Gaussian Mixture Probability Hypothesis Density Research Articles

Multisource‐multitarget cooperative positioning using probability hypothesis density filter in internet of vehicles

AbstractAccurate positioning of intelligent connected vehicle (ICV) is a key element for the development of cooperative intelligent transportation system. In vehicular networks, lots of state‐related measurements, especially the mutual measurements between ICVs, are shared. It is an advisable strategy to fuse these measurements for a more robust positioning. In this context, an innovative framework, referred to as multisource‐multitarget cooperative positioning (MMCP) is presented. In MMCP, ICVs are local information source, that upload both the states of ICVs estimated by on‐board sensors and the relative vectors between surrounding objects and vehicles to a fusion centre. In the fusion centre, ICVs are selected as the global targets, and the relative vectors are converted into global measurements. Then, the MMCP is modelled into a multi‐target tracking problem with specific targets. This paper proposes a low complexity Gaussian mixture probability hypothesis density (GM‐PHD‐LC) filter to match and fuse the global measurements to further improve the estimation of ICVs. The evaluation results show that our GM‐PHD‐LC can provide 10 Hz positioning services in urban area, and significantly improve the positioning accuracy compared to the standalone global navigation satellite system.

Advancing ADAS Perception: A Sensor-Parameterized Implementation of the GM-PHD Filter.

Modern vehicles equipped with Advanced Driver Assistance Systems (ADAS) rely heavily on sensor fusion to achieve a comprehensive understanding of their surrounding environment. Traditionally, the Kalman Filter (KF) has been a popular choice for this purpose, necessitating complex data association and track management to ensure accurate results. To address errors introduced by these processes, the application of the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is a good choice. This alternative filter implicitly handles the association and appearance/disappearance of tracks. The approach presented here allows for the replacement of KF frameworks in many applications while achieving runtimes below 1 ms on the test system. The key innovations lie in the utilization of sensor-based parameter models to implicitly handle varying Fields of View (FoV) and sensing capabilities. These models represent sensor-specific properties such as detection probability and clutter density across the state space. Additionally, we introduce a method for propagating additional track properties such as classification with the GM-PHD filter, further contributing to its versatility and applicability. The proposed GM-PHD filter approach surpasses a KF approach on the KITTI dataset and another custom dataset. The mean OSPA(2) error could be reduced from 1.56 (KF approach) to 1.40 (GM-PHD approach), showcasing its potential in ADAS perception.

Gaussian Mixture Probability Hypothesis Density Filter for Heterogeneous Multi-Sensor Registration

Spatial registration is a prerequisite for data fusion. Existing methods primarily focus on similar sensor scenarios and rely on accurate data association assumptions. To address the heterogeneous sensor registration in complex data association scenarios, this paper proposes a Gaussian mixture probability hypothesis density (GM-PHD)-based algorithm for heterogeneous sensor bias registration, accompanied by an adaptive measurement iterative update algorithm. Firstly, by constructing augmented target state motion and measurement models, a closed-form expression for prediction is derived based on Gaussian mixture (GM). In the subsequent update, a two-level Kalman filter is used to achieve an approximate decoupled estimation of the target state and measurement bias, taking into account the coupling between them through pseudo-likelihood. Notably, for heterogeneous sensors that cannot directly use sequential update techniques, sequential updates are first performed on sensors that can obtain complete measurements, followed by filtering updates using extended Kalman filter (EKF) sequential update techniques for incomplete measurements. When there are differences in sensor quality, the GM-PHD fusion filter based on measurement iteration update is sequence-sensitive. Therefore, the optimal subpattern assignment (OSPA) metric is used to optimize the fusion order and enhance registration performance. The proposed algorithms extend the multi-target information-based spatial registration algorithm to heterogeneous sensor scenarios and address the impact of different sensor-filtering orders on registration performance. Our proposed algorithms significantly improve the accuracy of bias estimation compared to the registration algorithm based on significant targets. Under different detection probabilities and clutter intensities, the average root mean square error (RMSE) of distance and angular biases decreased by 11.8% and 8.6%, respectively.

