Random Finite Set

The problem of state estimation for a linear, time-varying, gaussian system from measurements which are communicated over an imperfect channel is considered from several perspectives. The communication imperfections include intermittency, channel noise, quantization, etc. The first part of the thesis examines the stochastic behavior of the state estimation error and of the regulated state itself in situations of intermittent and quantized measurements via the formulation of an escape time problem dealing with the cumulative distribution function of the probability of escape of these signals from a given set. This is compared to and contrasted with earlier analyses which x considered the behavior of Kalman filters with intermittent data based on moments and conditional moments, and the evaluation of the minimal number of bits required for mean square stabilization. The main result shows the escape time is characterized by a Markov chain which is amenable to explicit analysis through the calculation of the its cumulative distribution function. The second part of the thesis focuses on developing an exact formulation of the conditional probability density function of the system state given quantized innovations signals communicated from a linear Kalman filter at the transmitter. This is based on Bayesian filtering and extends previous works on the subject but without the requirement for simplifying assumptions. This latter result follows from a simple observation concerning the correct choice of state for the transmitter, which includes the transmitters' Kalman filter estimate. This leads to an exact and recursive approach. xi

A robust Kalman filter method for positioning using a database of wireless base station coverage areas is presented. In tests with simulated and real data, the proposed filter is found to be more accurate than static positioning or conventional Kalman filtering.

A robust Kalman filter method for positioning using a database of wireless base station coverage areas is presented. In tests with simulated and real data, the proposed filter is found to be more accurate than static positioning or conventional Kalman filtering.

This paper proposes a probabilistic approach for the detection and the tracking of particles in fluorescent time-lapse imaging. In presence of very noised and poor quality data, particles and trajectories can be characterized by ana-contrario model, that estimates the probability of observing the structures of interest in random data. This approach, first introduced in the modeling of human visual perception and then successfully applied in many image processing tasks, leads to algorithms that do not require a previous learning stage, nor a tedious parameter tuning and are very robust to noise. Comparative evaluations against a well established baseline show that the proposed approach outperforms the state of the art.

Joint detection and tracking of drones is a challenging radar technology; especially estimating their states with unknown measurement variances. The Bayesian track-before-detect (TBD) approach is an efficient way to detect low observable targets. In this paper, we proposed a new variational Bayesian (VB)-TBD technique for drones based on Multi-Bernoulli filter, which implemented with unknown measurement variances. Current implementation includes an analytical Gaussian inverse Gamma mixtures solution, which applied to estimate augmented kinematic drones state under the same circumstance. The results demonstrate that the proposed filter is more accurate than other Multi-Bernoulli filters in cardinality estimation. The proposed algorithm estimates the fluctuated parameters for each drone and it has no difficulty in handling the crossing of multiple drones. The Optimal Subpattern Assignment (OSPA) distances of proposed algorithm under different SNR are less than the other filters. It can be seen that at SNR (-5dB), the proposed algorithm and the other filters settle to errors 51 m, 125 m and 200 m, respectively.

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.

Environment perception and situation awareness are keystones for autonomous road vehicles. The problem of maneuver classification for road vehicles in the context of multi-model state estimation under model uncertainty is addressed in this paper. The conventional approach is to define different motion models that match the desired type of movements. In this work we used a single motion model as a starting point and applied constraints to construct such filters that are fine tuned for the predefined maneuvers. The estimation is carried out in the interacting multiple model framework, where the elemental filters are constrained Kalman filters. To capture the characteristics of the considered maneuvers linear equality and non-equality state constraints were used. The performance of the proposed method is demonstrated in a simulation environment participating an observer and a maneuvering vehicle.

The Bernoulli filter (BF) in the interacting multiple model (IMM) framework is proposed for detecting and tracking a maneuvering target. The BF is implemented as a particle filter and embedded in the IMM structure. The communication between the IMM and the BF is achieved through a Gaussian layer. Particles are drawn from the mixture densities at each recursion and the model likelihoods are computed from the filter innovations. Simulations show that the proposed filter outperforms the single model variant and it can effectively choose the correct motion model and estimate the state of the tracked object.

