Poisson multi-Bernoulli Mixture Research Articles

Extended target trajectory Poisson multi-Bernoulli mixture filters with unknown detection probability

In most multi-extended target tracking scenarios, the target detection probability is usually unknown and time-varying, which leads to biased estimation of the state and cardinality of extended targets in online filtering. In addressing the challenge, this paper presents the unknown detection probability extended target trajectory Poisson multi-Bernoulli mixture (U-TPMBM) filter. Compared to the existing extended target Poisson multi-Bernoulli Mixture (PMBM) filter, the U-TPMBM is firstly based on sets of trajectories, which allows for direct output of target trajectory and can lead to improved trajectory estimation performance. Besides, the U-TPMBM filter integrates the unknown detection probability with the target trajectory state and thus obtains the augmented state space. By recursively estimating the augmented states via multi-target filtering approaches, it successfully realizes online and joint estimates of the unknown detection probability and the target trajectory. Finally, the U-TPMBM filter is implemented by the Beta-Gamma Gaussian Inverse Wishart (BGGIW) mixture method, especially the BGGIW-TPMBM filter. The Beta distribution is utilized to propagate densities of the unknown detection probability and the GGIW distribution to propagate densities of the target trajectory. Based on the BGGIW distribution, the trackers's recursive and closed solutions are derived in detail. The simulation experiments demonstrate that the BGGIW-TPMBM proposed in this paper can achieve robust tracking performance, even when dealing with unknown detection probabilities.

RCS Information Aided Poisson Multi-Bernoulli Mixture Filter in Clutter Background

RCS Information Aided Poisson Multi-Bernoulli Mixture Filter in Clutter Background

Cluster target tracking based on multi-sensor continuous-discrete PMBM filter

Coordination effectively enhances the detection capabilities of sensors towards cluster targets. However, due to the dense distribution of cluster members and the cooperative interaction among them, continuous tracking of these targets becomes challenging. To address these issues, we propose a novel multi-sensor continuous-discrete Poisson multi-Bernoulli mixture filter, abbreviated as MS-CDPMBM-CT filter. Based on the cooperative interaction rules, we use the multivariate stochastic differential equation (SDE) to model the dynamics of cluster members in continuous time. To adapt to the Bayesian recursive process, we derive a Gaussian state transition form of the above model in the state space. In addition, by utilizing a cluster structure undirected graph and a multi-dimensional assignment (MDA) algorithm, we improve the multi-sensor continuous-discrete PMBM filter, which can iteratively estimate the posterior probability density of the target based on the continuous time state model and discrete multi-sensor measurements. During prediction, the cluster structure is exploited to provide cooperative interaction inputs that constrain member motions. During the update, the partitioning problem of multi-sensor measurements is transformed into the MDA problem for updating the global hypotheses. Simulation experiments show that the proposed method can better adapt to the cluster interaction behavior, distinguish the members within the cluster, and achieve high filtering accuracy.

A Poisson multi-Bernoulli mixture filter for tracking multiple resolvable group targets

This paper presents a novel Poisson multi-Bernoulli mixture (PMBM) filter for tracking multiple resolvable group targets (MRGT) based on graph theory. Firstly, the number of groups and the relationships between members within the group are modelled by the adjacency matrix. Then, considering that a single dynamic evolution model is insufficient to guarantee stable tracking performance for group targets, the virtual leader-follower model (VLFM) is introduced to predict the evolution trend of unknown and potentially detected targets, respectively. Furthermore, we prove the conjugation of the proposed algorithm with the probability generating functionals (PGF) and give a detailed implementation of the Gaussian mixture (GM). Based on the coexistence scenario of splitting, merging and non-linear motion of the group targets, the simulation results show the effectiveness of the proposed algorithm in comparison with the existing methods.

