Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering
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Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering
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Author : Marcelo G. S. Bruno
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2013-01-01
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering written by Marcelo G. S. Bruno and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Technology & Engineering categories.
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering
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Author : Marcelo G. S. Bruno
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Sequential Monte Carlo Methods For Nonlinear Discrete Time Filtering written by Marcelo G. S. Bruno and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary
Sequential Monte Carlo Methods In Practice
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Author : Arnaud Doucet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Sequential Monte Carlo Methods In Practice written by Arnaud Doucet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Monte Carlo methods are revolutionising the on-line analysis of data in fields as diverse as financial modelling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survial of the fittest, have made it possible to solve numerically many complex, non-standarard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modelling, neural networks,optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practicioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris- XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning.
An Introduction To Sequential Monte Carlo
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Author : Nicolas Chopin
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
An Introduction To Sequential Monte Carlo written by Nicolas Chopin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.
This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book. Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed. The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a “Python corner,” which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.
Nonlinear Time Series
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Author : Randal Douc
language : en
Publisher: CRC Press
Release Date : 2014-01-06
Nonlinear Time Series written by Randal Douc and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-06 with Mathematics categories.
Designed for researchers and students, Nonlinear Times Series: Theory, Methods and Applications with R Examples familiarizes readers with the principles behind nonlinear time series models—without overwhelming them with difficult mathematical developments. By focusing on basic principles and theory, the authors give readers the background required to craft their own stochastic models, numerical methods, and software. They will also be able to assess the advantages and disadvantages of different approaches, and thus be able to choose the right methods for their purposes. The first part can be seen as a crash course on "classical" time series, with a special emphasis on linear state space models and detailed coverage of random coefficient autoregressions, both ARCH and GARCH models. The second part introduces Markov chains, discussing stability, the existence of a stationary distribution, ergodicity, limit theorems, and statistical inference. The book concludes with a self-contained account on nonlinear state space and sequential Monte Carlo methods. An elementary introduction to nonlinear state space modeling and sequential Monte Carlo, this section touches on current topics, from the theory of statistical inference to advanced computational methods. The book can be used as a support to an advanced course on these methods, or an introduction to this field before studying more specialized texts. Several chapters highlight recent developments such as explicit rate of convergence of Markov chains and sequential Monte Carlo techniques. And while the chapters are organized in a logical progression, the three parts can be studied independently. Statistics is not a spectator sport, so the book contains more than 200 exercises to challenge readers. These problems strengthen intellectual muscles strained by the introduction of new theory and go on to extend the theory in significant ways. The book helps readers hone their skills in nonlinear time series analysis and their applications.
Bayesian Signal Processing
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Author : James V. Candy
language : en
Publisher: John Wiley & Sons
Release Date : 2016-07-12
Bayesian Signal Processing written by James V. Candy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-12 with Technology & Engineering categories.
Presents the Bayesian approach to statistical signal processing for a variety of useful model sets This book aims to give readers a unified Bayesian treatment starting from the basics (Baye’s rule) to the more advanced (Monte Carlo sampling), evolving to the next-generation model-based techniques (sequential Monte Carlo sampling). This next edition incorporates a new chapter on “Sequential Bayesian Detection,” a new section on “Ensemble Kalman Filters” as well as an expansion of Case Studies that detail Bayesian solutions for a variety of applications. These studies illustrate Bayesian approaches to real-world problems incorporating detailed particle filter designs, adaptive particle filters and sequential Bayesian detectors. In addition to these major developments a variety of sections are expanded to “fill-in-the gaps” of the first edition. Here metrics for particle filter (PF) designs with emphasis on classical “sanity testing” lead to ensemble techniques as a basic requirement for performance analysis. The expansion of information theory metrics and their application to PF designs is fully developed and applied. These expansions of the book have been updated to provide a more cohesive discussion of Bayesian processing with examples and applications enabling the comprehension of alternative approaches to solving estimation/detection problems. The second edition of Bayesian Signal Processing features: “Classical” Kalman filtering for linear, linearized, and nonlinear systems; “modern” unscented and ensemble Kalman filters: and the “next-generation” Bayesian particle filters Sequential Bayesian detection techniques incorporating model-based schemes for a variety of real-world problems Practical Bayesian processor designs including comprehensive methods of performance analysis ranging from simple sanity testing and ensemble techniques to sophisticated information metrics New case studies on adaptive particle filtering and sequential Bayesian detection are covered detailing more Bayesian approaches to applied problem solving MATLAB® notes at the end of each chapter help readers solve complex problems using readily available software commands and point out other software packages available Problem sets included to test readers’ knowledge and help them put their new skills into practice Bayesian Signal Processing, Second Edition is written for all students, scientists, and engineers who investigate and apply signal processing to their everyday problems.
