Parallelized Particle and Gaussian Sum Particle Filters for Large Scale Freeway Traffic Systems

Large scale traffic systems require techniques able to: 1) deal with high amounts of data and heterogenous data coming from different types of sensors, 2) provide robustness in the presence of sparse sensor data, 3) incorporate different models that can deal with various traffic regimes, 4) cope with multimodal conditional probability density functions for the states. Often centralized architectures face challenges due to high communication demands. This paper develops new estimation techniques able to cope with these problems of large traffic network systems. These are Parallelized Particle Filters (PPFs) and a Parallelized Gaussian Sum Particle Filter (PGSPF) that are suitable for on-line traffic management. We show how complex probability density functions of the high dimensional trafc state can be decomposed into functions with simpler forms and the whole estimation problem solved in an efcient way. The proposed approach is general, with limited interactions which reduces the computational time and provides high estimation accuracy. The efciency of the PPFs and PGSPFs is evaluated in terms of accuracy, complexity and communication demands and compared with the case where all processing is centralized

Optimal state estimation and control of space systems under severe uncertainty

This thesis presents novel methods and algorithms for state estimation and optimal control under generalised models of uncertainty. Tracking, scheduling, conjunction assessment, as well as trajectory design and analysis, are typically carried out either considering the nominal scenario only or under assumptions and approximations of the underlying uncertainty to keep the computation tractable. However, neglecting uncertainty or not quantifying it properly may result in lengthy design iterations, mission failures, inaccurate estimation of the satellite state, and poorly assessed risk metrics. To overcome these challenges, this thesis proposes approaches to incorporate proper uncertainty treatment in state estimation, navigation and tracking, and trajectory design. First, epistemic uncertainty is introduced as a generalised model to describe partial probabilistic models, ignorance, scarce or conflicting information, and, overall, a larger umbrella of uncertainty structures. Then, new formulations for state estimation, optimal control, and scheduling under mixed aleatory and epistemic uncertainties are proposed to generalise and robustify their current deterministic or purely aleatory counterparts. Practical solution approaches are developed to numerically solve such problems efficiently. Specifically, a polynomial reinitialisation approach for efficient uncertainty propagation is developed to mitigate the stochastic dimensionality in multi-segment problems. For state estimation and navigation, two robust filtering approaches are presented: a generalisation of the particle filtering to epistemic uncertainty exploiting samples’ precomputations; a sequential filtering approach employing a combination of variational inference and importance sampling. For optimal control under uncertainty, direct shooting-like transcriptions with a tunable high-fidelity polynomial representation of the dynamical flow are developed. Uncertainty quantification, orbit determination, and navigation analysis are incorporated in the main optimisation loop to design trajectories that are simultaneously optimal and robust. The methods developed in this thesis are finally applied to a variety of novel test cases, ranging from LEO to deep-space missions, from trajectory design to space traffic management. The epistemic state estimation is employed in the robust estimation of debris’ conjunction analyses and incorporated in a robust Bayesian framework capable of autonomous decision-making. An optimisation-based scheduling method is presented to efficiently allocate resources to heterogeneous ground stations and fusing information coming from different sensors, and it is applied to the optimal tracking of a satellite in highly perturbed very-low Earth orbit, and a low-resource deep-space spacecraft. The optimal control methods are applied to the robust optimisation of an interplanetary low-thrust trajectory to Apophis, and to the robust redesign of a leg of the Europa Clipper tour with an initial infeasibility on the probability of impact with Jupiter’s moon.This thesis presents novel methods and algorithms for state estimation and optimal control under generalised models of uncertainty. Tracking, scheduling, conjunction assessment, as well as trajectory design and analysis, are typically carried out either considering the nominal scenario only or under assumptions and approximations of the underlying uncertainty to keep the computation tractable. However, neglecting uncertainty or not quantifying it properly may result in lengthy design iterations, mission failures, inaccurate estimation of the satellite state, and poorly assessed risk metrics. To overcome these challenges, this thesis proposes approaches to incorporate proper uncertainty treatment in state estimation, navigation and tracking, and trajectory design. First, epistemic uncertainty is introduced as a generalised model to describe partial probabilistic models, ignorance, scarce or conflicting information, and, overall, a larger umbrella of uncertainty structures. Then, new formulations for state estimation, optimal control, and scheduling under mixed aleatory and epistemic uncertainties are proposed to generalise and robustify their current deterministic or purely aleatory counterparts. Practical solution approaches are developed to numerically solve such problems efficiently. Specifically, a polynomial reinitialisation approach for efficient uncertainty propagation is developed to mitigate the stochastic dimensionality in multi-segment problems. For state estimation and navigation, two robust filtering approaches are presented: a generalisation of the particle filtering to epistemic uncertainty exploiting samples’ precomputations; a sequential filtering approach employing a combination of variational inference and importance sampling. For optimal control under uncertainty, direct shooting-like transcriptions with a tunable high-fidelity polynomial representation of the dynamical flow are developed. Uncertainty quantification, orbit determination, and navigation analysis are incorporated in the main optimisation loop to design trajectories that are simultaneously optimal and robust. The methods developed in this thesis are finally applied to a variety of novel test cases, ranging from LEO to deep-space missions, from trajectory design to space traffic management. The epistemic state estimation is employed in the robust estimation of debris’ conjunction analyses and incorporated in a robust Bayesian framework capable of autonomous decision-making. An optimisation-based scheduling method is presented to efficiently allocate resources to heterogeneous ground stations and fusing information coming from different sensors, and it is applied to the optimal tracking of a satellite in highly perturbed very-low Earth orbit, and a low-resource deep-space spacecraft. The optimal control methods are applied to the robust optimisation of an interplanetary low-thrust trajectory to Apophis, and to the robust redesign of a leg of the Europa Clipper tour with an initial infeasibility on the probability of impact with Jupiter’s moon

