Probability Hypothesis Density Research Articles

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.

Multi-target identity management for unknown and time-varying number of targets in clutter

A novel multi-target identity management algorithm, called IM-GMPHD (Identity management with Gaussian mixture probability hypothesis density) algorithm, is proposed to simultaneously track an unknown and time-varying number of targets in clutter and manage the targets’ identities effectively and efficiently over time. The targets’ identities are managed by recursively computing the target identity beliefs using the target-measurement correlation. An augmented GMPHD filter is also developed in this paper to calculate the target-measurement correlation. In addition, the target identity beliefs can be updated to a lower uncertainty level whenever there is available target identity information. The proposed multi-target identity management algorithm is demonstrated through various illustrative simulation scenarios.

A PHD-SLAM Method for Mixed Birth Map Information Based on Amplitude Information

The Simultaneous Localization and Mapping (SLAM) method of mobile robots has the problem of low accuracy in complex environments with dense clutter and various map features, such as complex indoor environments and underwater environments. This problem is mainly embodied in estimating the location and number of feature points on the map and the position of the robot itself. In order to solve this problem, a new method based on the probability hypothesis density (PHD) SLAM is proposed in this paper, a PHD-SLAM Method for Mixed Birth Map Information Based on Amplitude Information (AI-MBMI-PHD-SLAM). Firstly, this paper proposes a PHD-SLAM method based on amplitude information (AI-PHD-SLAM). The method uses the amplitude information of map features to obtain more precise map features. Then, the clutter likelihood function is used to improve the estimation accuracy of the feature map in the SLAM process. Meanwhile, this paper studies the performance of the PHD-SLAM method with the amplitude information under the condition of the known signal-to-noise ratio or the unknown signal-to-noise ratio. Secondly, aiming at the problem that PHD-SLAM lacks a priori information in the prediction stage, an AI-PHD-SLAM-based mixed birth map information method is added. In this method, map information that has been detected before the previous moment is added to the observation information in the map prediction phase as a new map information set in the prediction phase. This can increase the prior information and improve the problem of insufficient prior information in the prediction stage. The results of the experiments show that the proposed method and the improved method outperform the RB-PHD-SLAM method in estimating the number and location accuracy of map features and have higher computational efficiency.

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.

PHD-SLAM 2.0: Efficient SLAM in the Presence of Missdetections and Clutter

This article addresses <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneous localization and mapping</i> (SLAM) via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">probability hypothesis density</i> (PHD) filtering. The resulting approach, named PHD-SLAM, has demonstrated its effectiveness, especially when measurements provided by the sensors onboard the vehicle are highly contaminated by missdetections and clutter. However, since the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proposal distribution</i> (PD) of standard PHD-SLAM does not take into account most recently received measurements, a huge amount of particles are typically needed in order to achieve satisfactory performance. In this article, a new PD, which aims to approximate the vehicle pose posterior, is proposed for PHD-SLAM. The resulting algorithm, named PHD-SLAM 2.0, allows for drastically reducing the number of particles, and hence, the computational burden, while preserving the SLAM performance. The computational complexity of PHD-SLAM 2.0 is analyzed, and its performance is assessed via both simulated and real-data experiments.

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.

Multi-GMTI fusion for Doppler blind zone suppression using PHD fusion

For ground moving target indication (GMTI) sensor tracking, the existence of the Doppler blind zone (DBZ) seriously deteriorates tracking performance. In order to minimize the adverse effects of the DBZ factor, this paper puts forward the idea of using sensor fusion technique to suppress the DBZ masking problem. First, we derive the probability hypothesis density (PHD) fusion under the generalized covariance intersection (GCI) framework and its Gaussian mixture (GM) implementation for fusing local PHDs from the local trackers. However, we find that there is the problem of cardinality underestimation (CUE) in the original PHD fusion, which is exacerbated when targets are masked by the DBZ. After analyzing this problem in detail, we propose an improved PHD fusion algorithm through operations such as scale coefficient correction, GM component partition, and fused label correction. Finally, the feasibility and effectiveness of the proposed fusion are verified through numerical examples, and it is proved that it alleviates the CUE problem and is significantly better than local trackers.

