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The probability hypothesis density (PHD) and Poisson multi-Bernoulli (PMB) filters are two popular set-type multi-object filters. Motivated by the fact that the multi-object filtering density after each update step in the PHD filter is a PMB without approximation, in this paper we present a multi-object smoother involving PHD forward filtering and PMB backward smoothing. This is achieved by first running the PHD filtering recursion in the forward pass and extracting the PMB filtering densities after each update step before the Poisson Point Process approximation, which is inherent in the PHD filter update. Then in the backward pass we apply backward simulation for sets of trajectories to the extracted PMB filtering densities. We call the resulting multi-object smoother hybrid PHD-PMB trajectory smoother. Notably, the hybrid PHD-PMB trajectory smoother can provide smoothed trajectory estimates for the PHD filter without labeling or tagging, which is not possible for existing PHD smoothers. Also, compared to the trajectory PHD filter, which can only estimate alive trajectories, the hybrid PHD-PMB trajectory smoother enables the estimation of the set of all trajectories. Simulation results demonstrate that the hybrid PHD-PMB trajectory smoother outperforms the PHD filter in terms of both state and cardinality estimates, and the trajectory PHD filter in terms of false detections., Comment: 2024 IEEE International conference on multisensor fusion and integration (MFI 2024). arXiv admin note: text overlap with arXiv:2206.08112

Simultaneous localization and mapping (SLAM) methods need to both solve the data association (DA) problem and the joint estimation of the sensor trajectory and the map, conditioned on a DA. In this paper, we propose a novel integrated approach to solve both the DA problem and the batch SLAM problem simultaneously, combining random finite set (RFS) theory and the graph-based SLAM approach. A sampling method based on the Poisson multi-Bernoulli mixture (PMBM) density is designed for dealing with the DA uncertainty, and a graph-based SLAM solver is applied for the conditional SLAM problem. In the end, a post-processing approach is applied to merge SLAM results from different iterations. Using synthetic data, it is demonstrated that the proposed SLAM approach achieves performance close to the posterior Cram\'er-Rao bound, and outperforms state-of-the-art RFS-based SLAM filters in high clutter and high process noise scenarios.

Accurate and timely determination of a vehicle's current lane within a map is a critical task in autonomous driving systems. This paper utilizes an Early Time Series Classification (ETSC) method to achieve precise and rapid ego-lane identification in real-world driving data. The method begins by assessing the similarities between map and lane markings perceived by the vehicle's camera using measurement model quality metrics. These metrics are then fed into a selected ETSC method, comprising a probabilistic classifier and a tailored trigger function, optimized via multi-objective optimization to strike a balance between early prediction and accuracy. Our solution has been evaluated on a comprehensive dataset consisting of 114 hours of real-world traffic data, collected across 5 different countries by our test vehicles. Results show that by leveraging road lane-marking geometry and lane-marking type derived solely from a camera, our solution achieves an impressive accuracy of 99.6%, with an average prediction time of only 0.84 seconds., Comment: 8 pages, 5 figures

High-definition map with accurate lane-level information is crucial for autonomous driving, but the creation of these maps is a resource-intensive process. To this end, we present a cost-effective solution to create lane-level roadmaps using only the global navigation satellite system (GNSS) and a camera on customer vehicles. Our proposed solution utilizes a prior standard-definition (SD) map, GNSS measurements, visual odometry, and lane marking edge detection points, to simultaneously estimate the vehicle's 6D pose, its position within a SD map, and also the 3D geometry of traffic lines. This is achieved using a Bayesian simultaneous localization and multi-object tracking filter, where the estimation of traffic lines is formulated as a multiple extended object tracking problem, solved using a trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. In TPMBM filtering, traffic lines are modeled using B-spline trajectories, and each trajectory is parameterized by a sequence of control points. The proposed solution has been evaluated using experimental data collected by a test vehicle driving on highway. Preliminary results show that the traffic line estimates, overlaid on the satellite image, generally align with the lane markings up to some lateral offsets., Comment: 27th International Conference on Information Fusion