Modified Gaussian Mixture Probability Hypothesis Density Filtering using Clutter Density Estimation for Multiple Target Tracking

Modified Gaussian Mixture Probability Hypothesis Density Filtering using Clutter Density Estimation for Multiple Target Tracking

A Gaussian Mixture PHD Filter for Multitarget Tracking in Target-Dependent False Alarms

A Gaussian Mixture PHD Filter for Multitarget Tracking in Target-Dependent False Alarms

An augmented state Gaussian mixture probability hypothesis density filter for multitarget tracking of autonomous underwater vehicles

Multitarget tracking is an important task for autonomous underwater vehicles (AUVs). Due to the limited space on AUVs, the aperture of the sonar array mounted on an AUV is small. The finite resolution of AUV sonar systems results in weak targets being masked by strong targets when they are close in angular space, leading to the trajectory fracture problem of weak targets in the azimuth crossing scenario. To address this problem, an augmented state Gaussian mixture probability hypothesis density (GM-PHD) filter is proposed. Since the acoustic signals radiated by targets contain some narrowband discrete components (known simply as tonals or lines), we focus on leveraging the tonals to enhance tracking performance. First, we model the augmented state dynamics, which contain both direction-of-arrival (DOA) and tonal components, and DOA tracks can be generated by the augmented state GM-PHD filter. Second, track segments are clustered by the modified density-based spatial clustering of applications with noise (DBSCAN) algorithm according to the estimated tonals. Finally, track segments with the same clustering results are associated with the same target, and the track stitching method is applied to overcome the trajectory fracture problem. The effectiveness of the algorithm is verified by simulation experiments in different scenarios.

Gaussian Process Gaussian Mixture PHD Filter for 3D Multiple Extended Target Tracking

This paper addresses the problem of tracking multiple extended targets in three-dimensional space. We propose the Gaussian process Gaussian mixture probability hypothesis density (GP-PHD) filter, which is capable of tracking multiple extended targets with complex shapes in the presence of clutter. Our approach combines the Gaussian process regression measurement model with the probability hypothesis density filter to estimate both the kinematic state and the shape of the targets. The shape of the extended target is described by a 3D radial function and is estimated recursively using the Gaussian process regression model. Furthermore, we transform the recursive Gaussian process regression problem into a state estimation problem by deriving a state space model such that the estimation of the extent can be integrated into the kinematic part. We derive the predicted likelihood function of the PHD filter and provide a closed-form Gaussian mixture implementation. To evaluate the performance of the proposed filter, we simulate a typical extended target tracking scenario and compare the GP-PHD filter with the traditional Gamma Gaussian Inverse-Wishart PHD (GGIW-PHD) filter. Our results demonstrate that the proposed algorithm outperforms the GGIW-PHD filter in terms of estimating both kinematic states and shape. We also investigate the impact of the measurement rates on both filters; it is observed that the proposed filter exhibits robustness across various measurement rates, while the GGIW-PHD filter suffers under low-measurement-rate conditions.

Contact-Free Multitarget Tracking Using Distributed Massive MIMO-OFDM Communication System: Prototype and Analysis

Wireless-based human activity recognition has become an essential technology that enables contact-free human-machine and human-environment interactions. In this paper, we consider contact-free multi-target tracking (MTT) based on available communication systems. A radar-like prototype is built upon a sub-6 GHz distributed massive multiple-input and multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) communication system. Specifically, the raw channel state information (CSI) is calibrated in the frequency and antenna domain before being used for tracking. Then the targeted CSIs reflected or scattered from the moving pedestrians are extracted. To evade the complex association problem of distributed massive MIMO-based MTT, we propose to use a complex Bayesian compressive sensing (CBCS) algorithm to estimate the targets’ locations based on the extracted target-of-interest CSI signal directly. The estimated locations from CBCS are fed to a Gaussian mixture probability hypothesis density (GM-PHD) filter for tracking. A multi-pedestrian tracking experiment is conducted in a room with a size of 6.5 m×10 m to evaluate the performance of the proposed algorithm. According to experimental results, we achieve 75th and 95th percentile accuracy of 12.7 cm and 18.2 cm for single-person tracking and 28.9 cm and 45.7 cm for multi-person tracking, respectively. Furthermore, the proposed algorithm achieves tracking purposes in real-time, which is promising for practical MTT use cases.

