard GM-PHD degrades seriously in close targets tracking. Although the renormalization scheme is proposed to improve the estimation results, the identification problem of measurements generated by different targets and clutter is still unresolved. To this end, this paper develops a radiation intensity PHD filter (RIGM-PHD). First, the Gaussian distribution with signal-to-noise (SNR) information is proposed to model the radiation intensity and describe the relationship between the target radiation intensity and clutter level. Then, in order to circumvent the issue that the real target SNR can't be obtained precisely, we construct a likelihood function of radiation intensity for unknown target SNR and derive new PHD recursion equations. Second, a labeling update scheme is also provided to prevent the incorrect propagation of identities of close targets. Finally, comprehensive Monte Carlo simulations in terms of various detection probabilities and clutter rates for parallel and crossing targets are performed to investigate the effectiveness of the proposed filter.

Distributed multi-view multi-target tracking based on CPHD filtering

This paper addresses distributed multi-target tracking over a network of sensors having different fields-of-view (FoVs). Specifically, a cardinalized probability hypothesis density (CPHD) filter is run at each sensor node. Due to the fact that each sensor node has limited FoV, the standard fusion methods need to be suitably modified. In fact, the monitored area of multiple sensor nodes consists of several parts that are either exclusive of a single node, i.e. or common to multiple (at least two) nodes. In this setting, the crucial issue is how to account for these different information sets in the fusion rule. The problem is particularly challenging when the knowledge of the FoVs is unreliable, for example because of the presence of unknown occlusions, and when local sensors can have valuable information also on targets located outside the current nominal FoV, for example thanks to the diffusion of information in the network or because the FoVs are time-varying. In this context, we propose a distributed CPHD filter based on the idea of decomposing the posterior densities to be fused so as to account for the different information sets. A new decomposition method is proposed that does not rely on the nominal FoVs and, instead, uses clustering to decompose the posterior intensity function into multiple sub-intensities, and reconstructing the corresponding cardinality distribution via multi-Bernoulli approximation. Then, fusion is performed in parallel according to either the geometric average or arithmetic average rule. Simulation experiments are provided to demonstrate the effectiveness of the proposed approach.

A Labeled GM-PHD Filter for Explicitly Tracking Multiple Targets.

In this study, an explicit track continuity algorithm is proposed for multitarget tracking (MTT) based on the Gaussian mixture (GM) implementation of the probability hypothesis density (PHD) filter. Trajectory maintenance and multitarget state extraction in the GM-PHD filter have not been effectively integrated to date. To address this problem, we propose an improved GM-PHD filter. In this approach, the Gaussian components are classified and labeled, and multitarget state extraction is converted into multiple single-state extractions. This provides the identity label of the individual target and can shield against the negative effects of clutter in the prior density region on the estimates, thus realizing the integration of trajectory maintenance with state extraction in the GM-PHD filter. As no additional associated procedures are required, the overall real-time performance of the proposed filter is similar to or slightly lower than that of the basic GM-PHD filter. The results of numerical experiments demonstrate that the proposed approach can achieve explicit track continuity.

Resilience in Multirobot Multitarget Tracking With Unknown Number of Targets Through Reconfiguration

We address the problem of maintaining resource availability in a networked multirobot team performing distributed tracking of an unknown number of targets in a bounded environment. Robots are equipped with sensing and computational resources, enabling them to cooperatively track a set of targets using a distributed probability hypothesis density (PHD) filter. We use the trace of a robot's sensor measurement noise covariance matrix to quantify its sensing quality. While executing the tracking task, if a robot experiences sensor quality degradation, the team's communication network is reconfigured such that the robot with the faulty sensor may share information with other robots to improve the team's target-tracking ability without enforcing a large change in the number of active communication links. A central system monitor executes the network reconfiguration computations. We consider two different PHD fusion methods and propose four different mixed-integer semi-definite programming (MISDP) formulations (two formulations for each PHD fusion method) to accomplish our objective. All MISDP formulations are validated in simulation.

A new PHD-SLAM method based on memory attenuation filter

Aiming at the problem that the low signal-to-noise ratio in the complex indoor environment will lead to the complex data association and low accuracy of the simultaneous localization and mapping (SLAM) method, a PHD-SLAM method based on the memory attenuation (MA) filter and mixed newborn maps information (MBMA-PHD-SLAM) is proposed in this paper. First of all, this method based on a probability hypothesis density (PHD) filter. Therefore, this method avoids data association and solves the problem of high computational complexity. Besides, the general PHD-SLAM method tends to cause the filter to diverge when the indoor signal-to-noise ratio is low. Therefore, MA filter is combined into PHD-SLAM. This method can reduce the influence of old data on SLAM, which improves the filtering divergence problem and improves the accuracy of SLAM. What’s more, since conventional SLAM algorithms usually have a problem of lack of prior information and in order to further improve the accuracy of SLAM on the basis of the above method, a method of mixed newborn maps information is proposed to solve this problem. Finally, the experiment mainly compares the method in this paper with the classic Rao-Blackwellised (RB) implementation of the PHD-SLAM (RB-PHD-SLAM). The results show that this method outperforms the PHD-SLAM method in terms of estimating map features and localization accuracy. The method in this paper effectively improves the ability of the mobile robot to explore unknown indoor environments.