Nonlinear Approaches In Engineering Applications
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Author : Reza N. Jazar
language : en
Publisher: Springer
Release Date : 2016-05-27
Nonlinear Approaches In Engineering Applications written by Reza N. Jazar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-27 with Technology & Engineering categories.
This book looks at the broad field of engineering science through the lens of nonlinear approaches. Examples focus on issues in vehicle technology, including vehicle dynamics, vehicle-road interaction, steering, and control for electric and hybrid vehicles. Also included are discussions on train and tram systems, aerial vehicles, robot-human interaction, and contact and scratch analysis at the micro/nanoscale. Chapters are based on invited contributions from world-class experts in the field who advance the future of engineering by discussing the development of more optimal, accurate, efficient, and cost and energy effective systems. This book is appropriate for researchers, students, and practicing engineers who are interested in the applications of nonlinear approaches to solving engineering and science problems.
Predictive Maintenance In Dynamic Systems
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Author : Edwin Lughofer
language : en
Publisher: Springer
Release Date : 2019-02-28
Predictive Maintenance In Dynamic Systems written by Edwin Lughofer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-28 with Technology & Engineering categories.
This book provides a complete picture of several decision support tools for predictive maintenance. These include embedding early anomaly/fault detection, diagnosis and reasoning, remaining useful life prediction (fault prognostics), quality prediction and self-reaction, as well as optimization, control and self-healing techniques. It shows recent applications of these techniques within various types of industrial (production/utilities/equipment/plants/smart devices, etc.) systems addressing several challenges in Industry 4.0 and different tasks dealing with Big Data Streams, Internet of Things, specific infrastructures and tools, high system dynamics and non-stationary environments . Applications discussed include production and manufacturing systems, renewable energy production and management, maritime systems, power plants and turbines, conditioning systems, compressor valves, induction motors, flight simulators, railway infrastructures, mobile robots, cyber security and Internet ofThings. The contributors go beyond state of the art by placing a specific focus on dynamic systems, where it is of utmost importance to update system and maintenance models on the fly to maintain their predictive power.
Intelligent Robotics And Applications
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Author : Zhiyong Chen
language : en
Publisher: Springer
Release Date : 2018-08-02
Intelligent Robotics And Applications written by Zhiyong Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Computers categories.
The two volume set LNAI 10984 and LNAI 10985 constitutes the refereed proceedings of the 11th International Conference on Intelligent Robotics and Applications, ICIRA 2018, held in Newcastle, NSW, Australia, in August 2018. The 81 papers presented in the two volumes were carefully reviewed and selected from 129 submissions. The papers in the first volume of the set are organized in topical sections on multi-agent systems and distributed control; human-machine interaction; rehabilitation robotics; sensors and actuators; and industrial robot and robot manufacturing. The papers in the second volume of the set are organized in topical sections on robot grasping and control; mobile robotics and path planning; robotic vision, recognition and reconstruction; and robot intelligence and learning.
Readings In Unobserved Components Models
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Author : Andrew Harvey
language : en
Publisher: OUP Oxford
Release Date : 2005-04-07
Readings In Unobserved Components Models written by Andrew Harvey and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-07 with Business & Economics categories.
This volume presents a collection of readings which give the reader an idea of the nature and scope of unobserved components (UC) models and the methods used to deal with them. The book is intended to give a self-contained presentation of the methods and applicative issues. Harvey has made major contributions to this field and provides substantial introductions throughout the book to form a unified view of the literature. - ;This book presents a collection of readings which give the reader an idea of the nature and scope of unobserved components (UC) models and the methods used to deal with them. It contains four parts, three of which concern recent theoretical developments in classical and Bayesian estimation of linear, nonlinear, and non Gaussian UC models, signal extraction and testing, and one is devoted to selected econometric applications. The first part focuses on the linear state space model; the readings provide insight on prediction theory, signal extraction, and likelihood inference for non stationary and non invertible processes, diagnostic checking, and the use of state space methods for spline smoothing. Part II deals with applications of linear UC models to various estimation problems concerning economic time series, such as trend-cycle decompositions, seasonal adjustment, and the modelling of the serial correlation induced by survey sample design. The issues involved in testing in linear UC models are the theme of part III, which considers tests concerned with whether or not certain variance parameters are zero, with special reference to stationarity tests. Finally, part IV is devoted to the advances concerning classical and Bayesian inference for non linear and non Gaussian state space models, an area that has been evolving very rapidly during the last decade, paralleling the advances in computational inference using stochastic simulation techniques. The book is intended to give a relatively self-contained presentation of the methods and applicative issues. For this purpose, each part comes with an introductory chapter by the editors that provides a unified view of the literature and the many important developments that have occurred in the last years. -