Labeled Random Finite Set

In this paper, we present an expectationmaximisation (EM) algorithm for maximum likelihood estimation in multiple target models (MTT) with Gaussian linear state-space dynamics. We show that estimation of sufficient statistics for EM in a single Gaussian linear state-space model can be extended to the MTT case along with a Monte Carlo approximation for inference of unknown associations of targets. The stochastic approximation EM algorithm that we present here can be used along with any Monte Carlo method which has been developed for tracking in MTT models, such as Markov chain Monte Carlo and sequential Monte Carlo methods. We demonstrate the performance of the algorithm with a simulation.

In this paper, we propose an online multi-object tracking (MOT) method in a delta Generalized Labeled Multi-Bernoulli (δ-GLMB) filter framework to address occlusion and miss-detection issues, reduce false alarms, and recover identity switch (ID switch). To handle occlusion and missdetection issues, we propose a measurement-to-disappeared track association method based on onestep δ-GLMB filter, so it is possible to manage these difficulties by jointly processing occluded or miss-detected objects. The proposed method is based on a proposed similarity metric which is responsible for defining the weight of hypothesized reappeared tracks. We also extend the δ-GLMB filter to efficiently recover switched IDs using the cardinality density, size and color features of the hypothesized tracks. We also propose a novel birth model to achieve more effective clutter removal performance. In both occlusion/miss-detection handler and newly-birthed object detector sections of the proposed method, unassigned measurements play a significant role, since they are used as the candidates for reappeared or birth objects. We evaluate the proposed method on well-known and publicly available MOT15 and MOT17 test datasets which are focused on pedestrian tracking. Experimental results show that the proposed tracker performs better or at least at the same level of the state-of-the-art online and offline MOT methods. It effectively handles the occlusion and ID switch issues and reduces false alarms as well.

Advanced driver assistance systems and highly automated driving functions require an enhanced frontal perception system. The requirements of a frontal environment perception system cannot be satisfied by either of the existing automotive sensors. A commonly used sensor cluster for these functions consists of a mono-vision smart camera and automotive radar. The sensor fusion is intended to combine the data of these sensors to perform a robust environment perception. Multi-object tracking algorithms have a suitable software architecture for sensor data fusion. Several multi-object tracking algorithms, such as JPDAF or MHT, have good tracking performance; however, the computational requirements of these algorithms are significant according to their combinatorial complexity. The GM-PHD filter is a straightforward algorithm with favorable runtime characteristics that can track an unknown and time-varying number of objects. However, the conventional GM-PHD filter has a poor performance in object cardinality estimation. This paper proposes a method that extends the GM-PHD filter with an object birth model that relies on the sensor detections and a robust object extraction module, including Bayesian estimation of objects' existence probability to compensate for drawbacks of the conventional algorithm.

In this paper, we propose a new metric which measures the distance between two finite sets of tracks (a track is a path of either a real or estimated target). This metric is based on the same principle as the Optimal Subpattern Assignment (OSPA) metric devised by Schuhmacher et al. Importantly however, the new metric measures the distance between two finite sets of tracks whereas the OSPA metric measures the distance between two finite sets of target states. By also considering the properties of false tracks, missed tracks and many tracks assigned to one track situations caused by missed detections and false alarms, the minimization of all distances between tracks across two finite sets of tracks employed by the new OSPAMT metric enables performance evaluation of multi-target tracking (MTT) algorithms in a more comprehensive and accurate manner than existing metrics such as the OSPA metric and the enhanced OSPAT metric introduced by Ristic et al which measures the distance between two finite sets of labeled target states.

Multi-target tracking (MTT) is a classical signal processing task, where the goal is to estimate the states of an unknown number of moving targets from noisy sensor measurements. In this paper, we revisit MTT from a deep learning perspective and propose a convolutional neural network (CNN) architecture to tackle it. We represent the target states and sensor measurements as images and recast the problem as an image-to-image prediction task. Then we train a fully convolutional model at small tracking areas and transfer it to much larger areas with numerous targets and sensors. This transfer learning approach enables MTT at a large scale and is also theoretically supported by our novel analysis that bounds the generalization error. In practice, the proposed transferable CNN architecture outperforms random finite set filters on the MTT task with 10 targets and transfers without retraining to a larger MTT task with 250 targets with a 29% performance improvement.