Roadside perception is a key component in intelligent transportation systems. In this paper, we present a novel three-dimensional (3D) extended object tracking (EOT) method, which simultaneously estimates the object kinematics and extent state, in roadside perception using both the radar and camera data. Because of the influence of sensor viewing angle and limited angle resolution, radar measurements from objects are sparse and non-uniformly distributed, leading to inaccuracies in object extent and position estimation. To address this problem, we present a novel spherical Gaussian function weighted Gaussian mixture model. This model assumes that radar measurements originate from a series of probabilistic weighted radar reflectors on the vehicle's extent. Additionally, we utilize visual detection of vehicle keypoints to provide additional information on the positions of radar reflectors. Since keypoints may not always correspond to radar reflectors, we propose an elastic skeleton fusion mechanism, which constructs a virtual force to establish the relationship between the radar reflectors on the vehicle and its extent. Furthermore, to better describe the kinematic state of the vehicle and constrain its extent state, we develop a new 3D constant turn rate and velocity motion model, considering the complex 3D motion of the vehicle relative to the roadside sensor. Finally, we apply variational Bayesian approximation to the intractable measurement update step to enable recursive Bayesian estimation of the object's state. Simulation results using the Carla simulator and experimental results on the nuScenes dataset demonstrate the effectiveness and superiority of the proposed method in comparison to several state-of-the-art 3D EOT methods.

Multiple extended target tracking (ETT) has gained increasing attention due to the development of high-precision LiDAR and radar sensors in automotive applications. For LiDAR point cloud-based vehicle tracking, this paper presents a probabilistic measurement-region association (PMRA) ETT model, which can describe the complex measurement distribution by partitioning the target extent into different regions. The PMRA model overcomes the drawbacks of previous data-region association (DRA) models by eliminating the approximation error of constrained estimation and using continuous integrals to more reliably calculate the association probabilities. Furthermore, the PMRA model is integrated with the Poisson multi-Bernoulli mixture (PMBM) filter for tracking multiple vehicles. Simulation results illustrate the superior estimation accuracy of the proposed PMRA-PMBM filter in terms of both positions and extents of the vehicles comparing with PMBM filters using the gamma Gaussian inverse Wishart and DRA implementations., Comment: 8 pages, 5 figures, accepted by the 27th International Conference on Information Fusion (FUSION 2024)

Multi-object tracking (MOT) is the task of estimating the state trajectories of an unknown and time-varying number of objects over a certain time window. Several algorithms have been proposed to tackle the multi-object smoothing task, where object detections can be conditioned on all the measurements in the time window. However, the best-performing methods suffer from intractable computational complexity and require approximations, performing suboptimally in complex settings. Deep learning based algorithms are a possible venue for tackling this issue but have not been applied extensively in settings where accurate multi-object models are available and measurements are low-dimensional. We propose a novel DL architecture specifically tailored for this setting that decouples the data association task from the smoothing task. We compare the performance of the proposed smoother to the state-of-the-art in different tasks of varying difficulty and provide, to the best of our knowledge, the first comparison between traditional Bayesian trackers and DL trackers in the smoothing problem setting.

This paper considers a batch solution to the multi-object tracking problem based on sets of trajectories. Specifically, we present two offline implementations of the trajectory Poisson multi-Bernoulli mixture (TPMBM) filter for batch data based on Markov chain Monte Carlo (MCMC) sampling of the data association hypotheses. In contrast to online TPMBM implementations, the proposed offline implementations solve a large-scale, multi-scan data association problem across the entire time interval of interest, and therefore they can fully exploit all the measurement information available. Furthermore, by leveraging the efficient hypothesis structure of TPMBM filters, the proposed implementations compare favorably with other MCMC-based multi-object tracking algorithms. Simulation results show that the TPMBM implementation using the Metropolis-Hastings algorithm presents state-of-the-art multiple trajectory estimation performance., Comment: Accepted for publication in IEEE Transactions on Aerospace and Electronic Systems. MATLAB implementation available at https://github.com/yuhsuansia/Batch-TPMBM-using-MCMC-sampling