Multi-target tracking requires the joint estimation of the number of target trajectories and their states from a sequence of observations. In low signal-to-noise ratio (SNR) scenarios, the poor detection probability and large number of false observations can greatly degrade the tracking performance. In this case an approach called Track-Before-Detect (TBD) that operates on the pre-detection signal, is needed. In this paper we present a labeled random finite set solution to the multitarget TBD problem. To the best of our knowledge this is the first provably Bayes optimal approach to multi-target tracking using image data. Simulation results using realistic radar-based TBD scenarios are also presented to demonstrate the capability of the proposed approach.

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.

Joint detection and tracking of drones is a challenging radar technology; especially estimating their states with unknown measurement variances. The Bayesian track-before-detect (TBD) approach is an efficient way to detect low observable targets. In this paper, we proposed a new variational Bayesian (VB)-TBD technique for drones based on Multi-Bernoulli filter, which implemented with unknown measurement variances. Current implementation includes an analytical Gaussian inverse Gamma mixtures solution, which applied to estimate augmented kinematic drones state under the same circumstance. The results demonstrate that the proposed filter is more accurate than other Multi-Bernoulli filters in cardinality estimation. The proposed algorithm estimates the fluctuated parameters for each drone and it has no difficulty in handling the crossing of multiple drones. The Optimal Subpattern Assignment (OSPA) distances of proposed algorithm under different SNR are less than the other filters. It can be seen that at SNR (-5dB), the proposed algorithm and the other filters settle to errors 51 m, 125 m and 200 m, respectively.

For the standard Gaussian mixture probability hypothesis density (GM-PHD) filter, the number of targets can be overestimated if the clutter rate is too high or underestimated if the detection rate is too low. These problems seriously affect the accuracy of multitarget tracking for the number and the value of measurements and clutters cannot be distinguished and recognized. Therefore, we proposed an improved GM-PHD filter to tackle these problems. Firstly, a track-estimate association was implemented in the filtering process to detect and remove false-alarm targets. Secondly, a numerical interpolation technique was used to compensate the missing targets caused by low detection rate. At the end of this paper, simulation results were presented to demonstrate the proposed GM-PHD algorithm is more effective in estimating the number and state of targets than the previous ones.

This paper proposes an approach for tracking multiple articulated targets using a combined data association and evolving population particle filter. A visual target is represented as a pictorial structure using a collection of parts together with a model of their geometry. Tracking multiple targets in video involves an iterative alternating scheme of selecting valid measurements belonging to a target from a clutter or other measurements that all fall within a validation gate. An algorithm with extended likelihood probabilistic data association and evolving groups of populations of particles representing a multiple-part distribution is designed. Variety in the particles is introduced using constrained genetic operators both in the sampling and resampling steps. We explore the effect of various model parameters on system performance and show that the proposed model achieves better accuracy than other widely used methods on standard datasets.

The gradually evolving automated driving and ADAS functions require more enhanced environment perception. The key to reliable environmental perception is large amounts of data that are hard to collect. Several simulators provide realistic, raw sensor data based on physical sensor models. However, besides their high price, they also require very high computation capacity. Furthermore, most sensor suppliers provide high-level data, such as object detections, that is complicated to reproduce from simulated raw sensor data. This paper proposes a method that directly simulates the detections or object tracks provided by smart sensors. The model involves several uncertainties of the sensors, such as missed-, false detections, and measurement noise. In contrast to the conventional sensor models, this method tackles with state-dependent clutter model and considers the field of view in the detections model. The parameters of the proposed model are identified for an automotive smart radar and camera based on pre-evaluated real-world measurements. The resulting model provides synthetic object-level data with higher fidelity than the conventional probabilistic models, differing less than 2% from the precision and recall metrics of the actual sensors.

In this paper, the multiple sensor measurement update is studied for the random matrix model. Four different updates are presented and evaluated: three updates based on parametric approximations of the extended target state probability density function, and one update based on a Rao-Blackwellized (RB) particle approximation of the state density. An extensive simulation study shows that the RB particle approach shows best performance, at the price of higher computational cost, compared to parametric approximations.

The dependence on model-fitting to evaluate particle trajectories makes it difficult for single particle tracking (SPT) to resolve the heterogeneous molecular motions typical of cells. We present here a global spatiotemporal sampler for SPT solutions using a Metropolis-Hastings algorithm. The sampler does not find just the most likely solution but also assesses its likelihood and presents alternative solutions. This enables the estimation of the tracking error. Furthermore the algorithm samples the parameters that govern the tracking process and therefore does not require any tweaking by the user. We demonstrate the algorithm on synthetic and single molecule data sets. Metrics for the comparison of SPT are generalised to be applied to a SPT sampler. We illustrate using the example of the diffusion coefficient how the distribution of the tracking solutions can be propagated into a distribution of derived quantities. We also discuss the major challenges that are posed by the realisation of a SPT sampler.

