Probability Hypothesis Density Filter 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.

Radar nonlinear multi-target tracking method with parallel PHD filter

Since probability hypothesis density (PHD) filters do not need explicit data association, they have recently been widely used in radar multi-target tracking (MTT). However, in existing PHD filters, sampling times are generally considered the same for all targets. Due to the limitation of antenna beam width in radar applications, the same sampling time for all targets will lead to a mismatch between the predicted data and measurement data, reducing the accuracy of radar MTT. In order to eliminate the estimation error with less computational cost, a radar nonlinear multi-target tracking method with a parallel PHD filter is proposed in this article. The measurement area is divided into several subspaces according to the beam width of the radar antenna, and the PHD of all subspaces is calculated in parallel. Then, multi-feature information in radar echo assists tracking and improves real-time performance. Experimental results in various scenarios illustrate that the proposed method can eliminate the estimation errors introduced by sampling time diversity at the cost of less computation cost, especially in cluttered environments.

The GM-JMNS-CPHD Filtering Algorithm for Nonlinear Systems Based on a Generalized Covariance Intersection.

Some fusion criteria in multisensor and multitarget motion tracking cannot be directly applied to nonlinear motion models, as the fusion accuracy applied in nonlinear systems is relatively low. In response to the above issue, this study proposes a distributed Gaussian mixture cardinality jumping Markov-cardinalized probability hypothesis density (GM-JMNS-CPHD) filter based on a generalized inverse covariance intersection. The state estimation of the JMNS-CPHD filter combines the state evaluation of traditional CPHD filters with the state estimation of jump Markov systems, estimating the target state of multiple motion models without knowing the current motion models. The performances of the generalized covariance intersection (GCI)GCI-GM-JMNS-CPHD and generalized inverse covariance intersection (GICI)GICI-GM-JMNS-CPHD methods are evaluated via simulation results. The simulation results show that, compared with algorithms such as Sensor1, Sensor2, GCI-GM-CPHD, and GICI-GM-CPHD, this algorithm has smaller optimal subpattern assignment (OSPA) errors and a higher fusion accuracy.

A Gaussian Mixture CPHD Filter for Multi-Target Tracking in Target-Dependent False Alarms

The estimation of the target number and individual tracks are two major tasks in multi-target tracking. The main shortcoming of traditional tracking methods is the cumbersome data association between measurements and targets. The cardinalized probability hypothesis density filter (CPHD) proposed in recent years can achieve the requirement for multitarget tracking. This kind of filter jointly estimates the cardinality distribution and the posterior density, which can achieve a more stable estimate of the target number. However, targets with complex micro-Doppler signatures (drones, birds, etc.) may generate target-dependent false alarms, which is contrary to the traditional uniform distribution assumption. In this case, the estimates of traditional CPHD filter will suffer from the abnormal transfer of PHD mass, causing the degradation of filtering performance. This paper studies the individual tracking of group targets with an improved GM-CPHD filter. First, the target-dependent false alarms are modeled with a general independent and identically distributed (I.I.D.) cluster process. Second, the update equations of cardinality and PHD density in target-dependent false alarms are derived. Finally, a practical solution using the Gaussian mixture method is proposed. The effectiveness of the proposed filter is verified by the simulation and experimental results.

Robust cardinalized probability hypothesis density filter based underwater multi-target direction-of-arrival tracking with uncertain measurement noise

Direction-of-arrival (DOA) tracking of underwater targets is an important research topic in sonar signal processing. Considering the underwater DOA tracking is a typical multi-target scenario with uncertain measurement noise caused by unknown underwater environment, a robust underwater multi-target DOA tracking method with uncertain measurement noise is proposed by implementing a spatial matrix filtering (SMF) technique in the framework of the cardinalized probability hypothesis density (CPHD) filter. Firstly, the kinematic model of underwater targets and the measurement model based on the received signal of the hydrophone array (array signal) are established. Thus, the multi-target DOA tracking algorithm is derived by using the CPHD filter based on the established model. Moreover, to avoid the effect of the uncertain measurement noise, the SMF technique is implemented to process the array signal to extract the signal in the bearing angle of the target. Then, the output of the SMF is substituted into the CPHD filter. In this manner, the robust underwater multi-target DOA tracking method for uncertain measurement noise scenario is proposed. Finally, comprehensive simulations and experimental data processing are performed to prove the robustness of the proposed method in the scenario of multi-target DOA tracking with uncertain measurement noise. Compared with the existing DOA estimation and DOA tracking methods, the proposed methods significantly improve the robustness and the precision of the DOA of the underwater target.

The trajectory motion model based TPHD and TCPHD filters for maneuvering targets

In this article, we present the TMM-TPHD and TMM-TCPHD filters, which are the alternative trajectory probability hypothesis density (TPHD) and the alternative trajectory cardinality probability hypothesis density (TCPHD) filters for tracking maneuvering targets. To describe the trajectory maneuver, we define the motion model history sequence of a trajectory as the trajectory motion model (TMM) variable. By incorporating the TMM, we augment the general trajectory model to accommodate the maneuver. Based on this augmented model, we propose the TMM extensions of the standard TPHD and TCPHD filters, namely TMM-TPHD and TMM-TCPHD filters. These filters can directly estimate the number, trajectory state, and TMM of maneuvering targets. In addition to the derivation of the filtering formulas, we also develop linear Gaussian mixture (LGM) implementations for TMM-TPHD and TMM-TCPHD filters. We verify the tracking performance and parameter stability of the proposed filters through tracking simulations involving multiple maneuvering targets.