Enlarging the Usable Hand Tracking Area by Using Multiple Leap Motion Controllers in VR

Leap Motion Controller (LMC) is a widely-used 3D user-interface device for virtual reality (VR) in hand tracking applications. However, the tracking area of a single LMC is not sufficient to cover the complete range of hand motion typically used in virtual reality applications, which can cause inconvenience and unnatural behavior of bare-hand interaction in a cooperated virtual environment. In this paper, we propose fusing the data from multiple LMCs to enlarge the tracking area. We present our shared-view calibration method based on a Least-squares Fitting algorithm. To track two hands in the enlarged tracking area, we propose a multi-targets tracking algorithm based on a Clustering-based Labeled Probability Hypothesis Density filter implemented by Gaussian mixture approach. A hand-recognition confidence is proposed to improve the tracking performance when hands are incorrectly recognized. The performance of the proposed algorithm was evaluated by three tests based on a five-LMCs system used on an Oculus Rift S. Results show that our system can track two hands stably in the range of 202.16 degrees horizontally and 164.43 degrees vertically, and the proposed algorithm shows superiority in tracking robustness under hand-recognition errors. The contribution of this paper is to provide a detailed guide for designing an enlarged hand-tracking system using sensor fusion.

A Robust SMC-PHD Filter for Multi-Target Tracking with Unknown Heavy-Tailed Measurement Noise.

In multi-target tracking, the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter is a practical algorithm. Influenced by outliers under unknown heavy-tailed measurement noise, the SMC-PHD filter suffers severe performance degradation. In this paper, a robust SMC-PHD (RSMC-PHD) filter is proposed. In the proposed filter, Student-t distribution is introduced to describe the unknown heavy-tailed measurement noise where the degrees of freedom (DOF) and the scale matrix of the Student-t distribution are respectively modeled as a Gamma distribution and an inverse Wishart distribution. Furthermore, the variational Bayesian (VB) technique is employed to infer the unknown DOF and scale matrix parameters while the recursion estimation framework of the RSMC-PHD filter is derived. In addition, considering that the introduced Student- t distribution might lead to an overestimation of the target number, a strategy is applied to modify the updated weight of each particle. Simulation results demonstrate that the proposed filter is effective with unknown heavy-tailed measurement noise.

Adaptive probability hypothesis density filter for multi-target tracking with unknown measurement noise statistics

Under the Gaussian noise assumption, the probability hypothesis density (PHD) filter represents a promising tool for tracking a group of moving targets with a time-varying number. However, inaccurate prior statistics of the random noise will degrade the performance of the PHD filter in many practical applications. This paper presents an adaptive Gaussian mixture PHD (AGM-PHD) filter for the multi-target tracking (MTT) problem in the scenario where both the mean and covariance of measurement noise sequences are unknown. The conventional PHD filters are extended to jointly estimate both the multi-target state and the aforementioned measurement noise statistics. In particular, the Normal-inverse-Wishart and Gaussian distributions are first integrated to represent the joint posterior intensity by transforming the measurement model into a new formulation. Then, the updating rule for the hyperparameters of the model is derived in closed form based on variational Bayesian (VB) approximation and Bayesian conjugate prior heuristics. Finally, the dynamic system state and the noise statistics are updated sequentially in an iterative manner. Simulations results with both constant velocity and constant turn model demonstrate that the AGM-PHD filter achieves comparable performance as the ideal PHD filter with true measurement noise statistics.

Strong Tracking PHD Filter Based on Variational Bayesian with Inaccurate Process and Measurement Noise Covariance.

Assuming that the measurement and process noise covariances are known, the probability hypothesis density (PHD) filter is effective in real-time multi-target tracking; however, noise covariance is often unknown and time-varying for an actual scene. To solve this problem, a strong tracking PHD filter based on Variational Bayes (VB) approximation is proposed in this paper. The measurement noise covariance is described in the linear system by the inverse Wishart (IW) distribution. Then, the fading factor in the strong tracking principle uses the optimal measurement noise covariance at the previous moment to control the state prediction covariance in real-time. The Gaussian IW (GIW) joint distribution adopts the VB approximation to jointly return the measurement noise covariance and the target state covariance. The simulation results show that, compared with the traditional Gaussian mixture PHD (GM-PHD) and the VB-adaptive PHD, the proposed algorithm has higher tracking accuracy and stronger robustness in a more reasonable calculation time.

Robust Target Detection and Tracking Algorithm Based on Roadside Radar and Camera.