The well-known Shepp-Vardi algorithm (1982) for positron emission tomography (PET) is used to estimate the intensity function of the emissions of short-lived radioisotopes absorbed by the brain or other tissues. In the PET application, radioisotope emissions are modeled as a nonhomogeneous Poisson point process. The Shepp-Vardi algorithm produces the maximum a posteriori (MAP) estimate of the intensity function of this process. The intensity function provides an image of the radioisotope density in the brain or other tissues. The PHD intensity filter is a multiple target tracking filter. Its information update is shown to be the first step of the Shepp-Vardi algorithm. The correspondence with PET reveals that the filter is estimating the intensity function of a nonhomogeneous Poisson point process that approximates the Bayes posterior multi-target point process. The iterated PHD intensity filter uses the Shepp-Vardi algorithm to the compute the MAP optimal approximation. PET estimation has a fundamental noise instability that is overcome in practice by various regularization procedures. Grenander's method of sieves is a regularization procedure that is compatible with the PHD intensity 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.

Let X and Y be two jointly distributed spatial Point Processes on X and Y respectively (both complete separable metric spaces). We address the problem of estimating X, which is the hidden Point Process (PP), given the realisation y of the observed PP Y. We characterise the posterior distribution of X when it is marginally distributed according to a Poisson and Gauss-Poisson prior and when the transformation from X to Y includes thinning, displacement and augmentation with extra points. These results are then applied in a filtering context when the hidden process evolves in discrete time in a Markovian fashion. The dynamics of X considered are general enough for many target tracking applications.

This paper describes the application of finite set statistics (FISST) to a real-time multiple target road constrained feature-aided tracking problem. A vehicle of interest traverses the road network while other confuser vehicles cross paths with this vehicle. Features extracted from sensors are used to disambiguate the vehicle of interest from the confuser vehicles. The FISST formalism naturally leads to understanding ambiguity in the identity of targets. 1.0 Introduction Many tracking applications address the issue of monitoring one (or a few) vehicles of interest (VOI) in a background of confuser vehicles. One such program is the DARPA Affordable Moving Surface Target Engagement (AMSTE) program [1, 2]. Monitoring vehicles traversing a dense road network poses several complications since target state vectors can change rapidly due to target maneuvers at intersections [1]. There is often an association ambiguity between the measurement and the target positions because multiple roads...

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.

The paper deals with resilient state estimation of cyber-physical systems subject to switching signal attacks and fake measurement injection. In particular, the random set paradigm is adopted in order to model the switching nature of the signal attack and the fake measurement injection via Bernoulli and/or Poisson random sets. The problem of jointly detecting a signal attack and estimating the system state in presence of fake measurements is then formulated and solved in the Bayesian framework leading to the analytical derivation of a hybrid Bernoulli filter that updates in real-time the joint posterior density of the detection attack Bernoulli set and of the state vector. Exploiting a Gaussian-mixture implementation of the filter, a simulation example is developed in order to demonstrate the effectiveness of the proposed method.

Navigation, mapping, and tracking are state estimation problems relevant to a wide range of applications. These problems have traditionally been formulated using random vectors in stochastic filtering, smoothing, or optimization-based approaches. Alternatively, the problems can be formulated using random finite sets, which offer a more robust solution in poor detection conditions (i.e., low probabilities of detection, and high clutter intensity). This paper mathematically shows that the two estimation frameworks are related, and equivalences can be determined under a set of ideal detection conditions. The findings provide important insights into some of the limitations of each approach. These are validated using simulations with varying detection statistics, along with a real experimental dataset.