Multi-target tracking (MTT) is a classical signal processing task, where the goal is to estimate the states of an unknown number of moving targets from noisy sensor measurements. In this paper, we revisit MTT from a deep learning perspective and propose a convolutional neural network (CNN) architecture to tackle it. We represent the target states and sensor measurements as images and recast the problem as an image-to-image prediction task. Then we train a fully convolutional model at small tracking areas and transfer it to much larger areas with numerous targets and sensors. This transfer learning approach enables MTT at a large scale and is also theoretically supported by our novel analysis that bounds the generalization error. In practice, the proposed transferable CNN architecture outperforms random finite set filters on the MTT task with 10 targets and transfers without retraining to a larger MTT task with 250 targets with a 29% performance improvement.

This paper proposes a smooth-trajectory estimator for the labelled multi-Bernoulli (LMB) filter by exploiting the special structure of the generalised labelled multi-Bernoulli (GLMB) filter. We devise a simple and intuitive approach to store the best association map when approximating the GLMB random finite set (RFS) to the LMB RFS. In particular, we construct a smooth-trajectory estimator (i.e., an estimator over the entire trajectories of labelled estimates) for the LMB filter based on the history of the best association map and all of the measurements up to the current time. Experimental results under two challenging scenarios demonstrate significant tracking accuracy improvements with negligible additional computational time compared to the conventional LMB filter. The source code is publicly available at https://tinyurl.com/ste-lmb, aimed at promoting advancements in MOT algorithms.

The multiple hypothesis tracker (MHT) and finite set statistics (FISST) are two approaches to multitarget tracking which both have been heralded as optimal. In this paper we show that the multitarget Bayes filter with basis in FISST can be expressed in terms the MHT formalism, consisting of association hypotheses with corresponding probabilities and hypothesis-conditional densities of the targets. Furthermore, we show that the resulting MHT-like method under appropriate assumptions (Poisson clutter and birth models, no target-death, linear-Gaussian Markov target kinematics) only differs from Reid's MHT with regard to the birth process.

The Generalized Labeled Multi-Bernoulli (GLMB) filter attains remarkable results in Multi-Object Tracking (MOT). Nevertheless, the GLMB filter relies on strong assumptions such as prior knowledge of targets' initial state. Pragmatic scenarios such as satellite video object tracking challenge these assumptions as objects appear at random locations and object detectors output numerous false positives. We present an enhanced version of the GLMB filter that learns from previous trajectories to estimate accurate hypotheses initializations. We keep track of previous target states and use this information to sample the initial velocities of newborn targets. This addition significantly improves the performance of the GLMB in videos with low Frames Per Second (FPS), where the target's initial states are paramount for object tracking. We test this enhanced GLMB filter versus comparable trackers and previous solutions for the GLMB filter

In multiple target tracking (MTT) it becomes necessary to use a multi-hypothesis approach if the trajectories of two or more targets cross. However, multi-hypothesis approaches, e.g. the Multiple Hypothesis Tracker (MHT) or the emerging Generalized Labelled Multi-Bernoulli (GLMB) filter, are computationally demanding. In this paper we propose a simple multi-Bernoulli (MB) filter and a post processing method, which together deliver a multi-hypothesis tracking estimate at a computational cost that is only slightly larger than the cost of a single-hypothesis tracking filter even for many targets. The proposed MB filter is shown to be similar to the labeled MB filter, itself an approximation of the multi-hypothesis GLMB filter. In a simulation study with multiple targets and several trajectory crossings the proposed filter is shown to be capable of correctly estimating the multihypothesis output. The filter is also tasked with presenting to an operator a principled perspective on a scene with many feasible track switches.

The paper presents the performance evaluation of a multi-sensor object detection algorithm applied in traffic situation. The chosen data fusion and estimation procedure is the Bernoulli particle filter, which is ideal for cooperative object detection, as it can handle the varying number of sensor measurement and object appearance-disappearance too. The simulated detectors are automotive radar sensors, capable of measuring object speed, distance and bearing. The filter performance is examined along four aspects: number of particles used, simulation timestep, sensor noise and object motion model noise. The applied noise models represent the quality of the equipped sensors and our lack of knowledge on object motion, therefore the robustness of the filter can be examined by varying these parameters. The amount of particles and the used timestep effect the demanded computational power and also the estimation error, hence the scaling of the algorithm can be measured. In order to obtain a statistically meaningful result, a batch of 50 runs for every parameter set were used.