Underwater multi-source DOA tracking using uniform linear array based on improved GM-PHD filter

Uniform linear array (ULA) is commonly used for collecting underwater acoustic signals, and the direction-of-arrival (DOA) is obtained by array signal processing methods. The ULA-based multi-source DOA tracking suffers from the performance degradation caused by the presence of false tracks from port-starboard ambiguity. To address this problem, we propose a bearing ambiguity discrimination algorithm. Firstly, the sum of real bearing motion velocity between truth and ambiguous targets is established with the Gaussian distribution. Secondly, an improved Gaussian mixture probability hypothesis density filter, which can adaptively generate target birth intensity, is utilized to select truth and ambiguous bearings generated by the same target from the estimated posterior intensity. Thirdly, truth and ambiguous bearings are discriminated according to the fact that the change of array heading will lead to a significant change in ambiguous bearing. Simulation and real experimental results illustrate that the proposed algorithm can provide unambiguous target-generated tracks and accurately estimate the number of targets.

Real-Time Trajectory Prediction Method for Intelligent Connected Vehicles in Urban Intersection Scenarios

Intelligent connected vehicles (ICVs) have played an important role in improving the intelligence degree of transportation systems, and improving the trajectory prediction capability of ICVs is beneficial for traffic efficiency and safety. In this paper, a real-time trajectory prediction method based on vehicle-to-everything (V2X) communication is proposed for ICVs to improve the accuracy of their trajectory prediction. Firstly, this paper applies a Gaussian mixture probability hypothesis density (GM-PHD) model to construct the multidimension dataset of ICV states. Secondly, this paper adopts vehicular microscopic data with more dimensions, which is output by GM-PHD as the input of LSTM to ensure the consistency of the prediction results. Then, the signal light factor and Q-Learning algorithm were applied to improve the LSTM model, adding features in the spatial dimension to complement the temporal features used in the LSTM. When compared with the previous models, more consideration was given to the dynamic spatial environment. Finally, an intersection at Fushi Road in Shijingshan District, Beijing, was selected as the field test scenario. The final experimental results show that the GM-PHD model achieved an average error of 0.1181 m, which is a 44.05% reduction compared to the LiDAR-based model. Meanwhile, the error of the proposed model can reach 0.501 m. When compared to the social LSTM model, the prediction error was reduced by 29.43% under the average displacement error (ADE) metric. The proposed method can provide data support and an effective theoretical basis for decision systems to improve traffic safety.

Adaptive tracking and classification algorithm for multiple extended targets based on irregular shape driven

The extended target Gaussian mixture probability hypothesis density (ET-GM-PHD) filter is considered as a promising algorithm for tracking multiple extended targets (METs). However, when the densities of the newborn targets are unknown and some closely spaced targets exist in the tracking scenarios, the tracking accuracy will decrease greatly, even some targets are missed tracking. For these problems, we propose an adaptive tracking and classification algorithm for METs based on B-spline shape driven. Firstly, the B-spline shape features of the estimated MET are extracted and employed for improving the measurement partition, especially for the closely spaced METs. Then shape-feature-based association matrix between the measurements and the predicted targets is calculated for identifying the newborn targets and reducing the time complexity of the Gaussian component calculation. Moreover, the extracted shape features are also used for target state update and classification, which can further enhance the tracking accuracy. Experimental results show that the proposed algorithm has a high execution efficiency and tracking accuracy for the complicated scenarios with irregular-shaped closely spaced METs and unknown newborn target densities.

Passive acoustic localization and tracking of Rice’s whales (Balaenoptera ricei) in the northeastern Gulf of Mexico

The endangered Rice’s whale (Balaenoptera ricei) is endemic to the Gulf of Mexico and is also the Gulf’s only resident baleen whale. Limited knowledge of this species’ ecology combined with the high industrialization of this region raises serious conservation concerns. As part of an ongoing project to study the Rice’s whale in its core habitat, an array of moored passive acoustic monitoring sites has been near-continuously deployed in the northeastern Gulf of Mexico since May 2021. While detecting Rice’s whale calls in these data provides valuable insight into the species’ spatiotemporal distribution, further analyses to localize and track individual whales would allow better characterization of their acoustic behavior and movement patterns, possibly allowing for density estimation. Here, we present a method for automated passive acoustic localization and tracking of calling Rice’s whales. The two key components of this approach are (1) the use of opportunistic sound sources to time-synchronize recordings across sites given clock-drift between acoustic recorders and (2) the implementation of automatic multi-target tracking techniques based on the Gaussian mixture probability hypothesis density filter. Analyses of the first four months of data show potential for measuring basic behavioral parameters such as calling rate, source level, and average swim speed.

