Multiple Space Object Tracking Using A Randomized Hypothesis Generation Technique

In order to protect assets and operations in space, it is critical to collect and maintain accurate information regarding Resident Space Objects (RSOs). This collection of information is typically known as Space Situational Awareness (SSA). Ground-based and space-based sensors provide information regarding the RSOs in the form of observations or measurement returns. However, the distance between RSO and sensor can, at times, be tens of thousands of kilometers. This and other factors lead to noisy measurements that, in turn, cause one to be uncertain about which RSO a measurement belongs to. These ambiguities are known as data association ambiguities. Coupled with uncertainty in RSO state and the vast number of objects in space, data association ambiguities can cause the multiple space object-tracking problem to become computationally intractable. Tracking the RSO can be framed as a recursive Bayesian multiple object tracking problem with state space containing both continuous and discrete random variables. Using a Finite Set Statistics (FISST) approach one can derive the Random Finite Set (RFS) based Bayesian multiple object tracking recursions. These equations, known as the FISST multiple object tracking equations, are computationally intractable when solved in full. This computational intractability provokes the idea of the newly developed alternative hypothesis dependent derivation of the FISST equations. This alternative derivation allows for a Markov Chain Monte Carlo (MCMC) based randomized sampling technique, termed Randomized FISST (R-FISST). R-FISST is found to provide an accurate approximation of the full FISST recursions while keeping the problem tractable. There are many other benefits to this new derivation. For example, it can be used to connect and compare the classical tracking methods to the modern FISST based approaches. This connection clearly defines the relationships between different approaches and shows that they result in the same formulation for scenarios with a fixed number of objects and are very similar in cases with a varying number of objects. Findings also show that the R-FISST technique is compatible with many powerful optimization tools and can be scaled to solve problems such as collisional cascading

A theoretical analysis of Bayes-optimal multi-target tracking and labelling

In multi-target tracking (MTT), we are often interested not only in finding the position of the multiple objects, but also allowing individual objects to be uniquely identified with the passage of time, by placing a label on each track. While there are many MTT algorithms that produce uniquely identified tracks as output, most of them make use of certain heuristics and/or unrealistic assumptions that makes the global result suboptimal of Bayesian sense. An innovative way of performing MTT is the so-called joint multi-target tracking, where the raw output of the algorithm, rather than being already the collection of output tracks, is a multi-target density calculated by approximating the Bayesian recursion that considers the entire system to have a single multidimensional state. The raw output, i.e. the calculated multi-target density, is thereafter processed to obtain output tracks to be displayed to the operator. This elegant approach, at least in theory, would allow us to precisely represent multi-target statistics. However, most joint MTT methods in the literature handle the problem of track labelling in an ad-hoc, i.e. non-Bayesian manner. A number of methods, however, have suggested that the multi-target density, calculated using the Bayesian recursion, should contain information not only about the location of the individual objects but also their identities. This approach, that we refer as joint MTTL (joint multi-target tracking and labelling), looks intuitively advantageous. It would allow us, at least in theory, to obtain an output consisting of labelled tracks that is optimal in Bayesian sense. Moreover, it would allow us to have statistical information about the assigned labels; for instance, we would know what is the probability that track swap may have occurred after some approximation of targets (or, in simpler words, we would know how much we can believe that a target is what the display says that it is). However, the methods proposed in the still emerging joint MTTL literature do not address some problems that may considerably reduce the usefulness of the approach. These problems include: track coalescence after targets move closely to each other, gradual loss of ambiguity information when particle filters or multiple hypotheses approaches are used, and dealing with unknown/varying number of targets. As we are going to see, each of the previously proposed methods handles only a subset of these problems. Moreover, while obtaining a Bayes-optimal output of labelled tracks is one of the main motivations for joint MTTL, how such output should be obtained is a matter of debate. This work will tackle the joint MTTL problem together with a companion memorandum. In this work, we look at the problem from a theoretical perspective, i.e. we aim to provide an accurate and algorithm-independent picture of the aforementioned problems. An algorithm that actually handles these problems will be proposed in the companion memorandum. As one of the contributions of the memorandum, we clearly characterize the so-called "mixed labelling" phenomenon that leads to track coalescence and other problems, and we verify that, unlike implied in previous literature, it is a physical phenomenon inherent of the MTTL problem rather than specific to a particular approach. We also show how mixed labelling leads to nontrivial issues in practical implementations of joint MTTL. As another of the contributions of the memorandum, we propose a conceptual, algorithm-independent track extraction method for joint MTTL estimators, that gives an output with clear physical interpretation for the user