Data fusion is an important issue for object tracking in autonomous systems such as robotics and surveillance. In this paper, we present a multiple-object tracking system whose design is based on multiple Kalman filters dealing with observations from two different kinds of physical sensors. Hardware integration which combines a cheap radar module and a CCD camera has been developed and data fusion method has been proposed to process measurements from those modules for multi-object tracking. Due to the limited resolution of bearing angle measurements of the cheap radar module, CCD measurements are used to compensate for the low angle resolution. Conversely, the radar module provides radial distance information which cannot be measured easily by the CCD camera. The proposed data fusion enables the tracker to efficiently utilize the radial measurements of objects from the cheap radar module and 2D location measurements of objects in image space of the CCD camera. To achieve the multi-object tracking we combine the proposed data fusion method with the integrated probability data association (IPDA) technique underlying the multiple-Kalman filter framework. The proposed complementary system based on the radar and CCD camera is experimentally evaluated through a multi-person tracking scenario. The experimental results demonstrate that the implemented system with fused observations considerably enhances tracking performance over a single sensor system.

This paper presents a new solution for statistical fusion of multi-sensor information acquired from different fields of view, in a centralized sensor network. The focus is on applications that involve tracking unknown number of objects with time-varying states. Our solution is a track-to-track fusion method in which the information contents of posteriors are combined. Existing information-theoretic solutions for track-to-track fusion in sensor networks are commonly devised based on minimizing the average information divergence from the local posteriors to the fused one. A common approach is to use Generalized Covariance Intersection rule for sensor fusion. This approach works best when all the sensors detect the same object(s), and performs poorly when fields-of-view are different. We suggest Cauchy-Schwarz divergence to be used for measuring information divergence. We demonstrate that employing Cauchy-Schwarz divergence leads to fusion rules that are generally more tolerant to imperfect consensus. We show that the proposed fusion rule for multiple Poisson posteriors is the weighted arithmetic mean of the Poisson densities. Furthermore, we derive the fusion rule for labeled multi Bernoulli filter by approximating the labeled multi Bernoulli density to its first order moment. Numerical experiments show the superior performance of our solution compared to Kullback-Leibler averaging method.

This paper addresses multi-agent multi-object tracking with labeled random finite sets via Generalized Covariance Intersection (GCI) fusion. While standard GCI fusion of Labeled Multi-Object (LMO) densities is labelwise and hence fully parallelizable, previous work unfortunately revealed that its fusion performance is highly sensitive to the unavoidable label inconsistencies among different agents. In order to overcome the label inconsistency sensitivity problem, we present a novel approach for the GCI fusion of LMO densities that is both robust to label inconsistencies and computationally efficient. The novel approach consists of, first, finding the best matching between labels of different agents by minimization of a suitable label inconsistency indicator, and, then, performing GCI fusion labelwise according to the obtained label matching. Furthermore, it is shown how the label matching problem, which is at the core of the proposed method, can be formulated as a linear assignment problem of finite length (efficiently solvable in polynomial time by the Hungarian algorithm), exactly for Labeled Multi-Bernoulli densities and approximately for arbitrary LMO densities. Simulation experiments are carried out to demonstrate the robustness and effectiveness of the proposed approach in challenging tracking scenarios.

An Informed Path Planning (IPP) algorithm for multiple agents is presented. It can be used to efficiently utilize available agents when surveying large areas, when total coverage is unattainable. Internally the algorithm has a Probability Hypothesis Density (PHD) representation, inspired by modern This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642153, as well as the Research Council of Norway through the Centres of Excellence funding scheme, grant number 223254-NTNU-AMOS. G. Hendeby has been funded by the Center for Industrial Information Technology at Linköping University (CENIIT). The tri campaign was funded by the Fram Centre project Ground-based radar measurements of sea-ice, icebergs, and growlers.

The challenges in multi-object tracking mainly stem from the random variations in the cardinality and states of objects during the tracking process. Further, the information on locations where the objects appear, their detection probabilities, and the statistics of the sensor's false alarms significantly influence the tracking accuracy of the filter. However, this information is usually assumed to be known and provided by the users. In this paper, we propose an adaptive generalized labeled multi-Bernoulli (GLMB) filter which can track multiple objects without prior knowledge of the aforementioned information. Experimental results show that the performance of the proposed filter is comparable to an ideal GLMB filter supplied with correct information of the tracking scenarios.

In multi-target tracking, targets can appear and disappear in the surveillance region, randomly varying the number of targets and their locations throughout the tracking process. Moreover, apart from measurement noise, observations of the targets are corrupted by misdetections, and false alarms. Therefore, prior information such as the target birth locations, amount of measurement clutter (false alarms) produced by the sensor, and the probability of detection targets have to be taken into account to model the multi-target system as realistic as possible. In general, such information is not available. As a result, the tracking algorithms have to be supplied with intuitive guesses of these values, which usually results in inferior performances. Therefore, accurate inference of these parameters is paramount for achieving acceptable tracking performance in practice. In this paper, we propose a plug-and-play multi-target tracking algorithm based on the recent $\delta$-Generalized Labeled...