Accurate perception is essential for advancing autonomous driving and addressing safety challenges in modern transportation systems. Despite significant advancements in computer vision for object recognition, current perception methods still face difficulties in complex real-world traffic environments. Challenges such as physical occlusion and limited sensor field of view persist for individual vehicle systems. Cooperative Perception (CP) with Vehicle-to-Everything (V2X) technologies has emerged as a solution to overcome these obstacles and enhance driving automation systems. While some research has explored CP's fundamental architecture and critical components, there remains a lack of comprehensive summaries of the latest innovations, particularly in the context of V2X communication technologies. To address this gap, this paper provides a comprehensive overview of the evolution of CP technologies, spanning from early explorations to recent developments, including advancements in V2X communication technologies. Additionally, a contemporary generic framework is also proposed to illustrate the V2X-based CP workflow, aiding in the structured understanding of CP system components. Furthermore, this paper categorizes prevailing V2X-based CP methodologies based on the critical issues they address. An extensive literature review is conducted within this taxonomy, evaluating existing datasets and simulators. Finally, open challenges and future directions in CP for autonomous driving are discussed by considering both perception and V2X communication advancements.

Online 3D multi-object tracking (MOT) has recently received significant research interests due to the expanding demand of 3D perception in advanced driver assistance systems (ADAS) and autonomous driving (AD). Among the existing 3D MOT frameworks for ADAS and AD, conventional point object tracking (POT) framework using the tracking-by-detection (TBD) strategy has been well studied and accepted for LiDAR and 4D imaging radar point clouds. In contrast, extended object tracking (EOT), another important framework which accepts the joint-detection-and-tracking (JDT) strategy, has rarely been explored for online 3D MOT applications. This paper provides the first systematic investigation of the EOT framework for online 3D MOT in real-world ADAS and AD scenarios. Specifically, the widely accepted TBD-POT framework, the recently investigated JDT-EOT framework, and our proposed TBD-EOT framework are compared via extensive evaluations on two open source 4D imaging radar datasets: View-of-Delft and TJ4DRadSet. Experiment results demonstrate that the conventional TBD-POT framework remains preferable for online 3D MOT with high tracking performance and low computational complexity, while the proposed TBD-EOT framework has the potential to outperform it in certain situations. However, the results also show that the JDT-EOT framework encounters multiple problems and performs inadequately in evaluation scenarios. After analyzing the causes of these phenomena based on various evaluation metrics and visualizations, we provide possible guidelines to improve the performance of these MOT frameworks on real-world data. These provide the first benchmark and important insights for the future development of 4D imaging radar-based online 3D MOT algorithms., Comment: 8 pages, 5 figures, accepted by IEEE 35th Intelligent Vehicles Symposium (IV 2024), oral presentation (top 5%), code is available at https://github.com/dinggh0817/4D_Radar_MOT

Online multi-object tracking (MOT) plays a pivotal role in autonomous systems. The state-of-the-art approaches usually employ a tracking-by-detection method, and data association plays a critical role. This paper proposes a learning and graph-optimized (LEGO) modular tracker to improve data association performance in the existing literature. The proposed LEGO tracker integrates graph optimization and self-attention mechanisms, which efficiently formulate the association score map, facilitating the accurate and efficient matching of objects across time frames. To further enhance the state update process, the Kalman filter is added to ensure consistent tracking by incorporating temporal coherence in the object states. Our proposed method utilizing LiDAR alone has shown exceptional performance compared to other online tracking approaches, including LiDAR-based and LiDAR-camera fusion-based methods. LEGO ranked 1st at the time of submitting results to KITTI object tracking evaluation ranking board and remains 2nd at the time of submitting this paper, among all online trackers in the KITTI MOT benchmark for cars1

We present 2SDS (Scene Separation and Data Selection algorithm), a temporal segmentation algorithm used in real-time video stream interpretation. It complements CNN-based models to make use of temporal information in videos. 2SDS can detect the change between scenes in a video stream by com-paring the image difference between two frames. It separates a video into segments (scenes), and by combining itself with a CNN model, 2SDS can select the optimal result for each scene. In this paper, we will be discussing some basic methods and concepts behind 2SDS, as well as presenting some preliminary experiment results regarding 2SDS. During these experiments, 2SDS has achieved an overall accuracy of over 90%., Comment: 5 pages, 4 figures, at IJCAI-ECAI 2022 workshop, First International Workshop on Spatio-Temporal Reasoning and Learning, July 24, 2022, Vienna, Austria

