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Principles of nonlinear filtering theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Principles of nonlinear filtering theoryby Stephen S.-T. Yau ... [et al.].
other author:	Yau, Stephen Shing-Toung.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xvii, 470 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Filters (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-031-77684-7
ISBN:	9783031776847$q(electronic bk.)

Principles of nonlinear filtering theory
Principles of nonlinear filtering theory[electronic resource] /by Stephen S.-T. Yau ... [et al.]. - Cham :Springer Nature Switzerland :2024. - xvii, 470 p. :ill., digital ;24 cm. - Algorithms and computation in mathematics ;v. 33. - Algorithms and computation in mathematics ;v.5..

Preface -- I. Preliminary knowledge -- 1. Probability theory -- 2. Stochastic processes -- 3. Stochastic differential equations -- 4. Optimization -- II. Filtering theory -- 5. The filtering equations -- 6. Estimation algebra -- III. Numerical algorithms -- 7. Yau-Yau algorithm -- 8. Direct methods -- 9. Classical filtering methods -- 10. Estimation algorithms based on deep learning.

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.

ISBN: 9783031776847$q(electronic bk.)

Standard No.: 10.1007/978-3-031-77684-7doiSubjects--Topical Terms:

185110
Filters (Mathematics)

LC Class. No.: QA427

Dewey Class. No.: 515

Principles of nonlinear filtering theory
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245 0 0 $a Principles of nonlinear filtering theory $h [electronic resource] / $c by Stephen S.-T. Yau ... [et al.].
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490 1 $a Algorithms and computation in mathematics ; $v v. 33
505 0 $a Preface -- I. Preliminary knowledge -- 1. Probability theory -- 2. Stochastic processes -- 3. Stochastic differential equations -- 4. Optimization -- II. Filtering theory -- 5. The filtering equations -- 6. Estimation algebra -- III. Numerical algorithms -- 7. Yau-Yau algorithm -- 8. Direct methods -- 9. Classical filtering methods -- 10. Estimation algorithms based on deep learning.
520 $a 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.
650 0 $a Filters (Mathematics) $3 185110
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650 2 4 $a Control and Systems Theory. $3 825946
650 2 4 $a Differential Equations. $3 285983
700 1 $a Yau, Stephen Shing-Toung. $3 965903
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830 0 $a Algorithms and computation in mathematics ; $v v.5. $3 591804
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950 $a Mathematics and Statistics (SpringerNature-11649)