Determining the trajectories of cells and their lineages or ancestries in live-cell experiments are fundamental to the understanding of how cells behave and divide. This paper proposes novel online algorithms for jointly tracking and resolving lineages of an unknown and time-varying number of cells from time-lapse video data. Our approach involves modeling the cell ensemble as a labeled random finite set with labels representing cell identities and lineages. A spawning model is developed to take into account cell lineages and changes in cell appearance prior to division. We then derive analytic filters to propagate multi-object distributions that contain information on the current cell ensemble including their lineages. We also develop numerical implementations of the resulting multi-object filters. Experiments using simulation, synthetic cell migration video, and real time-lapse sequence, are presented to demonstrate the capability of the solutions.

In multitarget tracking, knowledge of the backgrounds plays a crucial role in the accuracy of the tracker. Clutter and detection probability are the two essential background parameters which are usually assumed to be known constants although they are, in fact, unknown and time varying. Incorrect values of these parameters lead to a degraded or biased performance of the tracking algorithms. This paper proposes a method for online tracking multiple targets using multiple sensors which jointly adapts to the unknown clutter rate and the probability of detection. An effective filter is developed from parallel estimation of these parameters and then feeding them into the state-of-the-art generalized labeled multi-Bernoulli filter. Provided that the fluctuation of these unknown backgrounds is slowly-varying in comparison to the rate of measurement-update data, the validity of the proposed method is demonstrated via numerical study using multistatic Doppler data.

In this paper, we introduce a tracking algorithm based on labeled Random Finite Sets (RFS) and Rauch–Tung–Striebel (RTS) smoother via a Generalized Labeled Multi-Bernoulli (GLMB) multi-scan estimator to track multiple objects in a wide range of tracking scenarios. In the forward filtering stage, we use the GLMB filter to generate a set of labels and the association history between labels and the measurements. In the trajectory-estimating stage, we apply a track management strategy to eliminate tracks with short lifespan compared to a threshold value. Subsequently, we apply the information of trajectories captured from the forward GLMB filtering stage to carry out standard forward filtering and RTS backward smoothing on each estimated trajectory. For the experiment, we implement the tracker with standard GLMB filter, the hybrid track-before-detect (TBD) GLMB filter, and the GLMB filter with objects spawning. The results show improvements in tracking performance for all implemented tr...

As satellite proximity operations involving multiple neighbors, such as a nearby debris cloud or a cooperative swarm, become more common, satellite on-board relative navigation schemes must be augmented to be able to track more than one target. Multitarget intensity filter approaches have shown promise as tractable methods to track single or multiple targets using measurement data which is subject to noise, misdetections, and false alarms. One such filter, known as the cardinalized probability hypothesis density filter, is applied to the space-based tracking problem. The necessary models are developed and discussed, and simulation results from synthetic data are provided for two potential applications.

In this paper, we propose a new metric which measures the distance between two finite sets of tracks (a track is a path of either a real or estimated target). This metric is based on the same principle as the Optimal Subpattern Assignment (OSPA) metric devised by Schuhmacher et al. Importantly however, the new metric measures the distance between two finite sets of tracks whereas the OSPA metric measures the distance between two finite sets of target states. By also considering the properties of false tracks, missed tracks and many tracks assigned to one track situations caused by missed detections and false alarms, the minimization of all distances between tracks across two finite sets of tracks employed by the new OSPAMT metric enables performance evaluation of multi-target tracking (MTT) algorithms in a more comprehensive and accurate manner than existing metrics such as the OSPA metric and the enhanced OSPAT metric introduced by Ristic et al which measures the distance between two finite sets of labeled target states.

Sensor management in multi-object stochastic systems is a theoretically and computationally challenging problem. This paper presents a novel approach to the multi-target multi-sensor control problem within the partially observed Markov decision process (POMDP) framework. We model the multi-object state as a labeled multi-Bernoulli random finite set (RFS), and use the labeled multi-Bernoulli filter in conjunction with minimizing a task-driven control objective function: posterior expected error of cardinality and state (PEECS). A major contribution is a guided search for multi-dimensional optimization in the multi-sensor control command space, using coordinate descent method. In conjunction with the Generalized Covariance Intersection method for multi-sensor fusion, a fast multi-sensor algorithm is achieved. Numerical studies are presented in several scenarios where numerous controllable (mobile) sensors track multiple moving targets with different levels of observability. The results show that our method works significantly faster than the approach taken by a state of art method, with similar tracking errors. Index Terms partially observed Markov decision process, multi-target tracking, random finite sets, labeled multi-Bernoulli filter, coordinate descent.

