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.

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.

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

An Efficient Implementation Method for Distributed Fusion in Sensor Networks Based on CPHD Filters.

A highly efficient implementation method for distributed fusion in sensor networks based on CPHD filters is proposed to address the issues of unknown cross-covariance fusion estimation and long fusion times in multi-sensor distributed fusion. This method can effectively and efficiently fuse multi-node information in multi-target tracking applications. Discrete gamma cardinalized probability hypothesis density (DG-CPHD) can effectively reduce the computational burden while ensuring computational accuracy similar to that of CPHD filters. Parallel inverse covariance intersection (PICI) can effectively avoid solving high-dimensional weight coefficient convex optimization problems, reduce the computational burden, and efficiently implement filtering fusion strategies. The effectiveness of the algorithm is demonstrated through simulation results, which indicate that PICI-GM-DG-CPHD can substantially reduce the computational time compared to other algorithms and is more suitable for distributed sensor fusion.

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.

Multitarget Distributed Tracking With Probability Hypothesis Density in Large-Scale Sensor Networks

Multitarget Distributed Tracking With Probability Hypothesis Density in Large-Scale Sensor Networks

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 Improved PHD Filtering for DOA Tracking With Sparse Array via Unscented Transform Strategy

Traditional direction of arrival (DOA) tracking methods are sensitive to the number of sources, and their performance degrades when the number of sources changes with time. To solve the problem of multi-sources time-varying DOA tracking, an improved probability hypothesis density (PHD) method for DOA tracking is proposed in this paper. We improve the particle diversity of the resampling method and enhance the tracking performance by preprocessing the predicted particles in the prediction step of the traditional PHD particle filtering method. Moreover, the proposed method is extended to sparse array scenario to further improve the DOA tracking accuracy. Performance of the algorithm can be demonstrated by simulations with better performance than the spatial smoothing PAST (SS-PAST) and existing PHD methods.

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.

An interval SLAM algorithm for leg–arm mobile robots based on a CBMeMBer filter with Gaussian indicator box-particles

During the implementation of SLAM methods based on probability hypothesis density with sequential Monte Carlo (SMC), it is necessary to generate a relatively large number of particles for mapping and to cluster particles for target state extraction, which brings about heavy computing requirements and difficulty in enhancing the estimation accuracy. Along these lines, in this work, an interval SLAM algorithm for a leg–arm mobile robot (LA-MR) is presented, which is based on cardinality-balanced multi-target multi-Bernoulli filter (CBMeMBer) with Gaussian indicator box-particles (GIBPs). First, an effective strategy for improving the selection criterion of subdivision box-particles is given via the indicator subdivision resampling to provide more reliable box-particles. In addition, mixtures of Gauss distributions with box supports were developed to fit the posterior probability, i.e. GIBP. Then, the GIBP filter was employed to implement the CBMeMBer filter and thus the particle numbers were significantly reduced to decrease the computational complexity compared with the SMC-CBMeMBer filter. In this way, the feature map learning is considered as a multi-target tracking problem, whereas a kind of SLAM algorithm for LA-MR was also designed and implemented through the GIBP-CBMeMBer filter, in which the GIBP filter is used to realize simultaneous localization and the GIBP-CBMeMBer filter is utilized to build a map. A series of experiments and a case study clearly illustrated the performance superiority of the proposed algorithms.

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.