As an emerging technology and a relatively affordable device, the 4D imaging radar has already been confirmed effective in performing 3D object detection in autonomous driving. Nevertheless, the sparsity and noisiness of 4D radar point clouds hinder further performance improvement, and in-depth studies about its fusion with other modalities are lacking. On the other hand, as a new image view transformation strategy, "sampling" has been applied in a few image-based detectors and shown to outperform the widely applied "depth-based splatting" proposed in Lift-Splat-Shoot (LSS), even without image depth prediction. However, the potential of "sampling" is not fully unleashed. This paper investigates the "sampling" view transformation strategy on the camera and 4D imaging radar fusion-based 3D object detection. LiDAR Excluded Lean (LXL) model, predicted image depth distribution maps and radar 3D occupancy grids are generated from image perspective view (PV) features and radar bird's eye view (BEV) features, respectively. They are sent to the core of LXL, called "radar occupancy-assisted depth-based sampling", to aid image view transformation. We demonstrated that more accurate view transformation can be performed by introducing image depths and radar information to enhance the "sampling" strategy. Experiments on VoD and TJ4DRadSet datasets show that the proposed method outperforms the state-of-the-art 3D object detection methods by a significant margin without bells and whistles. Ablation studies demonstrate that our method performs the best among different enhancement settings., Comment: Accepted by IEEE Transactions on Intelligent Vehicles

Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random variables with a fixed and known number of vector elements, while certain applications rely on RFSs with an unknown number of vector elements. In this paper, we develop BP rules for factor graphs defined on sequences of RFSs where each RFS has an unknown number of elements, with the intention of deriving novel inference methods for RFSs. Furthermore, we show that vector-type BP is a special case of set-type BP, where each RFS follows the Bernoulli process. To demonstrate the validity of developed set-type BP, we apply it to the PMB filter for SLAM, which naturally leads to new set-type BP-mapping, SLAM, multi-target tracking, and simultaneous localization and tracking filters. Finally, we explore the relationships between the vector-type BP and the proposed set-type BP PMB-SLAM implementations and show a performance gain of the proposed set-type BP PMB-SLAM filter in comparison with the vector-type BP-SLAM filter., Comment: 17 pages, 7 figures

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., Comment: Matlab code available at https://github.com/Agarciafernandez/MTT and https://github.com/yuhsuansia/Extented-target-PMBM-filter-independent-clutter-sources

In this paper, we demonstrate that deep learning based method can be used to fuse multi-object densities. Given a scenario with several sensors with possibly different field-of-views, tracking is performed locally in each sensor by a tracker, which produces random finite set multi-object densities. To fuse outputs from different trackers, we adapt a recently proposed transformer-based multi-object tracker, where the fusion result is a global multi-object density, describing the set of all alive objects at the current time. We compare the performance of the transformer-based fusion method with a well-performing model-based Bayesian fusion method in several simulated scenarios with different parameter settings using synthetic data. The simulation results show that the transformer-based fusion method outperforms the model-based Bayesian method in our experimental scenarios., Comment: Accepted for publication in ICASSP 2023. Python implementation is available at https://github.com/Lechili/DeepFusion

In this paper, we propose a Poisson multi-Bernoulli (PMB) filter for extended object tracking (EOT), which directly estimates the set of object trajectories, using belief propagation (BP). The proposed filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the PMB mixture (PMBM) posterior after the update step is approximated as a PMB. The efficient PMB approximation relies on several important theoretical contributions. First, we present a PMBM conjugate prior on the posterior of sets of trajectories for a generalized measurement model, in which each object generates an independent set of measurements. The PMBM density is a conjugate prior in the sense that both the prediction and the update steps preserve the PMBM form of the density. Second, we present a factor graph representation of the joint posterior of the PMBM set of trajectories and association variables for the Poisson spatial measurement model. Importantly, leveraging the PMBM conjugacy and the factor graph formulation enables an elegant treatment on undetected objects via a Poisson point process and efficient inference on sets of trajectories using BP, where the approximate marginal densities in the PMB approximation can be obtained without enumeration of different data association hypotheses. To achieve this, we present a particle-based implementation of the proposed filter, where smoothed trajectory estimates, if desired, can be obtained via single-object particle smoothing methods, and its performance for EOT with ellipsoidal shapes is evaluated in a simulation study., Comment: Accepted for publication in IEEE Transactions on Aerospace and Electronic Systems. MATLAB implementation available at https://github.com/yuhsuansia/Trajectory-PMB-EOT-BP