The use of random finite sets (RFSs) in simultaneous localization and mapping (SLAM) for mobile robots is a new concept that provides several advantages over traditional vector-based approaches. These include: 1) the incorporation of detection statistics, as well as the usual spatial uncertainty, in an estimation algorithm, 2) the ability to estimate the number of landmarks in a map, and 3) the circumvention of the need for data association heuristics. Solutions to SLAM can be obtained through the Rao-Blackwellized Probability Hypothesis Density (RB-PHD) filter, which is an approximation of the Bayes filter for RFSs using both particles to represent the robot trajectories, and Gaussian mixtures to represent their associated maps. This paper proposes an improved multi-feature particle weighting strategy for the RB-PHD filter and shows through simulations that it outperforms existing weighting strategies. The proposed strategy makes the RB-PHD filter a generalization of multi-hypothesis (MH) FastSLAM, a vector-based SLAM solution that uses the RB-particle filter.

Joint detection and tracking of drones is a challenging radar technology; especially estimating their states with unknown measurement variances. The Bayesian track-before-detect (TBD) approach is an efficient way to detect low observable targets. In this paper, we proposed a new variational Bayesian (VB)-TBD technique for drones based on Multi-Bernoulli filter, which implemented with unknown measurement variances. Current implementation includes an analytical Gaussian inverse Gamma mixtures solution, which applied to estimate augmented kinematic drones state under the same circumstance. The results demonstrate that the proposed filter is more accurate than other Multi-Bernoulli filters in cardinality estimation. The proposed algorithm estimates the fluctuated parameters for each drone and it has no difficulty in handling the crossing of multiple drones. The Optimal Subpattern Assignment (OSPA) distances of proposed algorithm under different SNR are less than the other filters. It can be seen that at SNR (-5dB), the proposed algorithm and the other filters settle to errors 51 m, 125 m and 200 m, respectively.

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.

Bayesian estimators of a time-varying number of objects and their states are developed. The estimators are based on object superposition, a fundamental concept in finite point processes that is adapted to model multiobject state. The concept of superposition is introduced carefully step by step, starting with its application to the JPDA filter for a specified number of objects. This JPDAS filter lays the groundwork for the extension to a random number of objects, leading quickly and painlessly to the CPHD filter. This natural approach shows the many close connections between the CPHD and the JPDAS filters. A numerical device, new to tracking applications, called the complex step method is used to evaluate the intensity function to machine precision "for free" merely by evaluating the GFL of the Bayes posterior process in complex arithmetic. Examples are presented. Keywords Intensity function • Count density • State superposition • JPDAS intensity filter • PHD intensity filter • CPHD intensity filter • Complex step method • Multi-Bernoulli filter

Navigation, mapping, and tracking are state estimation problems relevant to a wide range of applications. These problems have traditionally been formulated using random vectors in stochastic filtering, smoothing, or optimization-based approaches. Alternatively, the problems can be formulated using random finite sets, which offer a more robust solution in poor detection conditions (i.e., low probabilities of detection, and high clutter intensity). This paper mathematically shows that the two estimation frameworks are related, and equivalences can be determined under a set of ideal detection conditions. The findings provide important insights into some of the limitations of each approach. These are validated using simulations with varying detection statistics, along with a real experimental dataset.

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean-Vlasov control problem.

In robotic mapping and simultaneous localization and mapping, the ability to assess the quality of estimated maps is crucial. While concepts exist for quantifying the error in the estimated trajectory of a robot, or a subset of the estimated feature locations, the difference between all current estimated and ground-truth features is rarely considered jointly. In contrast to many current methods, this paper analyzes metrics, which automatically evaluate maps based on their joint detection and description uncertainty. In the tracking literature, the optimal subpattern assignment (OSPA) metric provided a solution to the problem of assessing target tracking algorithms and has recently been applied to the assessment of robotic maps. Despite its advantages over other metrics, the OSPA metric can saturate to a limiting value irrespective of the cardinality errors and it penalizes missed detections and false alarms in an unequal manner. This paper therefore introduces the cardinalized optimal linear assignment (COLA) metric, as a complement to the OSPA metric, for feature map evaluation. Their combination is shown to provide a robust solution for the evaluation of map estimation errors in an intuitive manner. Index Terms-Map metric, simultaneous localization and mapping, mobile robots. I. INTRODUCTION F UNDAMENTAL to any state estimation problem is the concept of estimation error. Solutions to robotic mapping and simultaneous localization and mapping (SLAM), in which usually the location of an unknown number of features should be estimated, are numerous offering various degrees of performance. Examples include classical methods such as recursive EKF SLAM [1], [2], multihypothesis (MH) FastSLAM [3],