Automated extraction of baleen whale calls based on the pseudo-Wigner–Ville distribution

Baleen whales produce a wide variety of frequency-modulated calls. Extraction of the time-frequency (TF) structures of these calls forms the basis for many applications, including abundance estimation and species recognition. Typical methods to extract the contours of whale calls from a spectrogram are based on the short-time Fourier transform and are, thus, restricted by a fixed TF resolution. Considering the low-frequency nature of baleen whale calls, this work represents the contours using a pseudo-Wigner-Ville distribution for a higher TF resolution at the cost of introducing cross terms. An adaptive threshold is proposed followed by a modified Gaussian mixture probability hypothesis density filter to extract the contours. Finally, the artificial contours, which are caused by the cross terms, can be removed in post-processing. Simulations were conducted to explore how the signal-to-noise ratio influences the performance of the proposed method. Then, in experiments based on real data, the contours of the calls of three kinds of baleen whales were extracted in a highly accurate manner (with mean deviations of 5.4 and 0.051 Hz from the ground-truth contours at sampling rates of 4000 and 100 Hz, respectively) with a recall of 75% and a precision of 78.5%.

A Sector-Matching Probability Hypothesis Density Filter for Radar Multiple Target Tracking

The development of high-tech, dim, small targets, such as drones and cruise missiles, brings great challenges to radar multi-target tracking (MTT), making it necessary to extend the beam dwell time to obtain a high signal-to-noise ratio (SNR). In order to solve the problem of radar sampling time variation exacerbated by extending the beam dwell time when detecting weak targets, a sector-matching (SM) PHD filter is proposed, which combines the actual radar system with a PHD filter and quantifies the relationship between the beam dwell time, the false alarm rate and the detection probability. The proposed filter divides the scanning area into small sectors to obtain actual multi-target measurement times and rederives the prediction and update steps based on the actual sampling time. Furthermore, a state correction step is added before state extraction. Applying the SM structure to the basic Gaussian mixture PHD (GM-PHD) filter and labeled GM-PHD filter, the simulation results demonstrate that the proposed structure can improve the accuracy of multi-weak-target state estimation in the dense clutter and can continuously generate explicit trajectories. The overall real-time performance of the proposed filter is similar to that of the PHD filter.

Extended Object Tracking in Curvilinear Road Coordinates for Autonomous Driving

In literature, Extended Object Tracking (EOT) algorithms developed for autonomous driving predominantly provide obstacles state estimation in cartesian coordinates in the Vehicle Reference Frame. However, in many scenarios, state representation in road-aligned curvilinear coordinates is preferred when implementing autonomous driving subsystems like cruise control, lane-keeping assist, platooning, etc. This paper proposes a Gaussian Mixture Probability Hypothesis Density~(GM-PHD) filter with an Unscented Kalman Filter~(UKF) estimator that provides obstacle state estimates in curvilinear road coordinates. We employ a hybrid sensor fusion architecture between Lidar and Radar sensors to obtain rich measurement point representations for EOT. The measurement model for the UKF estimator is developed with the integration of coordinate conversion from curvilinear road coordinates to cartesian coordinates by using cubic hermit spline road model. The proposed algorithm is validated through Matlab Driving Scenario Designer simulation and experimental data collected at Monza Eni Circuit.

Robust fusion of GM-PHD filters based on geometric average

The Geometric Average (GA) fusion has recently been widely used in multi-sensor multi-target tracking. However, the classical GA-based fusion method performs poorly in the distributed Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters due to the inconsistency of the fused cardinality distribution. Moreover, the performance of the GA fusion method deteriorates further in the presence of missed detections. To this end, this paper presents a Robust Consistency-Balanced GA (RCB-GA) fusion algorithm for the distributed GM-PHD filters. First, we introduce a consistency compensation factor in the fused GM-PHD to dynamically adjust the consistency level of the cardinality distribution according to the spatial proximity of the Gaussian components contained in the local PHDs. Secondly, a three-step fusion strategy separating the fusion of the detection and prediction components is proposed. The robustness of the fusion algorithm is improved by reasonably utilizing the missed detection target information contained in the prediction components of the local PHD. Finally, simulation experiments evaluate the effectiveness and robustness of the proposed algorithm in multi-sensor multi-target tracking scenarios.