This paper provides a comparative analysis between the adaptive birth model used in the labelled random finite set literature and the track initiation in the Poisson multi-Bernoulli mixture (PMBM) filter, with point-target models. The PMBM track initiation is obtained via Bayes' rule applied on the predicted PMBM density, and creates one Bernoulli component for each received measurement, representing that this measurement may be clutter or a detection from a new target. Adaptive birth mimics this procedure by creating a Bernoulli component for each measurement using a different rule to determine the probability of existence and a user-defined single-target density. This paper first provides an analysis of the differences that arise in track initiation based on isolated measurements. Then, it shows that adaptive birth underestimates the number of objects present in the surveillance area under common modelling assumptions. Finally, we provide numerical simulations to further illustrate the differences., Comment: Matlab implementations of PMBM filters can be found at https://github.com/Agarciafernandez/MTT and https://github.com/yuhsuansia

Multi-object tracking (MOT) is among crucial applications in modern advanced driver assistance systems (ADAS) and autonomous driving (AD) systems. The global nearest neighbor (GNN) filter, as the earliest random vector-based Bayesian tracking framework, has been adopted in most of state-of-the-arts trackers in the automotive industry. The development of random finite set (RFS) theory facilitates a mathematically rigorous treatment of the MOT problem, and different variants of RFS-based Bayesian filters have then been proposed. However, their effectiveness in the real ADAS and AD application is still an open problem. In this paper, it is demonstrated that the latest RFS-based Bayesian tracking framework could be superior to typical random vector-based Bayesian tracking framework via a systematic comparative study of both traditional random vector-based Bayesian filters with rule-based heuristic track maintenance and RFS-based Bayesian filters on the nuScenes validation dataset. An RFS-based tracker, namely Poisson multi-Bernoulli filter using the global nearest neighbor (GNN-PMB), is proposed to LiDAR-based MOT tasks. This GNN-PMB tracker is simple to use, and it achieves competitive results on the nuScenes dataset. Specifically, the proposed GNN-PMB tracker outperforms most state-of-the-art LiDAR-only trackers and LiDAR and camera fusion-based trackers, ranking the $3^{rd}$ among all LiDAR-only trackers on nuScenes 3D tracking challenge leader board at the time of submission., Comment: accepted by IEEE Transactions on Intelligent Vehicles

This paper presents a general solution for computing the multi-object posterior for sets of trajectories from a sequence of multi-object (unlabelled) filtering densities and a multi-object dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multi-object filters that do not explicitly estimate trajectories. In this paper, we first derive a general multi-trajectory backward smoothing equation based on random finite sets of trajectories. Then we show how to sample sets of trajectories using backward simulation for Poisson multi-Bernoulli filtering densities, and develop a tractable implementation based on ranked assignment. The performance of the resulting multi-trajectory particle smoothers is evaluated in a simulation study, and the results demonstrate that they have superior performance in comparison to several state-of-the-art multi-object filters and smoothers., Comment: Accepted for publication in IEEE Transactions on Signal Processing

The automotive mmWave radar plays a key role in advanced driver assistance systems (ADAS) and autonomous driving. Deep learning-based instance segmentation enables real-time object identification from the radar detection points. In the conventional training process, accurate annotation is the key. However, high-quality annotations of radar detection points are challenging to achieve due to their ambiguity and sparsity. To address this issue, we propose a contrastive learning approach for implementing radar detection points-based instance segmentation. We define the positive and negative samples according to the ground-truth label, apply the contrastive loss to train the model first, and then perform fine-tuning for the following downstream task. In addition, these two steps can be merged into one, and pseudo labels can be generated for the unlabeled data to improve the performance further. Thus, there are four different training settings for our method. Experiments show that when the ground-truth information is only available for a small proportion of the training data, our method still achieves a comparable performance to the approach trained in a supervised manner with 100% ground-truth information., Comment: Accepted by IEEE ITSC 2022

Multi-object tracking (MOT) is the problem of tracking the state of an unknown and time-varying number of objects using noisy measurements, with important applications such as autonomous driving, tracking animal behavior, defense systems, and others. In recent years, deep learning (DL) has been increasingly used in MOT for improving tracking performance, but mostly in settings where the measurements are high-dimensional and there are no available models of the measurement likelihood and the object dynamics. The model-based setting instead has not attracted as much attention, and it is still unclear if DL methods can outperform traditional model-based Bayesian methods, which are the state of the art (SOTA) in this context. In this paper, we propose a Transformer-based DL tracker and evaluate its performance in the model-based setting, comparing it to SOTA model-based Bayesian methods in a variety of different tasks. Our results show that the proposed DL method can match the performance of the model-based methods in simple tasks, while outperforming them when the task gets more complicated, either due to an increase in the data association complexity, or to stronger nonlinearities of the models of the environment.