Data-Driven Clustering and Bernoulli Merging for the Poisson Multi-Bernoulli Mixture Filter

This paper proposes a clustering and merging approach for the Poisson multi-Bernoulli mixture (PMBM) filter to lower its computational complexity and make it suitable for multiple target tracking with a high number of targets. We define a measurement-driven clustering algorithm to reduce the data association problem into several subproblems, and we provide the derivation of the resulting clustered PMBM posterior density via Kullback-Leibler divergence minimisation. Furthermore, we investigate different strategies to reduce the number of single target hypotheses by approximating the posterior via merging and inter-track swapping of Bernoulli components. We evaluate the performance of the proposed algorithm on simulated tracking scenarios with more than one thousand targets.

Track-Oriented Marginal Poisson Multi-Bernoulli Mixture Filter for Extended Target Tracking

Track-Oriented Marginal Poisson Multi-Bernoulli Mixture Filter for Extended Target Tracking

Student’s t-Based Robust Poisson Multi-Bernoulli Mixture Filter under Heavy-Tailed Process and Measurement Noises

A novel Student’s t-based robust Poisson multi-Bernoulli mixture (PMBM) filter is proposed to effectively perform multi-target tracking under heavy-tailed process and measurement noises. To cope with the common scenario where the process and measurement noises possess different heavy-tailed degrees, the proposed filter models this noise as two Student’s t-distributions with different degrees of freedom. Furthermore, this method considers that the scale matrix of the one-step predictive probability density function is unknown and models it as an inverse-Wishart distribution to mitigate the influence of heavy-tailed process noise. A closed-form recursion of the PMBM filter for propagating the approximated Gaussian-based PMBM posterior density is derived by introducing the variational Bayesian approach and a hierarchical Gaussian state-space model. The overall performance improvement is demonstrated through three simulations.

АЛГОРИТМ ТРАЕКТОРНОЙ ОБРАБОТКИ ДЛЯ АВТОМАТИЧЕСКОГО ОТСЛЕЖИВАНИЯ РАСПРЕДЕЛЕННЫХ ДВИЖУЩИХСЯ ЦЕЛЕЙ В УСЛОВИЯХ МНОГОЛУЧЕВОГО РАССЕЯНИЯ

This work presents a modified Poisson multi-Bernoulli mixture (PMBM) algorithm, adapted to perform trajectory processing tasks under conditions of multipath radar reflection. Based on the evaluative data of the previous kinematic state, size, and orientation of the target obtained using the extended PMBM algorithm, a pre-processing stage is carried out. During this stage, the origins of primary radar detections are initially classified. Then, after classification, these radar detections are further processed to estimate the state of targets at the next point in time. To assess the effectiveness of the proposed algorithm, a simulation modeling method based on MATLAB is used. With its help, scenarios for tracking distributed targets are modeled under conditions of the emergence of false signals from multipath radar reflections. The simulation results endorse the algorithm's capability to concurrently track multiple targets upon receiving primary radar detections from an assortment of radars amidst multipath radar reflections. The application of the algorithm finds use in the field of autonomous driving, driver assistance systems, applications ensuring driver safety, and other areas.

PMBM Filter for Multiple Extended Targets With Unknown Clutter Rate and Detection Probability

In a multi-target tracking (MTT) scenario, the prior knowledge of parameters such as clutter rate and detection probability are usually uncertain or estimated offline from training data. However, significant parameters mismatch in the clutter and detection model will result in biased estimates. In such cases, the ability to adaptively online estimate clutter rate and detection probability is critical in MTT under the random finite sets (RFS) framework. In this paper, we propose a robust Poisson multi-Bernoulli mixture (PMBM) filter that can accommodate model mismatch in clutter rate and detection probability for multiple extended target tracking problems. Moreover, the closed-form solution to the proposed method is derived by the use of Beta and Gamma Gaussian inverse-Wishart (GGIW) distribution, where Beta is used to describe unknown detection probability and GGIW is used to model extended target extension as an ellipse. Simulation results are presented to verify the effectiveness of the proposed method.

