Filtering Theory

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Stochastic Filtering Theory

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Author : G. Kallianpur
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Stochastic Filtering Theory written by G. Kallianpur 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 2013-04-17 with Science categories.

This book is based on a seminar given at the University of California at Los Angeles in the Spring of 1975. The choice of topics reflects my interests at the time and the needs of the students taking the course. Initially the lectures were written up for publication in the Lecture Notes series. How ever, when I accepted Professor A. V. Balakrishnan's invitation to publish them in the Springer series on Applications of Mathematics it became necessary to alter the informal and often abridged style of the notes and to rewrite or expand much of the original manuscript so as to make the book as self-contained as possible. Even so, no attempt has been made to write a comprehensive treatise on filtering theory, and the book still follows the original plan of the lectures. While this book was in preparation, the two-volume English translation of the work by R. S. Liptser and A. N. Shiryaev has appeared in this series. The first volume and the present book have the same approach to the sub ject, viz. that of martingale theory. Liptser and Shiryaev go into greater detail in the discussion of statistical applications and also consider inter polation and extrapolation as well as filtering.

Stochastic Processes And Filtering Theory

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Author : Andrew H. Jazwinski
language : en
Publisher: Courier Corporation
Release Date : 2013-04-15

Stochastic Processes And Filtering Theory written by Andrew H. Jazwinski and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Science categories.

This unified treatment presents material previously available only in journals, and in terms accessible to engineering students. Although theory is emphasized, it discusses numerous practical applications as well. 1970 edition.

Bilateral Filtering

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Author : Sylvain Paris
language : en
Publisher: Now Publishers Inc
Release Date : 2009-08-20

Bilateral Filtering written by Sylvain Paris and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-20 with Computers categories.

Bilateral filtering is one of the most popular image processing techniques. The bilateral filter is a nonlinear process that can blur an image while respecting strong edges. Its ability to decompose an image into different scales without causing haloes after modification has made it ubiquitous in computational photography applications such as tone mapping, style transfer, relighting, and denoising. Bilateral Filtering: Theory and Applications provides a graphical, intuitive introduction to bilateral filtering, a practical guide for efficient implementation, an overview of its numerous applications, as well as mathematical analysis. This broad and detailed overview covers theoretical and practical issues that will be useful to researchers and software developers.

Kalman Filtering

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Author : Mohinder S. Grewal
language : en
Publisher: John Wiley & Sons
Release Date : 2015-02-02

Kalman Filtering written by Mohinder S. Grewal 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 2015-02-02 with Technology & Engineering categories.

The definitive textbook and professional reference on Kalman Filtering – fully updated, revised, and expanded This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.

Fundamentals Of Stochastic Filtering

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Author : Alan Bain
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-08

Fundamentals Of Stochastic Filtering written by Alan Bain 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 2008-10-08 with Mathematics categories.

This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient background to enable study of the recent literature. While no prior knowledge of stochastic filtering is required, readers are assumed to be familiar with measure theory, probability theory and the basics of stochastic processes. Most of the technical results that are required are stated and proved in the appendices. Exercises and solutions are included.

Principles Of Nonlinear Filtering Theory

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Author : Stephen S.-T. Yau
language : en
Publisher: Springer Nature
Release Date : 2024-12-17

Principles Of Nonlinear Filtering Theory written by Stephen S.-T. Yau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-17 with Mathematics categories.

This text presents a comprehensive and unified treatment of nonlinear filtering theory, with a strong emphasis on its mathematical underpinnings. It is tailored to meet the needs of a diverse readership, including mathematically inclined engineers and scientists at both graduate and post-graduate levels. What sets this book apart from other treatments of the topic is twofold. Firstly, it offers a complete treatment of filtering theory, providing readers with a thorough understanding of the subject. Secondly, it introduces updated methodologies and applications that are crucial in today’s landscape. These include finite-dimensional filters, the Yau-Yau algorithm, direct methods, and the integration of deep learning with filtering problems. The book will be an invaluable resource for researchers and practitioners for years to come. With a rich historical backdrop dating back to Gauss and Wiener, the exposition delves into the fundamental principles underpinning the estimation of stochastic processes amidst noisy observations—a critical tool in various applied domains such as aircraft navigation, solar mapping, and orbit determination, to name just a few. Substantive exercises and examples given in each chapter provide the reader with opportunities to appreciate applications and ample ways to test their understanding of the topics covered. An especially nice feature for those studying the subject independent of a traditional course setting is the inclusion of solutions to exercises at the end of the book. The book is structured into three cohesive parts, each designed to build the reader's understanding of nonlinear filtering theory. In the first part, foundational concepts from probability theory, stochastic processes, stochastic differential equations, and optimization are introduced, providing readers with the necessary mathematical background. The second part delves into theoretical aspects of filtering theory, covering topics such as the stochastic partial differential equation governing the posterior density function of the state, and the estimation algebra theory of systems with finite-dimensional filters. Moving forward, the third part of the book explores numerical algorithms for solving filtering problems, including the Yau-Yau algorithm, direct methods, classical filtering algorithms like the particle filter, and the intersection of filtering theory with deep learning.

An Introduction To Stochastic Filtering Theory

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Author : Jie Xiong
language : en
Publisher: OUP Oxford
Release Date : 2008-04-17

An Introduction To Stochastic Filtering Theory written by Jie Xiong and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-17 with Mathematics categories.

Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance. As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter; the stability of the filter with "incorrect" initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers; and although still in its infancy, the study of singular filtering models has yielded exciting results. In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering these key recent advances. The text is written in a style suitable for graduates in mathematics and engineering with a background in basic probability.

Stochastic Evolution Systems

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Author : B.L. Rozovskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stochastic Evolution Systems written by B.L. Rozovskii 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 2012-12-06 with Mathematics categories.

Covering the general theory of linear stochastic evolution systems with unbounded drift and diffusion operators, this book sureys Ito's second-order parabolic equations and explores filtering problems for processes whose trajectories can be described by them.

Spectral Analysis And Filter Theory In Applied Geophysics

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Author : Burkhard Buttkus
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Spectral Analysis And Filter Theory In Applied Geophysics written by Burkhard Buttkus 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 2012-12-06 with Science categories.

This book is intended to be an introduction to the fundamentals and methods of spectral analysis and filter theory and their appli cations in geophysics. The principles and theoretical basis of the various methods are described, their efficiency and effectiveness eval uated, and instructions provided for their practical application. Be sides the conventional methods, newer methods arediscussed, such as the spectral analysis ofrandom processes by fitting models to the ob served data, maximum-entropy spectral analysis and maximum-like lihood spectral analysis, the Wiener and Kalman filtering methods, homomorphic deconvolution, and adaptive methods for nonstation ary processes. Multidimensional spectral analysis and filtering, as well as multichannel filters, are given extensive treatment. The book provides a survey of the state-of-the-art of spectral analysis and fil ter theory. The importance and possibilities ofspectral analysis and filter theory in geophysics for data acquisition, processing and eval uation are illustrated with practical examples from various fields of applied geophysics. Although this book was planned primarily as a textbook for a course on the analysis of geophysical time· series, it may also be of interest to scientists and engineers who process other digital data. It provides a comprehensive discussion of the theoretical fundamen tals and a compilation of the extensive literature on the subject. I hope that I have succeeded in presenting the various principles and methods of time-series analysis comprehensively and without error. Comments on errors or suggestions for improvements are welcome.