Improvement of UAV Tracking Technology in Future 6G Complex Environment Based on GM-PHD Filter

Unmanned aerial vehicles (UAVs) will become an indispensable part of future sixth-generation (6G)-based mobile networks that can provide flexible deposition, strong adaptability, and high service quality. Under the guarantee of blockchain, UAVs can provide efficient communication or computing services for ground intelligence devices and promote the development of wireless communication. However, as the number of UAVs increases, issues regarding UAV path planning, the handling of emergencies, the intrusion of illegal UAVs, etc., will need to be addressed. This paper proposes an improved Gaussian mixture probability hypothesis density (GM-PHD) filter based on machine learning for the target tracking and recognition of non-cooperative UAV swarms. Simulation results demonstrate that the improved filter can effectively suppress clutter interference in complex environments and improve the performance of multi-target recognition and trajectory tracking compared with the traditional GM-PHD filter.

Gaussian mixture probability hypothesis density filter with dynamic probabilities: Application to road traffic surveillance

With the development of autonomous driving system, accurate tracking of the number of vehicles and their states is critical to ensure traffic safety. Since the numbers and states of the vehicles are unknown and time-varying, the road traffic surveillance can be considered as a multiple-target tracking (MTT) problem. The Gaussian mixture probability hypothesis density (GM-PHD) filter is a popular approach in solving MTT problem and has been successfully applied to a range of applications including ground vehicle tracking. However, due to the road constraint, the maneuverability of a ground vehicle is limited to the road lane. Thus, the target detection probability, survival probability, and birth rate, which are assumed to be constant in the original GM-PHD filter, vary according to the surveillance area as well as its own state. To address this, we propose an algorithm that dynamically updates the probability of detection and survival, and birth rate simultaneously in a mathematically rigorous way. This is done by integrating the semantic information inferred from the environment with the state-dependent GM-PHD filter. The performance and effectiveness of the proposed algorithm are demonstrated via illustrative road traffic scenarios.

Multiple‐model Gaussian mixture probability hypothesis density filter based on jump Markov system with state‐dependent probabilities

The Gaussian mixture probability density (GM-PHD) filter has become a popular approach to solve the multiple-target tracking (MTT) problem because it can effectively and efficiently estimate the number of targets and target states that change over time from noisy measurements. In the GM-PHD filter, the target detection and survival probabilities, and the birth rate are assumed to be constant, irrespective of the target state. However, in some applications, for example, when the target follows the planned trajectory, the detection, survival and birth of the target depend on its state. Besides, when the target reaches a waypoint along the planned trajectory, it will take a manoeuvre to go to the next waypoint, but the GM-PHD filter does not accommodate manoeuvring targets that switch between several motion models. To address this, we propose a multiple-model GM-PHD filter with state-dependent probabilities, which can explicitly consider the mode transition probabilities, the probabilities of detection and survival, and the birth rate as a function of the target state. The performance of the proposed algorithm is demonstrated by illustrative MTT scenarios which include target manoeuvres during occlusion.

Tracking Multiple Targets Using Bearing-Only Measurements in Underwater Noisy Environments.

This article handles tracking multiple targets using bearing-only measurements in underwater noisy environments. For tracking multiple targets in underwater noisy environments, the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter provides good performance with its low computational load. Bearing-only measurements are passive and do not provide position information of a target. Note that the nonlinearity of the bearing-only measurements can be handled by Extended Kalman Filters (EKF) when applying the GM-PHD filter. However, range uncertainty of the target is large for bearing-only measurements. Thus, a single EKF leads to poor performance when it is applied in the GM-PHD. In this article, every bearing measurement gives birth to multiple target samples, which are distributed considering the feasible range of the passive sensor. Thereafter, every target sample is updated utilizing the measurement update step of the EKF. In this way, we run multiple EKFs associated to multiple target samples, instead of running a single EKF. To the best of our knowledge, our article is novel in tracking multiple targets in noisy environments, using the observer with bearing-only measurements. The effectiveness of the proposed GM-PHD is verified utilizing MATLAB simulations.