The family of pointillist multitarget tracking filters is defined to be the class of filters that is characterized by a joint target-measurement finite point process. The probability generating functional (PGFL) of the joint process is derived directly from the probabilistic structure of the tracking problem. PGFLs exemplify the analytic combinatoric method applied to the measurement to target assignment problems that are fundamental to the tracking problem. It is shown that multi-hypothesis tracking (MHT), joint probabilistic data association (JPDA), and many other now-classic tracking filters can be derived via PGFLs, and thus are members of the family of pointillist filters. When one or more of the target processes are dimensionally compatible, targets can be superposed. It is shown that the classic MHT filter for superposed targets is closely related to the multi-Bernoulli filter. A technique is presented for deriving the functional derivatives by ordinary differentiation, and both exact and approximate methods for evaluating the ordinary derivatives are discussed.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

In this paper, we propose a new metric which measures the distance between two finite sets of tracks (a track is a path of either a real or estimated target). This metric is based on the same principle as the Optimal Subpattern Assignment (OSPA) metric devised by Schuhmacher et al. Importantly however, the new metric measures the distance between two finite sets of tracks whereas the OSPA metric measures the distance between two finite sets of target states. By also considering the properties of false tracks, missed tracks and many tracks assigned to one track situations caused by missed detections and false alarms, the minimization of all distances between tracks across two finite sets of tracks employed by the new OSPAMT metric enables performance evaluation of multi-target tracking (MTT) algorithms in a more comprehensive and accurate manner than existing metrics such as the OSPA metric and the enhanced OSPAT metric introduced by Ristic et al which measures the distance between two finite sets of labeled target states.

Determining the trajectories of cells and their lineages or ancestries in live-cell experiments are fundamental to the understanding of how cells behave and divide. This paper proposes novel online algorithms for jointly tracking and resolving lineages of an unknown and time-varying number of cells from time-lapse video data. Our approach involves modeling the cell ensemble as a labeled random finite set with labels representing cell identities and lineages. A spawning model is developed to take into account cell lineages and changes in cell appearance prior to division. We then derive analytic filters to propagate multi-object distributions that contain information on the current cell ensemble including their lineages. We also develop numerical implementations of the resulting multi-object filters. Experiments using simulation, synthetic cell migration video, and real time-lapse sequence, are presented to demonstrate the capability of the solutions.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

This paper deals with speaker localization in two dimensions from a mobile binaural head. A bootstrap particle filtering scheme is used to perform active localization, i.e. to infer source location by fusing the binaural perception with the sensor motor commands. It relies on an original pseudolikelihood of the source azimuth which captures both the interaural level and phase differences. Since the pseudo-likelihood is discrete, it is fitted with a mixture of circular distributions in order to enhance its resolution. For the fitting task two mixtures are compared and evalutated, namely the mixture of von Mises and wrapped Cauchy distributions. Furthermore, a solution is presented for calculating the von Mises curvefitting with low uncertainty, since the direct implementation can quickly surpass double precision floating number representation. The performance of the filter is compared using both the raw and fitted pseudo-likelihoods on experiments recorded in an acoustically prepared room with ground-truth obtained from a motion capture system. The results show that the proposed algorithm successfully localizes the speaker with an advantage in the direction of the fitted von Mises mixture likelihood.

Detection and tracking of small targets in sea clutter using highresolution radar is a challenging problem. Recently, a Bernoulli trackbefore-detect (TBD) filter has been developed for an airborne scanning radar in the maritime domain, with the purpose of detection and tracking of short-exposure targets by using a fast scanning mode (i.e., short dwell-time and noncoherent integration). This article investigates the potential benefits of coherent radar processing and exploitation of Doppler information in TBD, when the radar operates in a slower scanning mode (i.e., using longer dwell times). For this purpose, a new Bernoulli TBD filter is developed, which is capable of processing full three-dimensional (range-azimuth-Doppler) radar data. The amplitude of sea clutter is modeled using the K distribution with Doppler-dependent shape and scale parameters. Numerical results indicate that the new Bernoulli TBD outperforms the fast scanning TBD filter, at signal-to-interference ratios below 6 dB.