Decentralized Control of Large Collaborative Swarms Using Random Finite Set Theory

Controlling large swarms of robotic agents presents many challenges including but not limited to computational complexity due to a large number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. The contribution of this work is to decentralize random finite set (RFS)-based control of large collaborative swarms for controlling individual agents. The RFS-based control formulation assumes a Gaussian mixture probability hypothesis density approximation and a complete topology for centralized swarm control. To generalize the control topology in a localized or decentralized manner, a sparse linear quadratic regulator (LQR) is used to sparsify the RFS-based control gain matrix obtained using iterative LQR. This allows agents to use information of agents near each other (localized topology) or only the agent's own information (decentralized topology) to make a control decision. Sparsity and performance for decentralized RFS-based control are compared for different degrees of localization in feedback control gains which show that the stability and performance compared to centralized control do not degrade significantly in providing RFS-based control for large collaborative swarms.

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.

Joint tracking and classification of multiple extended targets via the PHD filter and star-convex RHM

For joint tracking and classification (JTC) of multiple extended targets in the presence of clutter and detection uncertainty, this paper proposes a recursive algorithm based on the probability hypothesis density (PHD) filter and star-convex random hypersurface model (RHM), resulting in the JTC-RHM-PHD filter. By modeling the extent state via the star-convex RHM, the JTC-RHM-PHD filter can classify the extended targets using the feature information of size and shape, instead of the size information only in the random matrix model (RMM)-based JTC method. To integrate the prior class-dependent information into the tracking procedure and obtain the recursive expressions of the JTC-RHM-PHD filter, the relationship between the instantaneous extent state and prior class-dependent information is first constructed. Then, the target state is remodeled by two vectors: one for the kinematic state and another for the extent state. The kinematic state is estimated via a Kalman-like filter. For the extent state, the measurement-based extent state and class-based extent state are obtained via the sensor measurements and prior class-dependent information, respectively. The two kinds of extent states are used to determine the target class. At last, a Gamma-Gaussian-Gaussian mixture implementation of the JTC-RHM-PHD filter is presented. Simulation results indicate that: (1) Compared with the RMM-based JTC method, the proposed JTC-RHM-PHD filter can correctly classify multiple extended targets with similar sizes. (2) Compared with the RHM-PHD filter, the proposed JTC-RHM-PHD filter has superior tracking performance with a similar algorithm complexity.

Robust Detection and Tracking Method for Moving Object Based on Radar and Camera Data Fusion

Obtaining the accurate and real-time state of surrounding objects is essential for automated vehicle planning and decision-making to ensure safe driving. In complex traffic scenarios, object occlusion, clutter interference, and limited sensor detection capabilities lead to false alarms and missed object detection, making it challenging to ensure the stability of tracking and state prediction. To address these challenges, in this study, we developed a robust multi-object detection and tracking method for moving objects based on radar and camera data fusion. First, the radar and camera perform target detection independently, and the detection results are correlated in the image plane to generate a random finite set with an object type. Then, based on the Gaussian mixture probability hypothesis density algorithm framework, the tracking process is improved using elliptic discriminant thresholds, an attenuation function, and simplified pruning methods. The experimental results demonstrate that the improved algorithm can accurately estimate the number and state of targets in object occlusion, measurement loss scenarios, and achieve robust continuous multi-object tracking. The proposed method could guide the design of safer and more efficient intelligent driving systems.

