Principles of Nonlinear Filtering Theory
暫譯: 非線性濾波理論原則

Yau, Stephen S. -T, Chen, Xiuqiong, Jiao, Xiaopei

Principles of Nonlinear Filtering Theory
  • 出版商: Springer
  • 出版日期: 2025-01-19
  • 售價: $2,960
  • 貴賓價: 9.5 折 $2,812
  • 語言: 英文
  • 頁數: 472
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031776836
  • ISBN-13: 9783031776830

    • 海外代購書籍(需單獨結帳)

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商品描述

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.

商品描述(中文翻譯)

這段文字全面且統一地介紹了非線性濾波理論，強調其數學基礎。內容旨在滿足多元讀者的需求，包括數學背景的工程師和科學家，無論是研究生還是博士後。這本書與其他相關書籍的不同之處有兩個方面。首先，它提供了濾波理論的完整處理，使讀者能夠深入理解該主題。其次，它介紹了在當今環境中至關重要的更新方法和應用，包括有限維濾波器、Yau-Yau 演算法、直接方法，以及深度學習與濾波問題的整合。這本書將成為研究人員和實務工作者多年來的重要資源。

本書的歷史背景可追溯至高斯和維納，內容深入探討了在噪聲觀測下估計隨機過程的基本原則——這是各種應用領域中的關鍵工具，例如飛機導航、太陽映射和軌道確定等。每章中提供的實質性練習和範例使讀者有機會欣賞應用並充分測試他們對所涵蓋主題的理解。對於那些在傳統課程環境之外獨立學習該主題的讀者來說，書末附上的練習解答是一個特別好的功能。

本書分為三個緊密相連的部分，每個部分旨在增進讀者對非線性濾波理論的理解。在第一部分中，介紹了概率論、隨機過程、隨機微分方程和優化的基礎概念，為讀者提供必要的數學背景。第二部分深入探討濾波理論的理論方面，涵蓋了控制狀態後驗密度函數的隨機偏微分方程以及有限維濾波器系統的估計代數理論。接下來，第三部分探討了解決濾波問題的數值演算法，包括 Yau-Yau 演算法、直接方法、經典濾波演算法如粒子濾波器，以及濾波理論與深度學習的交集。

作者簡介

Stephen Shing-Toung Yau (Life Fellow, IEEE) received the Ph.D. degree in mathematics from the State University of New York, Stony Brook, NY, USA, in 1976. He was a Member of the Institute of Advanced Study, Princeton, NJ, USA, from 1976 to 1977 and 1981 to 1982. He was a Benjamin Pierce Assistant Professor with Harvard University, Cambridge, MA, USA, from 1977 to 1980. He then joined the Department of Mathematics, Statistics and Computer Science (MSCS), University of Illinois at Chicago (UIC), Chicago, IL, USA, and served for more than 30 years. From 2005 to 2011, he was a Joint Professor with the Department of Electrical and Computer Engineering, MSCS, UIC. After retiring in 2011, he joined the Department of Mathematical Sciences at Tsinghua University in Beijing, China, where he served for over 10 years. In 2022, he became a research fellow at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) in Beijing, China, to begin his new research. His research interests include nonlinear filtering, bioinformatics, complex algebraic geometry, Cauchy-Riemann geometry, and singularities theory. Dr. Yau has been the Managing Editor and Founder of Journal of Algebraic Geometry since 1991 and the Editor-in-Chief and Founder of Communications in Information and Systems since 2000. He was the General Chairman of the 1995 IEEE International Conference on Control and Information. He received the Sloan Fellowship in 1980, the Guggenheim Fellowship in 2000, and the American Mathematical Society Fellow Award in 2013. In 2005, he was entitled the UIC Distinguished Professor. In 2019, He won the Chern Prize of Lifetime Achievement in Mathematics.

Xiuqiong Chen received the B.S. degree in the School of Mathematical Sciences, Beihang University, Beijing, China, in 2014, and the Ph.D. degree in applied mathematics from the Department of Mathematical Sciences, Tsinghua University, Beijing, China in 2019. After her graduation, she was a Postdoctoral Scholar with Yau Mathematical Sciences Center, Tsinghua University, Beijing, China, from 2019 to 2021. She joined in Renmin University of China, Beijing, China, since 2021. She is currently an Assistant Professor with School of Mathematics, Renmin University of China. Her research interests include nonlinear filtering and deep learning.