Space Target Tracking with the HRRP Characteristic-Aided Filter via Space-Based Radar

Approaching space target tracking is a typical and challenging mission in the space situational awareness (SSA) field. As the space-based radar is able to monitor the space targets of interest full-weather all-time, the space-based radar system is utilized in this paper. However, most multi-target tracking (MTT) filters in target tracking studies merely utilize the location or narrow measurements, and many potentially valuable electromagnetic scattering characteristics are missed, which leads to space target false tracking problems. The space-based radar transmits a wide-band signal, and the measured high-resolution range profile (HRRP) information is an effective characteristic for different target discrimination. Therefore, the HRRP characteristics of space targets are implemented into the update recursion of the MTT filter, which can be utilized to improve the tracking performance. Then, to predict the target HRRP sequence, the geometrical theory of diffraction (GTD) model is utilized. Additionally, a modified spatial spectrum method with a novel covariance matrix is designed to improve the scattering parameter estimation accuracy. Finally, an adapting threshold is devised for merging the Gaussian mixture (GM) components weights. The proposed threshold is on the basis of the proposed HRRP characteristic-aided probability hypothesis density (PHD) filter, and it can tackle the problem of space target discrimination. Simulation results validate the effectiveness and robustness of the proposed probability hypothesis density (HGI-PHD) filter aided by HRRP information and improved with GM weights.

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.

Building the method for multi-target tracking based on the combination of PHD filter and JPDA filter using particle filter in 3D mixed coordinate system

Changing the target number, non-linear measurement models and non-Gaussian noise faces a challenge to multi-target tracking problems which are factors affecting the accuracy, execution time and deciding the success of the method as well. In this paper, the authors present a method to solve these problems. Wherein, the motion of targets is represented in the mixed coordinate system 3D base on combining PHD (Probability Hypothesis Density) and JPDA (Joint Probability Data Association). This method can track multiple targets in the most general case, that is to change the target number, system model and measurement model which is non-linear as the noise is non-Gaussian. The result of this work can be applied to the real-time response system when the targets are moving in close distances with rapid maneuvering.

An RFS Time-Frequency Model for Decomposing Chirp Modes With Dynamic Cross, Appearance, and Disappearance

In this paper, the decomposition and retrieval of the chirp modes with dynamic cross, appearance, and/or disappearance in a signal are formulated as a process of tracking time-frequency (TF) trajectories. Analyses show that the amplitude and frequency evolutions of each chirp mode in the signal can be described by polynomial prediction models. When all these evolutions are viewed as state equations, it is illustrated that the random appearance and/or disappearance of these modes will make the state equations into a state random finite set (RFS). If the amplitudes and frequencies obtained by the short-time spectrum of the signal are taken as the measurements of the state equations, a measurement RFS model in the presence of data association and detection uncertainties is coined when the statistical properties of the existing and newborn chirp modes as well as the noise/clutter are taken into consideration. So, a RFS TF model for tracking the TF trajectories in a signal is established. It is then demonstrated that a modified probability hypothesis density filter can be used to infer the amplitude and frequency posterior distributions of the chirp modes in the signal when the intensity of the RFS states is modelled as a Gaussian mixture. Numerical simulation experiments verify the effectiveness of our model and analytical results. Meanwhile, a superior performance is achieved especially for the high readability, extractability, and decomposability of instantaneous frequency trajectories with dynamic cross, appearance, and disappearance in a signal.

Heterogeneous multi-sensor fusion for PHD filter in decentralized sensor networks

This paper addresses distributed multi-sensor multi-object tracking based on probability hypothesis density (PHD) filter. Due to the scalar fusion weights, existing distributed fusion methods only work well in cases where the information confidence within multi-object densities (MODs) returned by local filters remains unchanged over the object state space. Therefore, severe performance degradation can be observed as, in practice, the information confidence of an MOD is usually space-varying and can be utterly different due to the limited sensor abilities and various environment impacts. We make three contributions towards addressing this problem. Firstly, we propose a heterogeneous fusion method for multi-object Poisson process (MPP) MODs. The resulting MOD has a parallelizable structure that allows multiple clusters of sub-densities to be fused independently based on different sets of heterogeneous fusion weights. Secondly, a density-based heterogeneous fusion weights design method is proposed, in which the fusion weights are determined according to the relative information confidence of MODs. Lastly, to enhance the adaptability and robustness of the proposed fusion method, we extend it to decentralized sensor networks in conjunction with consensus and flooding protocols, respectively. The implementation of the proposed fusion algorithms using Gaussian approximation is also presented. The efficacy of the proposed fusion methods is demonstrated in various numerical experiments, including a challenging scenario in which each sensor in a decentralized network has dynamic detection probability and space-varying detection accuracy. In the experiments, the proposed method significantly outperforms the state-of-the-art in distributed fusion. In fact, the Optimal Sub-Pattern Assignment (OSPA) distances returned by the proposed method are at least 38.8% less than other solutions.

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.

Vardiational Bayesian Hybrid Multi-Bernoulli and CPHD Filters for Superpositional Sensors

This paper addresses the problem of multi-target tracking with superpositional sensors, while the covariance matrices of measurement noise are not known. The proposed method is based on the hybrid multi-Bernoulli cardinalized probability hypothesis density (HMB-CPHD) filter, which has been developed for superpositional sensors-based multi-target tracking with known measurement noises. Specifically, we firstly propose the Gaussian mixture (GM) implementation of the HMB-CPHD filter, and then the covariance matrices of measurement noises are augmented into the target state vector, resulting in the Gaussian and inverse Wishart mixture (GIWM) representation of the augmented state. Then the variational Bayesian (VB) method is exploited to approximate the posterior distribution so that it maintains the same form as the prior distribution. A remarkable feature of the proposed method is that it can jointly perform multi-target tracking and measurement noise covariance estimation. The performance of the proposed algorithm is demonstrated via simulations.

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.

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%.