Particle Probability Hypothesis Density Research Articles

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.

Multiple extended target tracking based on gamma box particle and labeled random finite sets

A gamma box particle (GBP) implementation of the extended target generalized labeled multi-Bernoulli (ET-GLMB) filter is proposed in this paper, named the ET-GBP-GLMB filter. The filter can simultaneously estimate the unknown number, measurement rate states, kinematics states, extension states and tracks of extended targets in the presence of clutter, missed detection and data association uncertainty. In order to obtain the GLMB recursion of the ET-GBP-GLMB filter, an appropriate measurement likelihood function that comprehensively considers the measurement rate state, kinematics state and extension state of each extended target is introduced for a given measurement partition cell, and the specific implementation steps of the filter are derived with necessary interval operations and approximations. Further, an extended target GBP labeled multi-Bernoulli (ET-GBP-LMB) filter is proposed as an effective approximation of the ET-GBP-GLMB filter. The advantages and disadvantages of the two proposed filters are presented in simulation examples. The simulation results show that, compared with the gamma sequential Monte Carlo (GSMC) implementation of the ET-GLMB filter, the GBP implementation of the ET-GLMB filter can effectively reduce the number of particles and the amount of computation. Compared with the ET-GBP-GLMB filter, the ET-GBP-LMB filter can further reduce the computational burden. Compared with the extended target box particle probability hypothesis density (ET-BP-PHD) filter, the two proposed filters can obtain better estimation results.

Equal probability embedded cubature particle PHD filter algorithm in multi-target tracking

In target tracking, multi-target tracking is the focus of research. It is primarily concerned with the issue of collaboratively estimating the number, state, or trajectory of targets based on sensor measurements in the presence of data association uncertainty, detection uncertainty, false observation, and noise. The current research hotspot in multi-target tracking is nonlinear multi-target tracking based on the probability hypothesis density algorithm. Furthermore, there are several considerations with this algorithm’s multi-target tracking, such as low estimate accuracy, filter divergence, and poor real-time performance. Based on equivalent probability sampling and the embedded volume criterion, this article demonstrates an equal probability embedded cubature particle probability hypothesis density filter algorithm. In the sampling stage, the algorithm implements the equal probability sampling method, divides the entire sampling area into several areas with equal probability, extracts particles from each region using the established criteria, generates limited integral points using the third-order embedded volume criterion, filters each sampling particle, fits the important density function, and predicts and updates the probability hypothesis density of multi-target state. The simulation results demonstrate that the equal probability sampling strategy outperforms other multi-target position and number estimation methods. Simultaneously, it demonstrates that the equal probability embedded cubature particle probability hypothesis density filter algorithm can effectively track multiple targets. The equal probability embedded cubature particle probability hypothesis density filter algorithm performs better in real-time and has a more accurate target number and state estimate than other algorithms.

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

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

Multisensor Box Particle PHD Multitarget Tracking Algorithm

As single sensors cannot detect and track targets with low detection probability,a new multisensor box particle probability hypothesis density filter is proposed in this paper.The MS-BOX-PHD filter converts and fuses multiple sensor measurement sets into a new set,and the multitarget states are predicted and updated using a box particle probability hypothesis density filter.Numerical experiments show that the MS-BOX-PHD filter can estimate the state and number of multitargets when the target detection probability is low,unlike a single sensor box particle probability hypothesis density filter.Compared with the multisensor standard probability hypothesis density filter with interval measurement,the computational efficiency increased by 38.57%for the same tracking performance.

Multi-target tracking in distributed sensor networks using particle PHD filters

Abstract Multi-target tracking is an important problem in civilian and military applications. This paper investigates multi-target tracking in distributed sensor networks. Data association, which arises particularly in multi-object scenarios, can be tackled by various solutions. We consider sequential Monte Carlo implementations of the Probability Hypothesis Density (PHD) filter based on random finite sets. This approach circumvents the data association issue by jointly estimating all targets in the region of interest. To this end, we develop the Diffusion Particle PHD Filter (D-PPHDF) as well as a centralized version, called the Multi-Sensor Particle PHD Filter (MS-PPHDF). Their performance is evaluated in terms of the Optimal Subpattern Assignment (OSPA) metric, benchmarked against a distributed extension of the Posterior Cramer-Rao Lower Bound (PCRLB), and compared to the performance of an existing distributed PHD Particle Filter. Furthermore, the robustness of the proposed tracking algorithms against outliers and their performance with respect to different amounts of clutter is investigated.