Intelligent transportation systems (ITSs) play an increasingly important role in traffic management and traffic safety. Smart cameras are the most widely used sensors in ITSs. However, cameras suffer from a reduction in detection and positioning accuracy due to target occlusion and external environmental interference, which has become a bottleneck restricting ITS development. This work designs a stable perception system based on a millimeter-wave radar and camera to address these problems. Radar has better ranging accuracy and weather robustness, which is a better complement to camera perception. Based on an improved Gaussian mixture probability hypothesis density (GM-PHD) filter, we also propose an optimal attribute fusion algorithm for target detection and tracking. The algorithm selects the sensors’ optimal measurement attributes to improve the localization accuracy while introducing an adaptive attenuation function and loss tags to ensure the continuity of the target trajectory. The verification experiments of the algorithm and the perception system demonstrate that our scheme can steadily output the classification and high-precision localization information of the target. The proposed framework could guide the design of safer and more efficient ITSs with low costs.

Measurement-driven sequential random sample consensus GM-PHD filter for ballistic target tracking

In this paper, a new filter named measurement-driven sequential random sample consensus Gaussian mixture probability hypothesis density (MD-S-RANSAC-GM-PHD) filter is proposed for estimating the trajectory of a ballistic target during its coast phase. Unlike the traditional multiple-target tracking (MTT) algorithms that require data association, the proposed method involves modelling the respective collections of targets and measurements as random finite sets (RFS) and applying the PHD recursion to propagate the posterior intensity in time. To generate the new birth target intensity adaptively, a measurement-driven birth intensity estimation algorithm is developed. Since the measurement set used for birth intensity estimation may contain a large amount of clutter, a measurement set pre-processing method based on density-based spatial clustering and sequential random sample consensus (S-RANSAC) algorithm is proposed to eliminate the interference of clutter on generating new target birth intensity. Specifically, the proposed filter extends the standard GM-PHD filter by distinguishing between the persistent and the newborn target, and the extended Kalman filter (EKF) implementation of our proposed filter for ballistic target tracking is also derived. Simulation results illustrate the advantages of our proposed filter in tracking ballistic missile.

Message Passing and Hierarchical Models for Simultaneous Tracking and Registration

Sensor registration is an important problem that must be considered when attempting to perform any kind of data fusion in multimodal, multisensor target tracking. In this multiple target tracking (MTT) application, any inaccuracies in the registration can lead to false tracks being created, and tracks of true targets being stopped prematurely. This article introduces a method for simultaneously tracking multiple targets in a surveillance region and estimating appropriate sensor registration parameters so that sensor fusion can be performed accurately. The proposed method is based around particle belief propagation (BP), a recent but highly efficient framework for tracking multiple targets. The proposed method also uses a hierarchical model which allows for multiple processes to be linked and interact with one another. We present a comprehensive set of simulations and results using differing, asynchronous sensor setups, and compare with a random finite set (RFS) approach, namely the sequential Monte Carlo (SMC)-probability hypothesis density (PHD) filter. The results show the proposed method is 17% more accurate than the RFS approach on average.

Bearings-only multitarget tracking based onRao-Blackwellized particle CPHD filter

Following Mahler’s framework forinformation fusion, this paper develops a implementationof cardinalized probability hypothesis density (CPHD)filter for bearings-only multitarget tracking.Rao-Blackwellized method is introduced in the CPHDfiltering framework for mixed linear/nonlinear state spacemodels. The sequential Monte Carlo (SMC) method is usedto predict and estimate the nonlinear state of targets.Kalman filter (KF) is adopted to estimate the linear stateswith the information embedded in the estimated nonlinearstates. The multitarget state estimates are extracted byutilizing the kernel density estimation (KDE) theory andmean-shift algorithm to enhance tracking performance.Moreover, the computational load of the filter is analyzedby introducing equivalent flop measure. Finally, theperformance of the proposed Rao-Blackwellized particleCPHD filter is evaluated through a challengingbearings-only multitarget tracking simulation experiment.

PHD Filter for Object Tracking in Road Traffic Applications Considering Varying Detectability.

This paper considers the object detection and tracking problem in a road traffic situation from a traffic participant’s perspective. The information source is an automotive radar which is attached to the ego vehicle. The scenario characteristics are varying object visibility due to occlusion and multiple detections of a vehicle during a scanning interval. The goal is to maintain and report the state of undetected though possibly present objects. The proposed algorithm is based on the multi-object Probability Hypothesis Density filter. Because the PHD filter has no memory, the estimate of the number of objects present can change abruptly due to erroneous detections. To reduce this effect, we model the occlusion of the object to calculate the state-dependent detection probability. Thus, the filter can maintain unnoticed but probably valid hypotheses for a more extended period. We use the sequential Monte Carlo method with clustering for implementing the filter. We distinguish between detected, undetected, and hidden particles within our framework, whose purpose is to track hidden but likely present objects. The performance of the algorithm is demonstrated using highway radar measurements.