This book discusses state estimation of stochastic dynamic systems from noisy measurements, specifically sequential Bayesian estimation and nonlinear or stochastic filtering. The class of solutions presented in this book is based on the Monte Carlo statistical method. Although the resulting algorithms, known as particle filters, have been around for more than a decade, the recent theoretical developments of sequential Bayesian estimation in the framework of random set theory have provided new opportunities which are not widely known and are covered in this book. This book is ideal for graduate students, researchers, scientists and engineers interested in Bayesian estimation.
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.
For most tracking applications the Kalman filter is reliable and efficient, but it is limited to a relatively restricted class of linear Gaussian problems. To solve problems beyond this restricted class, particle filters are proving to be dependable methods for stochastic dynamic estimation. Packed with 867 equations, this cutting-edge book introduces the latest advances in particle filter theory, discusses their relevance to defense surveillance systems, and examines defense-related applications of particle filters to nonlinear and non-Gaussian problems. With this hands-on guide, you can develop more accurate and reliable nonlinear filter designs and more precisely predict the performance of these designs. You can also apply particle filters to tracking a ballistic object, detection and tracking of stealthy targets, tracking through the blind Doppler zone, bi-static radar tracking, passive ranging (bearings-only tracking) of maneuvering targets, range-only tracking, terrain-aided tracking of ground vehicles, and group and extended object tracking.
What is Particle Filter Particle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the posterior distributions of the states of a Markov process, given the noisy and partial observations. The term "particle filters" was first coined in 1996 by Pierre Del Moral about mean-field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The term "Sequential Monte Carlo" was coined by Jun S. Liu and Rong Chen in 1998. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Particle filter Chapter 2: Importance sampling Chapter 3: Point process Chapter 4: Fokker-Planck equation Chapter 5: Wiener's lemma Chapter 6: Klein-Kramers equation Chapter 7: Mean-field particle methods Chapter 8: Dirichlet kernel Chapter 9: Generalized Pareto distribution Chapter 10: Superprocess (II) Answering the public top questions about particle filter. (III) Real world examples for the usage of particle filter in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Particle Filter.
This book provides a quick but insightful introduction to Bayesian tracking and particle filtering for a person who has some background in probability and statistics and wishes to learn the basics of single-target tracking. It also introduces the reader to multiple target tracking by presenting useful approximate methods that are easy to implement compared to full-blown multiple target trackers. The book presents the basic concepts of Bayesian inference and demonstrates the power of the Bayesian method through numerous applications of particle filters to tracking and smoothing problems. It emphasizes target motion models that incorporate knowledge about the target’s behavior in a natural fashion rather than assumptions made for mathematical convenience. The background provided by this book allows a person to quickly become a productive member of a project team using Bayesian filtering and to develop new methods and techniques for problems the team may face.
A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: * Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation * Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice * MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering. Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries.
Until recently, the complexity of the Diesel Particulate Filter (DPF) system has hindered its commercial success. Stringent regulations of diesel emissions has lead to advancements in this technology, therefore mainstreaming the use of DPFs in light- and heavy-duty diesel filtration applications. This book covers the latest and most important research in DPF systems, focusing mainly on the advancements of the years 2002-2006. Editor Timothy V. Johnson selected the top 29 SAE papers covering the most significant research in this technology.
Image processing-from basics to advanced applications Learn how to master image processing and compression with this outstanding state-of-the-art reference. From fundamentals to sophisticated applications, Image Processing: Principles and Applications covers multiple topics and provides a fresh perspective on future directions and innovations in the field, including: * Image transformation techniques, including wavelet transformation and developments * Image enhancement and restoration, including noise modeling and filtering * Segmentation schemes, and classification and recognition of objects * Texture and shape analysis techniques * Fuzzy set theoretical approaches in image processing, neural networks, etc. * Content-based image retrieval and image mining * Biomedical image analysis and interpretation, including biometric algorithms such as face recognition and signature verification * Remotely sensed images and their applications * Principles and applications of dynamic scene analysis and moving object detection and tracking * Fundamentals of image compression, including the JPEG standard and the new JPEG2000 standard Additional features include problems and solutions with each chapter to help you apply the theory and techniques, as well as bibliographies for researching specialized topics. With its extensive use of examples and illustrative figures, this is a superior title for students and practitioners in computer science, wireless and multimedia communications, and engineering.
Specially selected from The New Palgrave Dictionary of Economics 2nd edition, each article within this compendium covers the fundamental themes within the discipline and is written by a leading practitioner in the field. A handy reference tool.