Heterogeneous Multi-Sensor Fusion With Random Finite Set Multi-Object Densities

This paper addresses the density based multi-sensor cooperative fusion using random finite set (RFS) type multi-object densities (MODs). Existing fusion methods use scalar weights to characterize the relative information confidence among the local MODs, and in this way the portion of contribution of each local MOD to the fused global MOD can be tuned via adjusting these weights. Our analysis shows that the fusion mechanism of using a scalar coefficient can be oversimplified for practical scenarios, as the information confidence of an MOD is complex and usually space-varying due to the imperfection of sensor ability and the various impacts from surveillance environment. Consequently, severe fusion performance degradation can be observed when these scalar weights fail to reflect the actual situation. We make two contributions towards addressing this problem. Firstly, we propose a novel heterogeneous fusion method to perform the information averaging among local RFS MODs. By factorizing each local MODs into a number of smaller size sub-MODs, it can transform the original complicated fusion problem into a much easier parallelizable multi-cluster fusion problem. Secondly, as the proposed fusion strategy is a general procedure without any particular model assumptions, we further derive the detailed heterogeneous fusion equations, with centralized network architecture, for both the probability hypothesis density (PHD) filter and the multi-Bernoulli (MB) filter. The Gaussian mixture implementations of the proposed fusion algorithms are also presented. Various numerical experiments are designed to demonstrate the efficacy of the proposed fusion methods.

Digital Twin-Enabled Online Battlefield Learning with Random Finite Sets.

The digital twin is becoming the most promising emerging technology in the field of unmanned combat and has the potential to innovate future combat styles. Online battlefield learning is one of the key technologies for supporting the successful application of digital twin in unmanned combat. Since there is an urgent need for effective algorithms for online learning the battlefield states in real time, a new random finite set- (RFS-) based algorithm is proposed in the presence of detection uncertainty including clutters, missed detection, and noises. The system architecture and operational mode for implementing the digital twin-enabled online battlefield learning are provided. The unmanned ground vehicle (UGV) is employed as the experimental subject for systematically describing the proposed algorithm. The system architecture for implementing the digital twin-enabled online battlefield learning is firstly given, and its operational mode is also described in detail. The RFS-based digital twin models including the battlefield state model, UGV motion model, and sensor model are designed. The Bayesian inference is adopted, and the probability hypothesis density (PHD) filter is modified to implement the online learning process. At last, a group of experiments are conducted to verify the performance and effectiveness of the proposed algorithm. The research work in this paper will provide a good demonstration of the application of digital twin in unmanned combat.

A Linear Algorithm for Multi-Target Tracking in the Context of Possibility Theory

We present a modelling framework for multi-target tracking based on possibility theory and illustrate its ability to account for the general lack of knowledge that the target-tracking practitioner must deal with when working with real data. We also introduce and study variants of the notions of point process and intensity function, which lead to the derivation of an analogue of the probability hypothesis density (PHD) filter. The gains provided by the considered modelling framework in terms of flexibility lead to the loss of some of the abilities that the PHD filter possesses; in particular the estimation of the number of targets by integration of the intensity function. Yet, the proposed recursion displays a number of advantages such as facilitating the introduction of observation-driven birth schemes and the modelling the absence of information on the initial number of targets in the scene. The performance of the proposed approach is demonstrated on simulated data.

Multi-Person Activity Recognition in Continuously Monitored Smart Homes.

Activity recognizers are challenging to design for continuous, in-home settings. However, they are notoriously difficult to create when there is more than one resident in the home. Despite recent efforts, there remains a need for an algorithm that can estimate the number of residents in the house, split a time series stream into separate substreams, and accurately identify each resident's activities. To address this challenge, we introduce Gamut. This novel unsupervised method jointly estimates the number of residents and associates sensor readings with those residents, based on a multi-target Gaussian mixture probability hypothesis density filter. We hypothesize that the proposed method will offer robust recognition for homes with two or more residents. In experiments with labeled data collected from 50 single-resident and 11 multi-resident homes, we observe that Gamut outperforms previous unsupervised and supervised methods, offering a robust strategy to track behavioral routines in complex settings.