Multi-Target Tracking for SMARTnet: Multi-Layer Probability Hypothesis Filter for Near-Earth Object Tracking

In this paper, a modified version of the finite set statistics-based Probability Hypothesis Density (PHD) filter is developed specifically for the optical multi-target tracking of objects in the near-Earth realm for Space Situational Awareness (SAA). A two-step PHD filter is proposed in a modified version. One labeled PHD filter is used on the orthogonal image plane, in which linear dynamics in a fourparameter state is employed, forming so-called tracklets. Tracklets are associated sets of a few closelyspaced observations covering a negligible part of the overall orbit. Furthermore, tracklets are fed into a second PHD filter in a modified measurement update version, utilizing the full near-Earth astrodynamics with a six parameter state. In the modification, each tracklet leads to only one update in the PHD, but all observations within the tracklet are processed in the single target Markov transition process within the filter. In this case, the single target filter is an Extended Kalman Filter. In addition, the birth process that has been usually in typical SSA applications shifted to the birth step, forcing a data-driven birth with the disadvantage of a severe model mismatch, back to the propagation step, as in the original PHD filter formulation, avoiding the mismatch. In order to overcome the lack of probabilistic description availability (one of the triggers of the shift to the datadriven update step of previous authors), the data is preprocessed. This has the advantage that birth can employ traditional initial orbit determination methods and does not have to rely on the initialization with an incomplete state using, e.g., an admissible regions approach. The results are generated using the optical data of the DLR SMARTnet telescope network and are compared to the DLR BACARDI data processing

Space-based relative multitarget tracking

Access to space has expanded dramatically over the past decade. The growing popularity of small satellites, specifically cubesats, and the following launch initiatives have resulted in exponentially growing launch numbers into low Earth orbit. This growing congestion in space has punctuated the need for local space monitoring and autonomous satellite inspection. This work describes the development of a framework for monitoring local space and tracking multiple objects concurrently in a satellite\u27s neighborhood. The development of this multitarget tracking systems has produced collateral developments in numerical methods, relative orbital mechanics, and initial relative orbit determination. This work belongs to a class of navigation known as angles-only navigation, in which angles representing the direction to the target are measured but no range measurements are available. A key difference between this work and traditional angles-only relative navigation research is that angle measurements are collected from two separate cameras simultaneously. Such measurements, when coupled with the known location and orientation of the stereo cameras, can be used to resolve the relative range component of a target\u27s position. This fact is exploited to form initial statistical representations of the targets\u27 relative states, which are subsequently refined in Bayesian single-target and multitarget frameworks --Abstract, page iii

Multiple-Object Estimation Techniques for Challenging Scenarios

A series of methods for solving the multi-object estimation problem in the context sequential Bayesian inference is presented. These methods concentrate on dealing with challenging scenarios of multiple target tracking, involving fundamental problems of nonlinearity and non-Gaussianity of processes, high state dimensionality, high number of targets, statistical dependence between target states, and degenerate cases of low signal-to-noise ratio, high uncertainty, lowly observable states or uninformative observations. These difficulties pose obstacles to most practical multi-object inference problems, lying at the heart of the shortcomings reported for state-of-the-art methods, and so elicit novel treatments to enable tackling a broader class of real problems. The novel algorithms offered as solutions in this dissertation address such challenges by acting on the root causes of the associated problems. Often this involves essential dilemmas commonly manifested in Statistics and Decision Theory, such as trading off estimation accuracy with algorithm complexity, soft versus hard decision, generality versus tractability, conciseness versus interpretativeness etc. All proposed algorithms constitute stochastic filters, each of which is formulated to address specific aspects of the challenges at hand while offering tools to achieve judicious compromises in the aforementioned dilemmas. Two of the filters address the weight degeneracy observed in sequential Monte Carlo filters, particularly for nonlinear processes. One of these filters is designed for nonlinear non-Gaussian high-dimensional problems, delivering representativeness of the uncertainty in high-dimensional states while mitigating part of the inaccuracies that arise from the curse of dimensionality. This filter is shown to cope well with scenarios of multimodality, high state uncertainty, uninformative observations and high number of false alarms. A multi-object filter deals with the problem of considering dependencies between target states in a way that is scalable to a large number of targets, by resorting to probabilistic graphical structures. Another multi-object filter treats the problem of reducing the computational complexity of a state-of-the-art cardinalized filter to deal with a large number of targets, without compromising accuracy significantly. Finally, a framework for associating measurements across observation sessions for scenarios of low state observability is proposed, with application to an important Space Surveillance task: cataloging of space debris in the geosynchronous/geostationary belt. The devised methods treat the considered challenges by bringing about rather general questions, and provide not only principled solutions but also analyzes the essence of the investigated problems, extrapolating the implemented techniques to a wider spectrum of similar problems in Signal Processing