On the Bayesian estimation of jump-diffusion models in finance

The jump-diffusion framework introduced by Duffie et al. (2000) encompasses most one factor models used in finance. Due to the model complexity of this framework, the particle filter (e.g., Hurn et al., 2015; Jacobs & Liu, 2018) and combinations of Gibbs and Metropolis-Hastings samplers (e.g., Eraker et al., 2003; Eraker, 2004) have been the tools of choice for its estimation. However, Bégin & Boudreault (2020) recently showed that the discrete nonlinear filter (DNF) of Kitagawa (1987) can also be used for fast and accurate maximum likelihood estimation of jump-diffusion models. In this project report, we combine the DNF with Markov chain Monte Carlo (MCMC) methods for Bayesian estimation in the spirit of the particle MCMC algorithm of Andrieu et al. (2010). In addition, we show that derivative prices (i.e., European option prices) can be easily included into the DNF’s likelihood evaluations, which allows for efficient joint Bayesian estimation

Inference in sensor networks : graphical models and particle methods

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 175-183).Sensor networks have quickly risen in importance over the last several years to become an active field of research, full of difficult problems and applications. At the same time, graphical models have shown themselves to be an extremely useful formalism for describing the underlying statistical structure of problems for sensor networks. In part, this is due to a number of efficient methods for solving inference problems defined on graphical models, but even more important is the fact that many of these methods (such as belief propagation) can be interpreted as a set of message passing operations, for which it is not difficult to describe a simple, distributed architecture in which each sensor performs local processing and fusion of information, and passes messages locally among neighboring sensors. At the same time, many of the tasks which are most important in sensor networks are characterized by such features as complex uncertainty and nonlinear observation processes. Particle filtering is one common technique for dealing with inference under these conditions in certain types of sequential problems, such as tracking of mobile objects.(cont.) However, many sensor network applications do not have the necessary structure to apply particle filtering, and even when they do there are subtleties which arise due to the nature of a distributed inference process performed on a system with limited resources (such as power, bandwidth, and so forth). This thesis explores how the ideas of graphical models and sample-based representations of uncertainty such as are used in particle filtering can be applied to problems defined for sensor networks, in which we must consider the impact of resource limitations on our algorithms. In particular, we explore three related themes. We begin by describing how sample-based representations can be applied to solve inference problems defined on general graphical models. Limited communications, the primary restriction in most practical sensor networks, means that the messages which are passed in the inference process must be approximated in some way. Our second theme explores the consequences of such message approximations, and leads to results with implications both for distributed systems and the use of belief propagation more generally.(cont.) This naturally raises a third theme, investigating the optimal cost of representing sample-based estimates of uncertainty so as to minimize the communications required. Our analysis shows several interesting differences between this problem and traditional source coding methods. We also use the metrics for message errors to define lossy or approximate4 encoders, and provide an example encoder capable of balancing communication costs with a measure on inferential error. Finally, we put all of these three themes to work to solve a difficult and important task in sensor networks. The self-localization problem for sensors networks involves the estimation of all sensor positions given a set of relative inter-sensor measurements in the network. We describe this problem as a graphical model, illustrate the complex uncertainties involved in the estimation process, and present a method of finding for both estimates of the sensor positions and their remaining uncertainty using a sample-based message passing algorithm. This method is capable of incorporating arbitrary noise distributions, including outlier processes, and by applying our lossy encoding algorithm can be used even when communications is relatively limited.(cont.) We conclude the thesis with a summary of the work and its contributions, and a description of some of the many problems which remain open within the field.y Alexander T. Ihler.Ph.D

Digital signal processing algorithms and structures for adaptive line enhancing

Imperial Users onl

ADVANCES IN SYSTEM RELIABILITY-BASED DESIGN AND PROGNOSTICS AND HEALTH MANAGEMENT (PHM) FOR SYSTEM RESILIENCE ANALYSIS AND DESIGN

Failures of engineered systems can lead to significant economic and societal losses. Despite tremendous efforts (e.g., $200 billion annually) denoted to reliability and maintenance, unexpected catastrophic failures still occurs. To minimize the losses, reliability of engineered systems must be ensured throughout their life-cycle amidst uncertain operational condition and manufacturing variability. In most engineered systems, the required system reliability level under adverse events is achieved by adding system redundancies and/or conducting system reliability-based design optimization (RBDO). However, a high level of system redundancy increases a system's life-cycle cost (LCC) and system RBDO cannot ensure the system reliability when unexpected loading/environmental conditions are applied and unexpected system failures are developed. In contrast, a new design paradigm, referred to as resilience-driven system design, can ensure highly reliable system designs under any loading/environmental conditions and system failures while considerably reducing systems' LCC. In order to facilitate the development of formal methodologies for this design paradigm, this research aims at advancing two essential and co-related research areas: Research Thrust 1 - system RBDO and Research Thrust 2 - system prognostics and health management (PHM). In Research Thrust 1, reliability analyses under uncertainty will be carried out in both component and system levels against critical failure mechanisms. In Research Thrust 2, highly accurate and robust PHM systems will be designed for engineered systems with a single or multiple time-scale(s). To demonstrate the effectiveness of the proposed system RBDO and PHM techniques, multiple engineering case studies will be presented and discussed. Following the development of Research Thrusts 1 and 2, Research Thrust 3 - resilience-driven system design will establish a theoretical basis and design framework of engineering resilience in a mathematical and statistical context, where engineering resilience will be formulated in terms of system reliability and restoration and the proposed design framework will be demonstrated with a simplified aircraft control actuator design problem