Particle Probability Hypothesis Density Filter Based on Pairwise Markov Chains

Most multi-target tracking filters assume that one target and its observation follow a Hidden Markov Chain (HMC) model, but the implicit independence assumption of the HMC model is invalid in many practical applications, and a Pairwise Markov Chain (PMC) model is more universally suitable than the traditional HMC model. A set of weighted particles is used to approximate the probability hypothesis density of multi-targets in the framework of the PMC model, and a particle probability hypothesis density filter based on the PMC model (PF-PMC-PHD) is proposed for the nonlinear multi-target tracking system. Simulation results show the effectiveness of the PF-PMC-PHD filter and that the tracking performance of the PF-PMC-PHD filter is superior to the particle PHD filter based on the HMC model in a scenario where we kept the local physical properties of nonlinear and Gaussian HMC models while relaxing their independence assumption.

Box Particle Probability Hypothesis Density Filter for Multi-target Visual Tracking

Box Particle Probability Hypothesis Density Filter for Multi-target Visual Tracking

Hardware architecture and optimisation of FPP particle PHD filter for multi‐target tracking in cyber‐physical systems

To meet the rapidly growing demand of localisation and tracking information of mobile agents in cyber-physical systems, in this paper, we propose a fully pipelined and parallel (FPP) hardware architecture of particle probability hypothesis density (PHD) filter for multi-target tracking on the multi-cores processor hardware platforms, where an improved resampling algorithm is designed. We formulate the demand of minimising the processing delay in this architecture as an optimisation problem, which can be efficiently solved by transforming it to a group of mixed non-linear integer programming problems. Delay analysis shows that the proposed FPP particle PHD filter achieves significant improvement of real-time performance, and simulation results demonstrate that tracking performance remains at the same level as traditional particle PHD filters.

Social Force Model-Based MCMC-OCSVM Particle PHD Filter for Multiple Human Tracking

Video-based multiple human tracking often involves several challenges, including target number variation, object occlusions, and noise corruption in sensor measurements. In this paper, we propose a novel method to address these challenges based on probability hypothesis density (PHD) filtering with a Markov chain Monte Carlo (MCMC) implementation. More specifically, a novel social force model (SFM) for describing the interaction between the targets is used to calculate the likelihood within the MCMC resampling step in the prediction step of the PHD filter, and a one class support vector machine (OCSVM) is then used in the update step to mitigate the noise in the measurements, where the SVM is trained with features from both color and oriented gradient histograms. The proposed method is evaluated and compared with state-of-the-art techniques using sequences from the CAVIAR, TUD, and PETS2009 datasets based on the mean Euclidean tracking error on each frame, the optimal subpattern assignment metric, and the multiple object tracking precision metric. The results show improved performance of the proposed method over the baseline algorithms, including the traditional particle PHD filtering method, the traditional SFM-based particle filtering method, multi-Bernoulli filtering, and an online-learning-based tracking method.

Computation-distributed probability hypothesis density filter

Particle probability hypothesis density filtering has become a promising approach for multi-target tracking due to its capability of handling an unknown and time-varying number of targets in a nonlinear, non-Gaussian system. However, its computational complexity linearly increases with the number of obtained observations and the number of particles, which can be very time consuming, particularly when numerous targets and clutter exist in the surveillance region. To address this issue, we present a distributed computation particle probability hypothesis density(PHD) filter for target tracking. It runs several local decomposed particle PHD filters in parallel while processing elements. Each processing element takes responsibility for a portion of particles but all measurements and provides local estimates. A central unit controls particle exchange among the processing elements and specifies a fusion rule to match and fuse the estimates from different local filters. The proposed framework is suitable for parallel implementation. Simulations verify that the proposed method can significantly accelerate and maintain a comparative accuracy compared to the standard particle PHD filter.