Optical based statistical space objects tracking for catalogue maintenance

The number of space objects has grown substantially in the past decades due to new launches, regular mission activities, and breakup events. This has significantly affected the space environment and the development of the space industry. To ensure safe operation of space assets, Space Situational Awareness (SSA) has attracted considerable attention in recent years. One primary strategy in SSA is to establish and maintain a Space Object Catalogue (SOC) to provide timely updated data for SSA applications, e.g., conjunction analysis, collision avoidance manoeuvring. This thesis investigates three techniques for SOC maintenance, namely the tracklet association method for initial orbit determination, the multi-target tracking method for the refinement of orbital state estimation, and multi-sensor tasking method for the optimisation of sensor resources. Generally speaking, due to the limited number of optical sensors used to track the large population of space objects, the obtained observational arcs for many targets are very short. Such short arcs, which contain a small number of angular observations, are referred as tracklets. Given such limited data, typical orbit determination methods, e.g., Laplace, Gaussian, Double-R methods, may fail to produce a valid orbital solution. By contrast, tracklet association methods compare and correlate multiple tracklets across time, and following successful association, a reliable initial orbital state can be further determined for SOC maintenance. This thesis proposes an improved initial value problem optimisation method for accurate and efficient tracklet association, and a common ellipse method to distinguish false associations of tracklets from objects in the same constellation. The proposed methods are validated using real optical data collected from the Mount Stromlo Observatory, Canberra, Australia. Furthermore, another challenging task in SSA is to track multiple objects for the maintenance of a catalog. The Bayesian multi-target tracking filter addresses this issue by associating measurements to initially known or newly detected targets and simultaneously estimating the timevarying number of targets and their orbital states. In order to achieve efficient tracking of the new space objects, a novel birth model using the Boundary Value Problem (BVP) approach is proposed. The proposed BVP birth model is implemented in the Labelled Multi-Bernoulli (LMB) filter, which is an efficient multi-target tracker developed based on the Random Finite Set (RFS) theory, for improved computational efficiency of new space object tracking. Simulation results indicate that the computational efficiency of the proposed method significantly outperforms the state-of-the-art methods. Finally, as limited sensors are available for SOC maintenance, an appropriate sensor tasking scheme is essential for the optimisation of sensor resources. The optimal sensor tasking command allocates multiple sensors to take the best action and produce useful measurements for more accurate orbital state estimation. In this thesis, an analytical form is derived for the Rényi divergence of LMB RFS in which each target state density is a single Gaussian component. The obtained analytical Rényi divergence is formulated as a reward function for multi-sensor tasking, which improves the computational efficiency, especially for large-scale space object tracking. In addition, this thesis further investigates the benefits of using the analytical Rényi  divergence and various space-based and ground-based sensor networks for accurate tracking of objects in geosynchronous Earth orbit

Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced. © 2013 Elsevier Inc. All rights reserved

State space reparametrization for approximating nonlinear models in Bayesian state estimation

Recursive Bayesian state estimation is a powerful methodology which is useful for the integration of data about a process of interest while considering all the sources of uncertainty which are present in the observations and in modeling inaccuracies. However, in its general form it is intractable and approximations need to be made in order to use it in real life applications. The most widely used algorithm to perform recursive state estimation is the Kalman filter, which assumes that the probability distributions that it propagates are Gaussian and that the measurement and dynamical processes are linear. If these assumptions are satisfied, the Kalman filter is optimal. In most applications, however, this proves to be an oversimplification, due to which several techniques have arisen to handle model non-linearity and different types of distributions. In this thesis, a novel method for the estimation of distributions with nonlinear dynamical and measurement models is presented, which uses a reparametrization of the state space of the distributions in order to exploit the linear properties of the Kalman filter. This involves the mapping of the distribution into a different space, and a subsequent approximation as a Gaussian distribution. An analysis of the adequacy of this transformation is presented, which shows that it is a valid approach in a number of practically interesting filtering problems. The proposed approach is applied to the estimation of the state of Earth-orbiting objects, as it is a challenging estimation scenario which can benefit from the use of filter. Space situational awareness is increasingly important as near-Earth space becomes cluttered with satellites and debris. In this work, the sensors that are most commonly used to track objects in orbit, radars and telescopes, are modeled and a filter based on the previously discussed ideas is proposed. Finally, a multi-object estimation filter based on a recent estimation framework is presented which propagates high amounts of information while maintaining low computational complexity. This is important as there are many challenges to tracking large amounts of orbiting objects in a principled way using ground-based sensors, and naturally extends the single object filter described above to the multi-sensor, multi-object case

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

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