Poisson multi-Bernoulli Mixture Filter 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.

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.

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.

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.

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.

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.

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.

Robust PMBM Filter with Unknown Detection Probability Based on Feature Estimation.

This paper provides a solution for multi-target tracking with unknown detection probability. For the standard Poisson Multi-Bernoulli Mixture (PMBM) filter, the detection probability is generally considered a priori. However, affected by sensors, the features used for detection, and other environmental factors, the detection probability is time-varying and unknown in most multi-target tracking scenarios. Therefore, the standard PMBM filter is not feasible in practical scenarios. In order to overcome these practical restrictions, we improve the PMBM filter with unknown detection probability using the feature used for detection. Specifically, the feature is modeled as an inverse gamma distribution and the target kinematic state is modeled as a Gaussian distribution; the feature is integrated into the target kinematic state to iteratively estimate the target detection probability with the motion state. Our experimental results show that the proposed method outperforms the standard PMBM filter and the robust PMBM filter based on Beta distribution in the scenarios with unknown and time-varying detection probability. Further, we apply the proposed filter to a simulated infrared image to confirm the effectiveness and robustness of the filter.

Poisson Multi-Bernoulli Approximations for Multiple Extended Object Filtering

The Poisson multi-Bernoulli mixture (PMBM) is a multiobject conjugate prior for the closed-form Bayes random finite set filter. The extended object PMBM filter provides a closed-form solution for multiple extended object filtering with standard models. This article considers computationally lighter alternatives to the extended object PMBM filter by propagating a Poisson multi-Bernoulli (PMB) density through the filtering recursion. A new local hypothesis representation is presented, where each measurement creates a new Bernoulli component. This facilitates the developments of methods for efficiently approximating the PMBM posterior density after the update step as a PMB. Based on the new hypothesis representation, two approximation methods are presented: one is based on the track-oriented multi-Bernoulli (MB) approximation, and the other is based on the variational MB approximation via Kullback–Leibler divergence minimization. The performance of the proposed PMB filters with gamma Gaussian inverse-Wishart implementations are evaluated in a simulation study.

PMBM Filter With Partially Grid-Based Birth Model With Applications in Sensor Management

This paper introduces a Poisson multi-Bernoulli mixture (PMBM) filter in which the intensities of target birth and undetected targets are grid-based. A simplified version of the Rao-Blackwellized point mass filter is used to predict the intensity of undetected targets and to initialize tracks of targets detected for the first time. The grid approximation can efficiently represent intensities with abrupt changes with relatively few grid points compared to the number of Gaussian components needed in conventional PMBM implementations. This is beneficial in scenarios where the sensor's field of view is limited. The proposed method is illustrated in a sensor management setting where trajectories of sensors with limited fields of view are controlled to search for and track the targets in a region of interest.

Tracking Multiple Spawning Targets Using Poisson Multi-Bernoulli Mixtures on Sets of Tree Trajectories

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter on the space of sets of tree trajectories for multiple target tracking with spawning targets. A tree trajectory contains all trajectory information of a target and its descendants, which appear due to the spawning process. Each tree contains a set of branches, where each branch has trajectory information of a target or one of the descendants and its genealogy. For the standard dynamic and measurement models with multi-Bernoulli spawning, the posterior is a PMBM density, with each Bernoulli having information on a potential tree trajectory. To enable a computationally efficient implementation, we derive an approximate PMBM filter in which each Bernoulli tree trajectory has multi-Bernoulli branches, obtained by minimising the Kullback-Leibler divergence. The resulting filter improves tracking performance of state-of-the-art algorithms in a simulated scenario.

Centralized Multi-Sensor Poisson Multi-Bernoulli Mixture Tracker for Autonomous Driving

With recent advances in Advanced Driver Assistance Systems (ADAS), autonomous driving has increased the need for reliable perception techniques. To achieve reliability, automotive sensors are being applied to autonomous driving vehicles, such as cameras, LiDAR, and radars. Various methods for fusing sensors have been studied to increase performance. In this study, we propose a centralized multi-sensor tracker, which is a first attempt to take advantage of fusing heterogeneous onboard sensors while accounting for data uncertainties. The proposed approach uses a Random Finite Set based Poisson Multi-Bernoulli Mixture filter. Experimental results from an actual vehicle dataset show that the proposed method tracks accurately even when objects are occluded or overlapped. It demonstrates the capability of tracking objects for autonomous driving in an urban environment.

A Gaussian Filtering Method for Multitarget Tracking With Nonlinear/Non-Gaussian Measurements

This article proposes a Gaussian filtering method to approximate the single-target updates and normalizing constants for multitarget tracking with nonlinear, non-Gaussian measurements, and a state-dependent probability of detection. The Gaussian approximation is based on the posterior linearization technique, which seeks the optimal affine approximation of the nonlinearities in a mean square error sense. The normalizing constant is approximated using sigma-points based on the posterior. The proposed approach is implemented in a Poisson multi-Bernoulli mixture filter and compared against standard methods to approximate single-target posteriors and normalizing constants in two range-bearings tracking scenarios.