The Multiple Model Poisson Multi-Bernoulli Mixture Filter for Extended Target Tracking

In an intelligent transportation system (ITS), the single motion model is not enough to meet the needs of simulation systems (or practical applications) and guarantee good tracking performance for multiple maneuvering extended target tracking (ETT). This paper presents multiple models Poisson multi-Bernoulli mixture (MM-PMBM) filter for extended target tracking to address this problem. To make multiple models transform in an accurate manner, the jump Markov system (JMS) is timely introduced in filtering recursion. After that, the model probability of target is recursively updated and used to estimate the target position. In addition, we derive the closed-form solution to the proposed filter based on the Gamma Gaussian inverse-Wishart (GGIW) implementation. The approach to handling the merging problem of GGIW components via Kullback-Leibler divergence (KLD) minimization is also presented, resulting in better utilization of available components. Simulation results demonstrate that the proposed filter has superior performance in comparison to several state-of-the-art multi-target filters.

Multi-target tracking in underwater multistatic AUV networks with a robust Poisson Multi-Bernoulli filter

The study investigates underwater multi-target tracking (MTT) in a multistatic system using autonomous underwater vehicles (AUVs) as receivers separately from transmitters. The most critical aspect of MTT is the accurate extraction of target tracks from the collected measurements, which can be affected by clutter, missed detections, and port-starboard ambiguities. Moreover, the detection parameters—the target-detection probability and clutter rate—used in MTT methods are typically unknown and change with varying environmental conditions and geometric distributions of the AUV, target, and sound transmitter. In view of these challenges, we propose a robust multi-sensor Poisson Multi-Bernoulli Mixture (R-MS-PMBM) filter immune to unknown detection parameters that treats clutter rates and detection probabilities as continuous random variables modeled by beta and gamma distributions, respectively. The R-MS-PMBM filter is a conjugate prior, and its closed form is derived. We introduce a measurement-driven adaptive birth model to initiate target tracks quickly and efficiently. Furthermore, a suboptimal Gibbs sampler is used to reduce the computational complexity of its practical implementation. The simulation results show that the proposed filter is resilient to unknown detection parameters and can effectively perform in challenging underwater scenarios.

Non-Ellipsoidal Infrared Group/Extended Target Tracking Based on Poisson Multi-Bernoulli Mixture Filter and B-Spline

This study provides a solution for multiple group/extended target tracking with an arbitrary shape. Many tracking approaches for extended/group targets have been proposed. However, these approaches make assumptions about the target shape, which have limitations in practical applications. To address this problem, in this work, an extended/group target tracking algorithm based on B-spline is proposed. Specifically, the extension of an extended or a group target was modeled as a spatial probability distribution characterized by the control points of a B-spline function that was then jointly propagated with the measurement rate model and kinematic component model over time using the Poisson multi-Bernoulli mixture (PMBM) filter framework. In addition, an amplitude-aided measurement partitioning approach is proposed to improve the accuracy caused by distance-based approaches. The simulation results demonstrate that the extension, shape and orientation of targets can be estimated better by the proposed algorithm, even if the shape changes. The tracking performance is also improved by about 10% and 13% compared to the other two algorithms.

An Improved Multiple-Target Tracking Scheme Based on IGGM–PMBM for Mobile Aquaculture Sensor Networks

The Poisson multi-Bernoulli Mixture (PMBM) filter, as well as its variants, is a popular and practical multitarget tracking algorithm. There are some pending problems for the standard PMBM filter, such as unknown detection probability, random target newborn distribution, and high energy consumption for limited computational and processing capacity in sensor networks. For the sake of accommodating these existing problems, an improved multitarget tracking method based on a PMBM filter with adaptive detection probability and adaptive newborn distribution is proposed, accompanied by an associated distributed fusion strategy to reduce the computational complexities. Firstly, gamma (GAM) distribution is introduced to present the augmented state of unknown and changing target detection probability. Secondly, the intensity of newborn targets is adaptively derived from the inverse gamma (IG) distribution based on this augmented state. Then, the measurement likelihood is presented as a gamma distribution for the augmented state. On these bases, the detailed recursion and closed-form solutions to the proposed filter are derived by means of approximating the intensity of target birth and potential targets to an inverse gamma Gaussian mixture (IGGM) form and the density of existing Bernoulli components to a single IGGM form. Moreover, the associated distributed fusion strategy generalized covariance intersection (GCI), whose target states are measured by multiple sensors according to their respective fusion weights, is applied to a large-scale aquaculture tracking network. Comprehensive experiments are presented to verify the effectiveness of this IGGM–PMBM method, and comparisons with other multitarget tracking filters also demonstrate that tracking behaviors are largely improved; in particular, tracking energy consumption is reduced sharply, and tracking accuracy is relatively enhanced.