Automotive radar provides reliable environmental perception in all-weather conditions with affordable cost, but it hardly supplies semantic and geometry information due to the sparsity of radar detection points. With the development of automotive radar technologies in recent years, instance segmentation becomes possible by using automotive radar. Its data contain contexts such as radar cross section and micro-Doppler effects, and sometimes can provide detection when the field of view is obscured. The outcome from instance segmentation could be potentially used as the input of trackers for tracking targets. The existing methods often utilize a clustering-based classification framework, which fits the need of real-time processing but has limited performance due to minimum information provided by sparse radar detection points. In this paper, we propose an efficient method based on clustering of estimated semantic information to achieve instance segmentation for the sparse radar detection points. In addition, we show that the performance of the proposed approach can be further enhanced by incorporating the visual multi-layer perceptron. The effectiveness of the proposed method is verified by experimental results on the popular RadarScenes dataset, achieving 89.53% mean coverage and 86.97% mean average precision with the IoU threshold of 0.5, which is superior to other approaches in the literature. More significantly, the consumed memory is around 1MB, and the inference time is less than 40ms, indicating that our proposed algorithm is storage and time efficient. These two criteria ensure the practicality of the proposed method in real-world systems., Comment: 11 pages, 9 figures, 3 tables, accepted by IEEE Transactions on Intelligent Vehicles

Evaluating the performance of multi-object tracking (MOT) methods is not straightforward, and existing performance measures fail to consider all the available uncertainty information in the MOT context. This can lead practitioners to select models which produce uncertainty estimates of lower quality, negatively impacting any downstream systems that rely on them. Additionally, most MOT performance measures have hyperparameters, which makes comparisons of different trackers less straightforward. We propose the use of the negative log-likelihood (NLL) of the multi-object posterior given the set of ground-truth objects as a performance measure. This measure takes into account all available uncertainty information in a sound mathematical manner without hyperparameters. We provide efficient algorithms for approximating the computation of the NLL for several common MOT algorithms, show that in some cases it decomposes and approximates the widely-used GOSPA metric, and provide several illustrative examples highlighting the advantages of the NLL in comparison to other MOT performance measures., Comment: Accepted to IEEE Signal Processing Letters 2021

Multitarget Tracking (MTT) is the problem of tracking the states of an unknown number of objects using noisy measurements, with important applications to autonomous driving, surveillance, robotics, and others. In the model-based Bayesian setting, there are conjugate priors that enable us to express the multi-object posterior in closed form, which could theoretically provide Bayes-optimal estimates. However, the posterior involves a super-exponential growth of the number of hypotheses over time, forcing state-of-the-art methods to resort to approximations for remaining tractable, which can impact their performance in complex scenarios. Model-free methods based on deep-learning provide an attractive alternative, as they can, in principle, learn the optimal filter from data, but to the best of our knowledge were never compared to current state-of-the-art Bayesian filters, specially not in contexts where accurate models are available. In this paper, we propose a high-performing deep-learning method for MTT based on the Transformer architecture and compare it to two state-of-the-art Bayesian filters, in a setting where we assume the correct model is provided. Although this gives an edge to the model-based filters, it also allows us to generate unlimited training data. We show that the proposed model outperforms state-of-the-art Bayesian filters in complex scenarios, while matching their performance in simpler cases, which validates the applicability of deep-learning also in the model-based regime. The code for all our implementations is made available at https://github.com/JulianoLagana/MT3 ., Comment: 8 pages, 4 figures