Adaptive Retrodiction Particle PHD Filter for Multiple Human Tracking

The probability hypothesis density (PHD) filter is well known for addressing the problem of multiple human tracking for a variable number of targets, and the sequential Monte Carlo implementation of the PHD filter, known as the particle PHD filter, can give state estimates with nonlinear and non-Gaussian models. Recently, Mahler et al. have introduced a PHD smoother to gain more accurate estimates for both target states and number. However, as highlighted by Psiaki in the context of a backward-smoothing extended Kalman filter, with a nonlinear state evolution model the approximation error in the backward filtering requires careful consideration. Psiaki suggests that to minimize the aggregated least-squares error over a batch of data. We instead use the term retrodiction PHD filter to describe the backward filtering algorithm in recognition of the approximation error proposed in the original PHD smoother, and we propose an adaptive recursion step to improve the approximation accuracy. This step combines forward and backward processing through the measurement set and thereby mitigates the problems with the original PHD smoother when the target number changes significantly and the targets appear and disappear randomly. Simulation results show the improved performance of the proposed algorithm and its capability in handling a variable number of targets.

Parallel particle PHD filter implemented on multicore and cluster systems

The Probability Hypothesis Density (PHD) filter is a promising technique in terms of computational complexity to solve the multiple targets tracking problem. However, the amount of computation is prohibitive in critical situations when the clutter intensity and sample rate are high. Therefore, the execution time of the sequential particle PHD filter cannot meet the requirement for real-time processing applications. To address this problem, we propose a parallel scheme for efficient implementation of particle PHD filter on clusters of multicore distributed memory architecture. Since particles can be treated separately and spread among processors, the prediction and update step can be readily performed in parallel. However, the resampling and estimation step become the bottleneck that significantly affects the speedup and scalability achieved by the parallel implementation of particle PHD filter for the requirement of joint processing of all particles. We propose an approach to fulfill parallel resampling and stratified estimation in a unified architecture. Particle exchange to rebalance the work load among computing nodes is also discussed. Experiment results show that tracking performance of the parallel version is almost equivalent to or even better than the sequential one, while in terms of execution time we can achieve a tremendous speedup.

Micro-object motion tracking based on the probability hypothesis density particle tracker.

Tracking micro-objects in the noisy microscopy image sequences is important for the analysis of dynamic processes in biological objects. In this paper, an automated tracking framework is proposed to extract the trajectories of micro-objects. This framework uses a probability hypothesis density particle filtering (PF-PHD) tracker to implement a recursive state estimation and trajectories association. In order to increase the efficiency of this approach, an elliptical target model is presented to describe the micro-objects using shape parameters instead of point-like targets which may cause inaccurate tracking. A novel likelihood function, not only covering the spatiotemporal distance but also dealing with geometric shape function based on the Mahalanobis norm, is proposed to improve the accuracy of particle weight in the update process of the PF-PHD tracker. Using this framework, a larger number of tracks are obtained. The experiments are performed on simulated data of microtubule movements and real mouse stem cells. We compare the PF-PHD tracker with the nearest neighbor method and the multiple hypothesis tracking method. Our PF-PHD tracker can simultaneously track hundreds of micro-objects in the microscopy image sequence.

Improved Mult-agent Tracking Algorithm Based on Gaussian Mixture Particle PHD Filter

The paper proposes Gaussian mixture particle probability hypothesis density filter(PHD) algorithm ,which can effectively solve the problem that the object number is changing or unknown, based on particle PHD filter. This algorithm calculates the object number and state by recursive procedure, avoiding the uncertainty of target state estimation caused by particle sampling and clustering. Gaussian mixture particle is introduced to effectively maintain the multi-modal distribution of each target，reducing the complexity of calculation.