Poisson Multi-Bernoulli Mixture Filter With General Target-Generated Measurements and Arbitrary Clutter

This paper shows that the Poisson multi-Bernoulli mixture (PMBM) density is a multi-target conjugate prior for general target-generated measurement distributions and arbitrary clutter distributions. That is, for this multi-target measurement model and the standard multi-target dynamic model with Poisson birth model, the predicted and filtering densities are PMBMs. We derive the corresponding PMBM filtering recursion. Based on this result, we implement a PMBM filter for point-target measurement models and negative binomial clutter density in which data association hypotheses with high weights are chosen via Gibbs sampling. We also implement an extended target PMBM filter with clutter that is the union of Poisson-distributed clutter and a finite number of independent clutter sources. Simulation results show the benefits of the proposed filters to deal with non-standard clutter.

Shallow sea matching field continuous tracking method based on trajectory Poisson multi-Bernoulli hybrid filter

In the shallow water waveguide, matched field tracking methods use the continuity of the peak position of the moving source and the disorder of pseudo-peaks on the sequential ambiguity surfaces to track the underwater source trajectory. However, owing to the dual influence of the space-time fluctuating shallow water waveguide environment and the complex sources motion scene, the existing matching field tracking methods are prone to track interruption, switches and false track phenomena, leading to discontinuous tracking results. Using the consistency between the peak position distance likelihood and the peak amplitude likelihood of sequential ambiguity surfaces, a continuous matched field tracking method is proposed based on the trajectory Poisson multi-Bernoulli mixture filter in this paper. The proposed method is applied to SWellEx-96 experimental data, and the tracking performance is measured by the linear programming metric. The results show that compared with the existing matching field tracking method and multi-target tracking method via random finite set, the proposed method achieves continuous tracking and accurate quantity estimation of moving sources trajectory. Among them, the prediction step and updating step in the trajectory space can avoid the phenomenon of trajectory interruption and switches in unvoiced periods.

Best fit of mixture for multi-sensor poisson multi-Bernoulli mixture filtering

We propose a computationally efficient, the first so far, multi-sensor extension of the Poisson multi-Bernoulli mixture (PMBM) filter that accommodates both centralized and distributed sensor networks. In the distributed case, a distributed flooding algorithm is needed for internode communication, which iteratively shares the relevant multi-target posterior among neighbor sensors, thereby making each local sensor serve like a fusion center in the centralized case. The PMBM posterior yielded at each sensor is decomposed into two components corresponding to undetected and detected targets which are modelled by Poisson and multi-Bernoulli mixture (MBM) distributions, respectively. Both communication and fusion are performed with regard to the latter only. A “best-fit-of-mixture” fusion principle is adopted at each sensor to find an MBM that best fits the mixture of MBMs from distinct sensors, which results precisely in the arithmetic average (AA) of these MBMs. The information divergence of the AA from the true density is analyzed. We also provide a Bayesian model averaging interpretation of the MBM-AA fusion. Simulations in scenarios of different target detection probabilities demonstrate the performance of the proposed PMBM filter in terms of localization error, false-alarm/misdetection errors, and communication and computation costs, in comparison with the AA-based multisensor multi-Bernoulli filter.