Multi-Scan Implementation of the Trajectory Poisson Multi-Bernoulli Mixture Filter

The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multitarget distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multitarget tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multiscan trajectory PMBM filter and a multiscan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multiscan trajectory MBM01 filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented N-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multiframe assignment problem. The performance of the presented multitarget trackers, applied with an efficient fixed-lag smoothing method, is evaluated in a simulation study

Multiple Space Object Tracking Using A Randomized Hypothesis Generation Technique

In order to protect assets and operations in space, it is critical to collect and maintain accurate information regarding Resident Space Objects (RSOs). This collection of information is typically known as Space Situational Awareness (SSA). Ground-based and space-based sensors provide information regarding the RSOs in the form of observations or measurement returns. However, the distance between RSO and sensor can, at times, be tens of thousands of kilometers. This and other factors lead to noisy measurements that, in turn, cause one to be uncertain about which RSO a measurement belongs to. These ambiguities are known as data association ambiguities. Coupled with uncertainty in RSO state and the vast number of objects in space, data association ambiguities can cause the multiple space object-tracking problem to become computationally intractable. Tracking the RSO can be framed as a recursive Bayesian multiple object tracking problem with state space containing both continuous and discrete random variables. Using a Finite Set Statistics (FISST) approach one can derive the Random Finite Set (RFS) based Bayesian multiple object tracking recursions. These equations, known as the FISST multiple object tracking equations, are computationally intractable when solved in full. This computational intractability provokes the idea of the newly developed alternative hypothesis dependent derivation of the FISST equations. This alternative derivation allows for a Markov Chain Monte Carlo (MCMC) based randomized sampling technique, termed Randomized FISST (R-FISST). R-FISST is found to provide an accurate approximation of the full FISST recursions while keeping the problem tractable. There are many other benefits to this new derivation. For example, it can be used to connect and compare the classical tracking methods to the modern FISST based approaches. This connection clearly defines the relationships between different approaches and shows that they result in the same formulation for scenarios with a fixed number of objects and are very similar in cases with a varying number of objects. Findings also show that the R-FISST technique is compatible with many powerful optimization tools and can be scaled to solve problems such as collisional cascading

Spatial Sensor Network Based Target Tracking By Classification

The wide use of sensor networks in the day to day communication in recent trends made tracking a significant feature in monitoring systems. The automated systems capable of detection and tracking of targets is a desirable application in many fields. Firstly, deploy a sensor network with appropriate space between sensors and then introduce targets into the network. As the sensors detect the targets, each sensor communicates with neighborhood sensor nodes and one of those sensors are elected as cell-head which will calculate the position of target from the data and transmit that to sink. This process is repeated iteratively to track the moving target. Feature extraction methods and classification techniques have been studied to classify targets by their type. For the challenging task of Multi-target tracking, the methods of sequential Bayesian filtering and Sequential Monte Carlo-Particle Hypothesis Density filters are sought. Accurate algorithms have been simulated for Localization and tracking of target using the data of sensor strengths which are collaboratively communicated among the sensors. Direction of moving target inside a cell was estimated. Algorithm for Hierarchical multi-hop communication model was established

Random finite sets in multi-target tracking - efficient sequential MCMC implementation