Multiple-model Rao-Blackwellized particle probability hypothesis density filter for multitarget tracking

Multitarget tracking (MTT) is a frequent topic in visual surveillance systems. Although the multiple-model probability hypothesis density (MM-PHD) filter plays an important role in the MTT, both computerized intractability and imprecise estimate are still inevitable. To solve the problems, a novel filter is presented in this paper. Different from the previous work, the Rao-Blackwellized particle filtering algorithm is incorporated with the MM-PHD filter to reduce computational load, where the sequence Monte Carlo method is adopted to estimate the nonlinear state of targets, and the linear state is predicted using the Kalman filter with the information embedded in the estimated nonlinear state. With respect to tracking precision, we find that the reweighting scheme can be realized for the numberestimate of both undetected targets and false alarms. The result is useful in balancing the required particle number in order to stabilize target estimates during the surveillance period. The illustrative simulation is finally provided to show the effectiveness of the proposed filter.

Free clustering optimal particle probability hypothesis density (PHD) filter

As to the fact that it is difficult to obtain analytical form of optimal sampling density and tracking performance of standard particle probability hypothesis density (P-PHD) filter would decline when clustering algorithm is used to extract target states, a free clustering optimal P-PHD (FCO-P-PHD) filter is proposed. This method can lead to obtainment of analytical form of optimal sampling density of P-PHD filter and realization of optimal P-PHD filter without use of clustering algorithms in extraction target states. Besides, as sate extraction method in FCO-P-PHD filter is coupled with the process of obtaining analytical form for optimal sampling density, through decoupling process, a new single-sensor free clustering state extraction method is proposed. By combining this method with standard P-PHD filter, FC-P-PHD filter can be obtained, which significantly improves the tracking performance of P-PHD filter. In the end, the effectiveness of proposed algorithms and their advantages over other algorithms are validated through several simulation experiments.

POSE: Design of Hardware-Friendly Particle-Based Observation Selection PHD Filter

Particle probability hypothesis density (PHD) filtering is a promising technology for the multitarget-tracking problem. Traditional particle PHD filter solutions usually have high computational complexity, and the lack of dedicated hardware has seriously limited their usages in real-time industrial applications. The hardware implementation difficulty of the particle PHD filtering in field-programmable gate array (FPGA) platforms lies in that the number of observations for filtering is time varying while the number of parallel processing units in circuit is fixed. To overcome this challenge, we propose a novel particle-based observation selection (POSE) PHD filter algorithm and its hardware implementation in this paper. Specifically, we opportunistically select a fixed number of observations out of a varying number of observations for filtering, where the approximation error is proved to be negligible by adapting the circuit budget to the environment accordingly. To implement the proposed POSE PHD filter, the hardware design issues are addressed in depth. Extensive simulations demonstrate that the POSE PHD filter has a comparable performance with the traditional one while its hardware implementation challenge is overcome. The hardware experiment results of the POSE PHD filter on a Xilinx Virtex-II Pro FPGA platform match the simulation ones well. Furthermore, the execution time of the implemented hardware circuit is evaluated, and the results show that it can achieve a processing rate of 6.892 kHz with a 50-MHz system clock.

Marginalized particle PHD filters for multiple object Bayesian filtering

The Probability Hypothesis Density (PHD) filter is a recent solution to the multi-target filtering problem. Because the PHD filter is not computable, several implementations have been proposed including the Gaussian Mixture (GM) approximations and Sequential Monte Carlo (SMC) methods. In this paper, we propose a marginalized particle PHD filter which improves the classical solutions when used in stochastic systems with partially linear substructure.

Online Adapting the Magnitude of Target Birth Intensity in the PHD Filter

Capturing new targets that spontaneously appear in the multi-target tracking (MTT) scene requires a formation of TBI (target birth intensity) item in the PHD (probability hypothesis density) equations. That is, in the particle implementation of the PHD filter, a number of new particles with a certain weight mass are added to the underlying particle set during the propagation of the PHD. In general, TBI is assumed to hold for the same magnitude at all scans. This ad-hoc option is simple but is not always desirable. In this paper, a measurement-driven adaptive mechanism is proposed that determines the magnitude of TBI in real time based on the estimated number of new-born targets, which is calculated by employing the newest measurements. Simulation demonstration of the particle PHD filter has been provided.