PMBM-Based SLAM Filters in 5G mmWave Vehicular Networks

Radio-based vehicular simultaneous localization and mapping (SLAM) aims to localize vehicles while mapping the landmarks in the environment. We propose a sequence of three Poisson multi-Bernoulli mixture (PMBM) based SLAM filters, which handle the entire SLAM problem in a theoretically optimal manner. The complexity of the three proposed SLAM filters is progressively reduced while sustaining high accuracy by deriving SLAM density approximation with the marginalization of nuisance parameters (either vehicle state or data association). Firstly, the PMBM SLAM filter serves as the foundation, for which we provide the first complete description based on a Rao-Blackwellized particle filter. Secondly, the Poisson multi-Bernoulli (PMB) SLAM filter is based on the standard reduction from PMBM to PMB, but involves a novel interpretation based on auxiliary variables and a relation to Bethe free energy. Finally, using the same auxiliary variable argument, we derive a marginalized PMB SLAM filter, which avoids particles and is instead implemented with a low-complexity cubature Kalman filter. We evaluate the three proposed SLAM filters in comparison with the probability hypothesis density (PHD) SLAM filter in 5G mmWave vehicular networks and show the computation-performance trade-off between them.

PTMOT: A Probabilistic Multiple Object Tracker Enhanced by Tracklet Confidence for Autonomous Driving

Real driving scenarios, due to occlusions and disturbances, provide disordered and noisy measurements, which makes the task of multi-object tracking quite challenging. Conventional approach is to find deterministic data association; however, it has unstable performance in high clutter density. This paper proposes a novel probabilistic tracklet-enhanced multiple object tracker (PTMOT), which integrates Poisson multi-Bernoulli mixture (PMBM) filter with confidence of tracklets. The proposed method is able to realize efficient and robust probabilistic association for 3D multi-object tracking (MOT) and improve the PMBM filter’s continuity by smoothing single target hypothesis with global hypothesis. It consists of two key parts. First, the PMBM tracker based on sets of tracklets is implemented to realize probabilistic fusion of disordered measurements. Second, the confidence of tracklets is smoothed through a smoothing-while-filtering approach. Extensive MOT tests on nuScenes tracking dataset demonstrate that the proposed method achieves superior performance in different modalities.

A Computationally Efficient EK-PMBM Filter for Bistatic mmWave Radio SLAM

Millimeter wave (mmWave) signals are useful for simultaneous localization and mapping (SLAM), due to their inherent geometric connection to the propagation environment and the propagation channel. To solve the SLAM problem, existing approaches rely on sigma-point or particle-based approximations, leading to high computational complexity, precluding real-time execution. We propose a novel low-complexity SLAM filter, based on the Poisson multi-Bernoulli mixture (PMBM) filter. It utilizes the extended Kalman (EK) first-order Taylor series based Gaussian approximation of the filtering distribution, and applies the track-oriented marginal multi-Bernoulli/Poisson (TOMB/P) algorithm to approximate the resulting PMBM as a Poisson multi-Bernoulli (PMB). The filter can account for different landmark types in radio SLAM and multiple data association hypotheses. Hence, it has an adjustable complexity/performance trade-off. Simulation results show that the developed SLAM filter can greatly reduce the computational cost, while it keeps the good performance of mapping and user state estimation.

Poisson multi‐Bernoulli mixture filters with coloured measurement noise

To solve multitarget tracking (MTT) problems with coloured measurement noise, this study proposes a Poisson multi-Bernoulli mixture filter with coloured measurement noise (PMBM-CMN) and a robust PMBM-CMN filter. By using the measurement differencing method and state augmentation approach, the proposed PMBM-CMN filter transforms a state estimation problem with coloured measurement noise into a problem with white measurement noise. However, covariances of the true process and measurement noise in the proposed PMBM-CMN filter are time-varying and unknown, which may degrade the filtering performance. Therefore, a robust PMBM-CMN filter is proposed for estimating the augmented state, including the kinematic state, the predicted state covariance, and the white measurement noise covariance. For linear Gaussian systems, the augmented state is modelled as a Gaussian inverse Wishart inverse Wishart (GIWIW) distribution. The variational Bayesian method is also employed to guarantee the conjugacy of the GIWIW density. Simulation results demonstrate the ability of the PMBM-CMN filter to solve MTT problems with coloured measurement noise and show that the robust PMBM-CMN filter based on the GIWIW model (GIWIW-PMBM-CMN) has the best overall performance in comparison with existing state-of-the-art filters.