In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In particular, knowledge of a sensor's bounded field-of-view can be exploited to incorporate evidence of where an object was not observed. This paper presents a systematic approach for incorporating knowledge of the field-of-view geometry and position and object inclusion/exclusion evidence into object state densities and random finite set multi-object cardinality distributions. The resulting state estimation problem is nonlinear and solved using a new Gaussian mixture approximation based on recursive component splitting. Based on this approximation, a novel Gaussian mixture Bernoulli filter for imprecise measurements is derived and demonstrated in a tracking problem using only natural language statements as inputs. This paper also considers the relationship between bounded fields-of-view and cardinality distributions for a representative selection of multiobject distributions, which can be used for sensor planning, as is demonstrated through a problem involving a multi-Bernoulli process with up to one-hundred potential objects. Index Terms-Bounded field-of-view, Gaussian mixtures, imprecise measurements, negative information, Gaussian splitting, random finite set theory

The tracking of space objects poses unique challenges when compared to traditional applications. Direct application of standard multi-target tracking models fails to yield accurate results for the case of space objects. For example, dynamic models for traditional applications require simple, often linear, discrete-time models. This is not the case for space objects where motion is nonlinear and computation cost is too prohibitive for current Monte Carlo filters. This paper describes the multitarget tracking problem for space objects and summarizes system requirements for space situational awareness. Traditional multitarget filter models are compared to corresponding methods for space object tracking in the context of tracking performance via the δ-Generalized Labeled Multi-Bernoulli (δ-GLMB) filter. Using these tests, key research challenges for space situational awareness are discussed.

A large-scale multi-object tracker based on the generalised labeled multi-Bernoulli (GLMB) filter is proposed. The algorithm is capable of tracking a very large, unknown and timevarying number of objects simultaneously, in the presence of a high number of false alarms, as well as missed detections and measurement origin uncertainty due to closely spaced objects. The algorithm is demonstrated on a simulated tracking scenario, where the peak number objects appearing simultaneously exceeds one million. Additionally, we introduce a new method of applying the optimal sub-pattern assignment (OSPA) metric to determine a meaningful distance between two sets of tracks. We also develop an efficient strategy for its exact computation in large-scale scenarios to evaluate the performance of the proposed tracker.

This paper proposes an efficient implementation of the multi-sensor generalized labeled multi-Bernoulli (GLMB) filter. Like its single-sensor counterpart, such implementation requires truncating the GLMB sum. However the single-sensor case requires solving 2-D ranked assignment problems whereas the multi-sensor case require solving multi-dimensional ranked assignment problems, which are NP-hard. The proposed implementation exploits the GLMB joint prediction and update together with a new technique for truncating the GLMB filtering density based on Gibbs sampling. The resulting algorithm has a quadratic complexity in the number of hypothesized objects and linear in the total number of measurements from all sensors.

This paper proposes an efficient implementation of the generalized labeled multi-Bernoulli (GLMB) filter by combining the prediction and update into a single step. In contrast to an earlier implementation that involves separate truncations in the prediction and update steps, the proposed implementation requires only one truncation procedure for each iteration. Furthermore, we propose an efficient algorithm for truncating the GLMB filtering density based on Gibbs sampling. The resulting implementation has a linear complexity in the number of measurements and quadratic in the number of hypothesized objects.

Previous adaptations of the δ-generalized labeled multi-Bernoulli (δ-GLMB) filter to the multi-sensor case involve the sequential application of the update step for each sensor or Gibbs sampling for multi-sensor data association. The practical usage of the sequential δ-GLMB filter is limited due to the number of hypotheses growing with each additional sensor. Similarly, the Gibbs method requires a large number of samples for each hypothesis. In this paper, in the aim of finding the optimal or near-optimal multi-sensor assignments, we propose two novel methods, the combination and the cross entropy methods. Numerical simulations are conducted to evaluate the proposed multi-assignment methods together with the standard sequential processing method and a stochastic optimization algorithm based on Gibbs sampling. The combination method is able to significantly reduce running time with respect to the sequential method while yielding competitive performance across a wide range of test sce...