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter for coexisting point and extended targets, i.e., for scenarios where there may be simultaneous point and extended targets. The PMBM filter provides a recursion to compute the multi-target filtering posterior based on probabilistic information on data associations, and single-target predictions and updates. In this paper, we first derive the PMBM filter update for a generalised measurement model, which can include measurements originated from point and extended targets. Second, we propose a single-target space that accommodates both point and extended targets and derive the filtering recursion that propagates Gaussian densities for point targets and gamma Gaussian inverse Wishart densities for extended targets. As a computationally efficient approximation of the PMBM filter, we also develop a Poisson multi-Bernoulli (PMB) filter for coexisting point and extended targets. The resulting filters are analysed via numerical simulations., Comment: Matlab files can be found at https://github.com/Agarciafernandez/Coexisting-point-extended-target-PMBM-filter and https://github.com/yuhsuansia/Coexisting-point-extended-target-PMBM-filter. A relevant multi-object tracking course can be found at https://www.youtube.com/channel/UCa2-fpj6AV8T6JK1uTRuFpw

This paper presents a solution for recovering full trajectory information, via the calculation of the posterior of the set of trajectories, from a sequence of multitarget (unlabelled) filtering densities and the multitarget dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multitarget filters that do not explicitly estimate trajectories. In this paper, we first derive a general multitrajectory forward-backward smoothing equation based on sets of trajectories and the random finite set framework. Then we show how to sample sets of trajectories using backward simulation when the multitarget filtering densities are multi-Bernoulli processes. The proposed approach is demonstrated in a simulation study., Comment: Published in 23rd International Conference on Information Fusion. This arXiv version contains more detailed derivations

This paper presents two trajectory Poisson multi-Bernoulli (TPMB) filters for multi-target tracking: one to estimate the set of alive trajectories at each time step and another to estimate the set of all trajectories, which includes alive and dead trajectories, at each time step. The filters are based on propagating a Poisson multi-Bernoulli (PMB) density on the corresponding set of trajectories through the filtering recursion. After the update step, the posterior is a PMB mixture (PMBM) so, in order to obtain a PMB density, a Kullback-Leibler divergence minimisation on an augmented space is performed. The developed filters are computationally lighter alternatives to the trajectory PMBM filters, which provide the closed-form recursion for sets of trajectories with Poisson birth model, and are shown to outperform previous multi-target tracking algorithms., Comment: Matlab code is provided at https://github.com/Agarciafernandez/MTT

In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal contraints on trajectories can be used to answer a range of important questions, including, e.g., "where did the person that were in area A at time t, go afterwards?". We discuss how multiple constraints can be combined into sets of constraints, and we then apply sets of constraints to set of trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM) densities. For Poisson target birth, the exact posterior density is PMBM for both point targets and extended targets. In the paper we show that if the unconstrained set of trajectories density is PMBM, then the constrained density is also PMBM. Examples of constrained trajectory densities motivate and illustrate the key results.

For the standard point target model with Poisson birth process, the Poisson Multi-Bernoulli Mixture (PMBM) is a conjugate multi-target density. The PMBM filter for sets of targets has been shown to have state-of-the-art performance and a structure similar to the Multiple Hypothesis Tracker (MHT). In this paper we consider a recently developed formulation of multiple target tracking as a random finite set (RFS) of trajectories, and present three important and interesting results. First, we show that, for the standard point target model, the PMBM density is conjugate also for sets of trajectories. Second, based on this we develop PMBM trackers (trajectory RFS filters) that efficiently estimate the set of trajectories. Third, we establish that for the standard point target model the multi-trajectory density is PMBM for trajectories in any time window, given measurements in any (possibly non-overlapping) time window. In addition, the PMBM trackers are evaluated in a simulation study, and shown to yield state-of-the-art performance., Comment: arXiv admin note: text overlap with arXiv:1812.05131

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multi-target distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multi-target tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multi-scan trajectory PMBM filter and a multi-scan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multi-scan trajectory $\text{MBM}_{01}$ filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented $N$-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multi-frame assignment problem. The performance of the presented multi-target trackers, applied with an efficient fixed-lag smoothing method, are evaluated in a simulation study., Comment: Published in Journals of Advances in Information Fusion, Special issue on Multiple Hypothesis Tracking, Volume 14, Number 2, Page 213-235, December 2019. MATLAB code is available at https://github.com/yuhsuansia/Multi-scan-trajectory-PMBM-filter