Over the last few decades multi-target tracking (MTT) has proved to be a challenging and attractive research topic. MTT applications span a wide variety of disciplines, including robotics, radar/sonar surveillance, computer vision and biomedical research. The primary focus of this dissertation is to develop an effective and efficient multi-target tracking algorithm dealing with an unknown and time-varying number of targets. The emerging and promising Random Finite Set (RFS) framework provides a rigorous foundation for optimal Bayes multi-target tracking. In contrast to traditional approaches, the collection of individual targets is treated as a set-valued state. The intent of this dissertation is two-fold; first to assert that the RFS framework not only is a natural, elegant and rigorous foundation, but also leads to practical, efficient and reliable algorithms for Bayesian multi-target tracking, and second to provide several novel RFS based tracking algorithms suitable for the specific Track-Before-Detect (TBD) surveillance application. One main contribution of this dissertation is a rigorous derivation and practical implementation of a novel algorithm well suited to deal with multi-target tracking problems for a given cardinality. The proposed Interacting Population-based MCMC-PF algorithm makes use of several Metropolis-Hastings samplers running in parallel, which interact through genetic variation. Another key contribution concerns the design and implementation of two novel algorithms to handle a varying number of targets. The first approach exploits Reversible Jumps. The second approach is built upon the concepts of labeled RFSs and multiple cardinality hypotheses. The performance of the proposed algorithms is also demonstrated in practical scenarios, and shown to significantly outperform conventional multi-target PF in terms of track accuracy and consistency. The final contribution seeks to exploit external information to increase the performance of the surveillance system. In multi-target scenarios, kinematic constraints from the interaction of targets with their environment or other targets can restrict target motion. Such motion constraint information is integrated by using a fixed-lag smoothing procedure, named Knowledge-Based Fixed-Lag Smoother (KB-Smoother). The proposed combination IP-MCMC-PF/KB-Smoother yields enhanced tracking

Aircraft state estimation using cameras and passive radar

Multiple target tracking (MTT) is a fundamental task in many application domains. It is a difficult problem to solve in general, so applications make use of domain specific and problem-specific knowledge to approach the problem by solving subtasks separately. This work puts forward a MTT framework (MTTF) which is based on the Bayesian recursive estimator (BRE). The MTTF extends a particle filter (PF) to handle the multiple targets and adds a probabilistic graphical model (PGM) data association stage to compute the mapping from detections to trackers. The MTTF was applied to the problem of passively monitoring airspace. Two applications were built: a passive radar MTT module and a comprehensive visual object tracking (VOT) system. Both applications require a solution to the MTT problem, for which the MTTF was utilized. The VOT system performed well on real data recorded at the University of Cape Town (UCT) as part of this investigation. The system was able to detect and track aircraft flying within the region of interest (ROI). The VOT system consisted of a single camera, an image processing module, the MTTF module and an evaluation module. The world coordinate frame target localization was within ±3.2 km and these results are presented on Google Earth. The image plane target localization has an average reprojection error of ±17.3 pixels. The VOT system achieved an average area under the curve value of 0.77 for all receiver operating characteristic curves. These performance figures are typical over the ±1 hr of video recordings taken from the UCT site. The passive radar application was tested on simulated data. The MTTF module was designed to connect to an existing passive radar system developed by Peralex Electronics Pty Ltd. The MTTF module estimated the number of targets in the scene and localized them within a 2D local world Cartesian coordinate system. The investigations encompass numerous areas of research as well as practical aspects of software engineering and systems design

Online Audio-Visual Multi-Source Tracking and Separation: A Labeled Random Finite Set Approach

The dissertation proposes an online solution for separating an unknown and time-varying number of moving sources using audio and visual data. The random finite set framework is used for the modeling and fusion of audio and visual data. This enables an online tracking algorithm to estimate the source positions and identities for each time point. With this information, a set of beamformers can be designed to separate each desired source and suppress the interfering sources