Xiaopei Jiao received his Bachelor's degree from Shanghai Jiao Tong University in 2017 and completed his Ph.D. from the Department of Mathematics at Tsinghua University in 2022. From 2022 to 2024, he worked as a postdoctoral researcher at the Beijing Institute of Mathematical Science and Application. He is currently employed at the University of Twente in the Netherlands as postdoctoral researcher. His research focuses on nonlinear filtering, Lie estimation algebra, physics-informed deep learning, and bioinformatics.

Jiayi Kang received the B.S. degree from the college of mathematics, Sichuan University, Chengdu, China, in 2019 and Ph.D. degree from Department of Mathematical Sciences at Tsinghua University, China in 2024. He is currently an assistant professor at the Beijing Institute of Mathematical Sciences and Applications in Beijing, China.

Zeju Sun received the B.S. degree from Department of Mathematical Sciences, Tsinghua University, Beijing, China, in 2020. He is currently pursuing the Ph.D. degree in mathematics with the department of Mathematical Sciences, Tsinghua University, Beijing, China.

Yangtianze Tao received the B.S degree in College of Mathematics, Sichuan University, Sichuan, China in 2019. Now he is pursuing Ph.D. degree with Department of Mathematical Sciences, Tsinghua University, Beijing, China, under the supervision of Prof. Stephen Yau in the field of applied mathematics. His research interests include deep learning, machine learning and nonlinear filtering.

作者簡介(中文翻譯)

邱興棠 (Stephen Shing-Toung Yau, 生命會士, IEEE) 於1976年在美國紐約州立大學石溪校區獲得數學博士學位。他曾於1976年至1977年及1981年至1982年擔任普林斯頓高等研究院的成員。1977年至1980年，他擔任哈佛大學的本傑明·皮爾斯助理教授。隨後，他加入伊利諾伊大學芝加哥分校的數學、統計與計算機科學系（MSCS），並服務超過30年。2005年至2011年，他擔任電氣與計算機工程系的聯合教授。2011年退休後，他加入中國北京的清華大學數學科學系，並在此服務超過10年。2022年，他成為北京數學科學與應用研究所（BIMSA）的研究員，開始新的研究。他的研究興趣包括非線性過濾、生物資訊學、複雜代數幾何、柯西-黎曼幾何及奇異性理論。自1991年以來，邱博士一直擔任《代數幾何期刊》的主編及創辦人，自2000年以來擔任《信息與系統通訊》的主編及創辦人。他曾擔任1995年IEEE國際控制與信息會議的總主席。他於1980年獲得斯隆獎學金，2000年獲得古根海姆獎學金，2013年獲得美國數學學會會士獎。2005年，他被授予UIC傑出教授稱號。2019年，他獲得陳省身數學終身成就獎。

陳秀琼 (Xiuqiong Chen) 於2014年在中國北京的北京航空航天大學數學科學學院獲得學士學位，並於2019年在清華大學數學科學系獲得應用數學博士學位。畢業後，她於2019年至2021年在清華大學邱數學科學中心擔任博士後研究員。自2021年起，她加入中國人民大學，現為該校數學學院的助理教授。她的研究興趣包括非線性過濾和深度學習。

焦小培 (Xiaopei Jiao) 於2017年從上海交通大學獲得學士學位，並於2022年在清華大學數學系完成博士學位。2022年至2024年，他在北京數學科學與應用研究所擔任博士後研究員。目前，他在荷蘭特溫特大學擔任博士後研究員。他的研究專注於非線性過濾、李估計代數、物理知識深度學習及生物資訊學。

康佳怡 (Jiayi Kang) 於2019年在中國成都的四川大學數學學院獲得學士學位，並於2024年在清華大學數學科學系獲得博士學位。目前，他是北京數學科學與應用研究所的助理教授。

孫澤駿 (Zeju Sun) 於2020年在清華大學數學科學系獲得學士學位。目前，他正在清華大學數學科學系攻讀數學博士學位。

陶揚天澤 (Yangtianze Tao) 於2019年在四川大學數學學院獲得學士學位。現在，他在清華大學數學科學系攻讀博士學位，並在邱教授的指導下專注於應用數學領域。他的研究興趣包括深度學習、機器學習和非線性過濾。

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