In this letter, we apply a Bernoulli Filter for moving target detection and tracking using real Multiple Input Multiple Output radar data in a challenging environment. The interest in MIMO radars has been growing since they can provide high performance at lower cost than conventional antenna arrays. The Bernoulli Filter performs tracking using the Track-Before-Detect approach, which is required to achieve satisfactory tracking performance in low signal-to-noise scenarios. The algorithm is validated with real MIMO data of a walking person. Index Terms-Bernoulli filter, MIMO radar, TBD. I. INTRODUCTION A N IMPORTANT application of radar technology is to provide data from a surveillance area to support the detection and tracking of moving targets [14]. Recently, there has been a growing interest towards the use of Multiple-Input Multiple-Output (MIMO) radars because they can achieve high performance with low-cost hardware in comparison to the conventional antenna array [6]. Starting from these concepts, together with the idea of Frequency Modulated Continuous Wave (FMCW) Synthetic Aperture Radar (SAR) systems [10], a MIMO radar for SAR imaging was developed at the Joint Research Centre (JRC) [15] and was successfully used for displacement monitoring of the Costa Concordia [4]. Currently, we are investigating the applicability of the system for detection and tracking of a moving target. Tracking is usually performed on data preprocessed into point measurements or detections. Compressing the data image into a finite set of points is very effective for a wide range of applications [1]. However, this approach may not be adequate for low SNR due to the information loss [3]. Consequently, it is necessary to use all information contained in the images to improve the tracking performance. The idea of Track-Before-Detect (TBD) was first investigated in [3] and applied to a number of applications [5], [16], [18], [21]. For single-target scenarios, an optimal solution for TBD tracking/smoothing is obtained by means of the Bernoulli filter [22], an exact Bayesian filter Manuscript

Advanced driver assistance systems and highly automated driving functions require an enhanced frontal perception system. The requirements of a frontal environment perception system cannot be satisfied by either of the existing automotive sensors. A commonly used sensor cluster for these functions consists of a mono-vision smart camera and automotive radar. The sensor fusion is intended to combine the data of these sensors to perform a robust environment perception. Multi-object tracking algorithms have a suitable software architecture for sensor data fusion. Several multi-object tracking algorithms, such as JPDAF or MHT, have good tracking performance; however, the computational requirements of these algorithms are significant according to their combinatorial complexity. The GM-PHD filter is a straightforward algorithm with favorable runtime characteristics that can track an unknown and time-varying number of objects. However, the conventional GM-PHD filter has a poor performance in object cardinality estimation. This paper proposes a method that extends the GM-PHD filter with an object birth model that relies on the sensor detections and a robust object extraction module, including Bayesian estimation of objects' existence probability to compensate for drawbacks of the conventional algorithm.

This paper addresses fusion of labeled random finite set (LRFS) densities according to the criterion of minimum information loss (MIL). The MIL criterion amounts to minimizing the (weighted) sum of Kullback-Leibler divergences (KLDs) with the fused density appearing as righthand argument of the KLDs. In order to ensure the fused density to be consistent with the local ones when LRFS densities are marginal δ-generalized labeled multi-Bernoulli (Mδ-GLMB) or labeled multi-Bernoulli (LMB) densities, the MIL rule is further elaborated by imposing the constraint that the fused density be in the same family of local ones. In order to deal with different fields-of-view (FoVs) of the local densities, the global label space is divided into disjoint subspaces which represent the exclusive FoVs and the common FoV of the agents, and each local density is decomposed into the sub-densities defined in the corresponding subspaces. Then fusion is performed subspace-by-subspace to combine local subdensities into global ones, and the global density is obtained by multiplying the global sub-densities. Further, in order to tackle the label mismatching issue arising in practical applications, a rank assignment optimization (RAO) of a suitably defined cost is carried out so as to match labels from different agents. Moreover, issues concerning implementation of the MIL rule and its application to distributed multitarget tracking (DMT) are discussed. Finally, the performance of the proposed fusion approach is assessed via simulation experiments considering DMT with either the same or different FoVs of the agents.

The paper deals with the fusion of multiobject information over a network of heterogeneous and geographically dispersed nodes with sensing, communication and processing capabilities. To exploit the benefits of sensor networks for multiobject estimation problems, like e.g. multitarget tracking and multirobot SLAM (Simultaneous Localization and Mapping), a key issue to be addressed is how to consistently fuse (average) locally updated multiobject densities. In this paper we discuss the generalization of Kullback-Leibler average, originally conceived for single-object densities (i.e. probability density functions) to (both unlabeled and labeled) multiobject densities. Then, with a view to develop scalable and reliable distributed multiobject estimation algorithms, we review approaches to iteratively compute, in each node of the network, the collective multiobject average via scalable and neighborwise computations.

A key objective of multi-agent surveillance systems is to monitor a much larger region than the limited field-ofview (FoV) of any individual agent by successfully exploiting cooperation among multi-view agents. Whenever either a centralized or a distributed approach is pursued, this goal cannot be achieved unless an appropriately designed fusion strategy is adopted. This paper presents a novel principled information fusion approach for dealing with multi-view multi-agent case, on the basis of Generalized Covariance Intersection (GCI). The proposed method can be used to perform multi-object tracking on both a centralized and a distributed peer-to-peer sensor network. Simulation experiments on realistic multi-object tracking scenarios demonstrate effectiveness of the proposed solution.