Many threats in the form of human actions (terrorist attacks, military actions, etc.) can be stochastically modeled by someone with relevant expert knowledge. In this work, a threat is taken to be a modeled sequence of actions that evolve over time and culminate at some ultimate goal. A model would be a hypothesis as to how a threat would develop, and what kind of observable evidence it would produce along the way. This modeling method allows us to attempt detection using the preliminary evidence of a threat. This would theoretically allow the user to take preemptive action; i.e., the user can intercede before its culmination. This work presents a method of stochastically modeling these types of processes using Hidden Markov Models (HMMs). We then present a detection scheme based on random finite set (RFS) filters (Bernoulli filters) that allows for detection of multiple threat processes using a single cluttered stream of observed data.

This paper proposes using the number of range measurements that a detector utilizes to generate a detection as its descriptor. This one dimensional descriptor can be calculated with many range-based detectors, and its expected value is used to derive detection statistics which take into account feature occlusions to improve robotic navigation performance. To demonstrate the advantages of estimating detection statistics, they are estimated and tested within Random Finite Set and vector-based Simultaneous Localization and Mapping (SLAM) algorithms. Results from simulations and real experiments demonstrate the advantages of explicitly modeling feature detection statistics in both frameworks.

The simultaneous localization and mapping (SLAM) problem in mobile robotics has traditionally been formulated using random vectors. Alternatively, random finite sets (RFSs) can be used in the formulation, which incorporates non-heursiticbased data association and detection statistics within an estimator that provides both spatial and cardinality estimates of landmarks. This paper mathematically shows that the two formulations are actually closely related, and that RFS SLAM can be viewed as a generalization of vector-based SLAM. Under a set of ideal detection conditions, the two methods are equivalent. This is validated by using simulations and real experimental data, by comparing principled realizations of the two formulations.

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...

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.

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.

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...

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.

The efficiency and robustness of modern visual tracking systems are largely dependent on the object detection system at hand. Bernoulli and Multi-Bernoulli filters have been proposed for visual tracking without explicit detections (image observations). However, these previous approaches do not fully exploit discriminative features for tracking. In this paper, we propose a novel Bernoulli filter with determinantal point processes observations. The proposed observation model can select groups of detections with high detection scores and low correlation among the observed features; thus achieving a robust filter.

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.

In robotic mapping and simultaneous localization and mapping, the ability to assess the quality of estimated maps is crucial. While concepts exist for quantifying the error in the estimated trajectory of a robot, or a subset of the estimated feature locations, the difference between all current estimated and ground-truth features is rarely considered jointly. In contrast to many current methods, this paper analyzes metrics, which automatically evaluate maps based on their joint detection and description uncertainty. In the tracking literature, the optimal subpattern assignment (OSPA) metric provided a solution to the problem of assessing target tracking algorithms and has recently been applied to the assessment of robotic maps. Despite its advantages over other metrics, the OSPA metric can saturate to a limiting value irrespective of the cardinality errors and it penalizes missed detections and false alarms in an unequal manner. This paper therefore introduces the cardinalized optimal linear assignment (COLA) metric, as a complement to the OSPA metric, for feature map evaluation. Their combination is shown to provide a robust solution for the evaluation of map estimation errors in an intuitive manner. Index Terms-Map metric, simultaneous localization and mapping, mobile robots. I. INTRODUCTION F UNDAMENTAL to any state estimation problem is the concept of estimation error. Solutions to robotic mapping and simultaneous localization and mapping (SLAM), in which usually the location of an unknown number of features should be estimated, are numerous offering various degrees of performance. Examples include classical methods such as recursive EKF SLAM [1], [2], multihypothesis (MH) FastSLAM [3],

The Bernoulli filter (BF) is a Bayes-optimal method for target tracking when the target can be present or absent in unknown time intervals and the measurements are affected by clutter and missed detections. We propose a distributed particle-based multisensor BF algorithm that approximates the centralized multisensor BF for arbitrary nonlinear and non-Gaussian system models. Our distributed algorithm uses a new extension of the likelihood consensus (LC) scheme that accounts for both target presence and absence and includes an adaptive pruning of the LC expansion coefficients. Simulation results for a heterogeneous sensor network with significant noise and clutter show that the performance of our algorithm is close to that of the centralized multisensor BF.