Generalized covariance intersection (GCI) has been effective in fusing multiobject densities from multiple agents for multitarget tracking and mapping purposes. From an information-theoretic viewpoint, it has been shown that GCI fusion essentially minimizes the weighted information gain (WIG) from local densities to the fused one. In this paper, the interest is in the fusion rule that dually minimizes the information loss (IL) and it turns out that such a fusion rule is consistent with the so-called linear opinion pool (LOP). However, the LOP cannot be directly applied to multiobject fusion since the resulting fused multiobject density (FMD), in general, no longer belongs to the same family of the local ones, thus it cannot be utilized as prior information for the next recursion in the context of Bayesian multiobject filtering. In order to overcome such a difficulty, the principle of minimizing IL is further exploited in that the optimal FMD in the same family of the local ones is looked for. Implementation issues relative to the proposed minimum IL (MWIL) fusion rule are discussed. Finally, the performance of the MWIL rule is assessed via simulation experiments concerning distributed multitarget tracking over a wireless sensor network.

This paper addresses distributed registration of a sensor network for multitarget tracking. Each sensor gets measurements of the target position in a local coordinate frame, having no knowledge about the relative positions (referred to as drift parameters) and azimuths (referred to as orientation parameters) of its neighboring nodes. The multitarget set is modeled as an independent and identically distributed (i.i.d.) cluster random finite set (RFS), and a consensus cardinality probability hypothesis density (CPHD) filter is run over the network to recursively compute in each node the posterior RFS density. Then a suitable cost function, expressing the discrepancy between the local posteriors in terms of averaged Kullback-Leibler divergence, is minimized with respect to the drift and orientation parameters for sensor registration purposes. In this way, a computationally feasible optimization approach for joint sensor registraton and multitarget tracking is devised. Finally, the effectiveness of the proposed approach is demonstrated through simulation experiments on both tree networks and networks with cycles, as well as with both linear and nonlinear sensors.

In this paper, we propose a method for optimal stochastic sensor control, where the goal is to minimise the estimation error in multi-object tracking scenarios. Our approach is based on an information theoretic divergence measure between labelled random finite set densities. The multi-target posteriors are generalised labelled multi-Bernoulli (GLMB) densities, which do not permit closed form solutions for traditional information divergence measures such as Kullback-Leibler or Rényi. However, we demonstrate that the Cauchy-Schwarz divergence admits a closed form solution for GLMB densities, thus it can be used as a tractable objective function for multi-target sensor control. This is demonstrated with an application to sensor trajectory optimisation for bearings-only multi-target tracking.

In this contribution, we propose to use road and lane information as contextual cues in order to increase the precision of multi-object object tracking. For tracking, we employ a Monte Carlo implementation of a Probability Hypothesis Density (PHD)-filter, whereas scene context (road and lane information) is taken from annotated street maps. The novel aspect of the presented work is the tightly coupling of context information and the particle filtering process. This is achieved by injecting a priori particles representing locally expected motions, which are in turn determined by the local road and the lane configuration. This approach is evaluated on objects (tracklets) from the public KITTI benchmark database. Our experimental findings demonstrate a considerable tracking precision increasing when including this kind of a priori knowledge. At the same time, the approach is able to determine objects whose movements differ from the locally expected motion, which is an important feature for safety applications.

Through automatic control, intelligent sensors can be manipulated to obtain the most informative measurements about objects in their environment. In object tracking applications, sensor actions are chosen based on the predicted improvement in estimation accuracy, or information gain. Although random finite set theory provides a formalism for measuring information gain for multi-object tracking problems, predicting the information gain remains computationally challenging. This paper presents a new tractable approximation of the random finite set expected information gain applicable to multi-object search and tracking. The approximation presented in this paper accounts for noisy measurements, missed detections, false alarms, and object appearance/disappearance. The effectiveness of the approach is demonstrated through a ground vehicle tracking problem using real video data from a remote optical sensor.

In search-detect-track problems, knowledge of where objects were not seen can be as valuable as knowledge of where objects were seen. Exploiting the sensor's known sensing extents, or field-of-view (FoV), this type of evidence can be incorporated in a Bayesian framework to improve tracking accuracy and form better sensor schedules. This paper presents new techniques for incorporating bounded FoV inclusion/exclusion evidence in object state densities and multi-object cardinality distributions. Some examples of how the proposed techniques may be applied to tracking and sensor planning problems are given.