State Estimation for Nonlinear Continuous-Discrete Stochastic Systems: Numerical Aspects and Implementation Issues
Kulikov, Gennady Yu, Kulikova, Maria V.
- 出版商: Springer
- 出版日期: 2024-09-07
- 售價: $7,130
- 貴賓價: 9.5 折 $6,774
- 語言: 英文
- 頁數: 780
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031613708
- ISBN-13: 9783031613708
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商品描述
This book addresses the problem of accurate state estimation in nonlinear continuous-time stochastic models with additive noise and discrete measurements. Its main focus is on numerical aspects of computation of the expectation and covariance in Kalman-like filters rather than on statistical properties determining a model of the system state. Nevertheless, it provides the sound theoretical background and covers all contemporary state estimation techniques beginning at the celebrated Kalman filter, including its versions extended to nonlinear stochastic models, and till the most advanced universal Gaussian filters with deterministically sampled mean and covariance. In particular, the authors demonstrate that, when applying such filtering procedures to stochastic models with strong nonlinearities, the use of adaptive ordinary differential equation solvers with automatic local and global error control facilities allows the discretization error--and consequently the state estimation error--to be reduced considerably. For achieving that, the variable-stepsize methods with automatic error regulation and stepsize selection mechanisms are applied to treating moment differential equations arisen. The implemented discretization error reduction makes the self-adaptive nonlinear Gaussian filtering algorithms more suitable for application and leads to the novel notion of accurate state estimation.
The book also discusses accurate state estimation in mathematical models with sparse measurements. Of special interest in this regard, it provides a means for treating stiff stochastic systems, which often encountered in applied science and engineering, being exemplified by the Van der Pol oscillator in electrical engineering and the Oregonator model of chemical kinetics. Square-root implementations of all Kalman-like filters considered and explored in this book for state estimation in Ill-conditioned continuous-discrete stochastic systems attract the authors' particular attention.
This book covers both theoretical and applied aspects of numerical integration methods, including the concepts of approximation, convergence, stiffness as well as of local and global errors, suitably for applied scientists and engineers. Such methods serve as a basis for the development of accurate continuous-discrete extended, unscented, cubature and many other Kalman filtering algorithms, including the universal Gaussian methods with deterministically sampled expectation and covariance as well as their mixed-type versions. The state estimation procedures in this book are presented in the fashion of complete pseudo-codes, which are ready for implementation and use in MATLAB(R) or in any other computation platform. These are examined numerically and shown to outperform traditional variants of the Kalman-like filters in practical prediction/filtering tasks, including state estimations of stiff and/or ill-conditioned continuous-discrete nonlinear stochastic systems.
商品描述(中文翻譯)
本書探討在具有加性噪聲和離散測量的非線性連續時間隨機模型中進行準確狀態估計的問題。其主要重點在於計算期望值和協方差的數值方面，特別是在類似卡爾曼濾波器的過程中，而非在於決定系統狀態模型的統計特性。儘管如此，本書提供了堅實的理論基礎，並涵蓋了所有當代狀態估計技術，從著名的卡爾曼濾波器開始，包括其擴展到非線性隨機模型的版本，直到最先進的通用高斯濾波器，這些濾波器具有確定性取樣的均值和協方差。特別是，作者展示了在將此類濾波程序應用於具有強非線性的隨機模型時，使用具有自動局部和全局誤差控制功能的自適應常微分方程求解器，可以顯著減少離散化誤差，從而減少狀態估計誤差。為了實現這一點，應用具有自動誤差調節和步長選擇機制的變步長方法來處理所產生的矩量微分方程。實施的離散化誤差減少使得自適應非線性高斯濾波算法更適合應用，並引入了準確狀態估計的新概念。
本書還討論了在具有稀疏測量的數學模型中進行準確狀態估計的問題。在這方面，特別關注的是提供了一種處理剛性隨機系統的方法，這在應用科學和工程中經常遇到，以電氣工程中的范德波爾振盪器和化學動力學中的俄勒岡模型為例。本書中考慮和探討的所有卡爾曼類濾波器的平方根實現，特別吸引了作者的注意，這些濾波器用於在條件不良的連續-離散隨機系統中進行狀態估計。
本書涵蓋了數值積分方法的理論和應用方面，包括近似、收斂、剛性以及局部和全局誤差的概念，適合應用科學家和工程師使用。這些方法作為準確的連續-離散擴展、無味、立方和許多其他卡爾曼濾波算法的開發基礎，包括具有確定性取樣的期望和協方差的通用高斯方法及其混合型版本。本書中的狀態估計程序以完整的偽代碼形式呈現，這些代碼可直接在MATLAB(R)或任何其他計算平台上實現和使用。這些程序經過數值檢驗，顯示在實際預測/濾波任務中超越了傳統的卡爾曼類濾波器變體，包括剛性和/或條件不良的連續-離散非線性隨機系統的狀態估計。
作者簡介
Gennady Yu. Kulikov graduated in Mathematics from the Faculty of Mechanics and Mathematics of the Moscow State University in 1988 (Diploma Cum Laude), and earned his Ph.D. (Russian degree "Candidate of Sciences in Physics and Mathematics") in computational mathematics from the Computer Engineering Center at the Russian Academy of Sciences in 1994. He obtained his Habilitation (Russian degree "Doctor of Sciences in Physics and Mathematics") in 2002. G. Yu. Kulikov worked at the Faculty of Mechanics and Mathematics of the Ulyanovsk State University in Russia from 1993 till his relocation to South Africa in 2004, where he became a senior lecturer and, then, a reader at the University of the Witwatersrand. In 2009, he immigrated to Portugal and became a full-time researcher at Centro de Matemática Computacional e Estocástica (CEMAT), Instituto Superior Técnico, Universidade de Lisboa.
Kulikov's research interests are twofold. First, these focus on numerical methods for differential equations with special emphasis to global error estimation and control strategies. Second, his research topics include applications of such methods with global error control in fluid mechanics, nonlinear Kalman filtering and mathematical neuroscience. He has published widely in quality peer-reviewed journals (about 150 articles in journals, book chapters, and conference proceedings) and gained 16 research grants. In addition, G. Yu. Kulikov has served as a referee for various national and international peer reviewed publications and as a reviewer for the Mathematical Reviews of the American Mathematical Society (AMS). Over the years, he taught several undergraduate and graduate courses in computational mathematics, numerical methods for differential equations, computational linear algebra, prepared a number of M.Sc. and Ph.D. students, and supervised postdoctoral research projects in the area of his expertise. In recent years, G. Yu. Kulikov has been recognized as a TOP 2% cited researcher in the world according to Scopus' data.
Maria V. Kulikova graduated from the Faculty of Mechanics and Mathematics of the Ulyanovsk State University in 2001, and earned her Ph.D. (degree "Candidate of Sciences in Physics and Mathematics") in applied mathematics in 2006. She worked (2007-2009) as a post-doctoral fellow at the University of the Witwatersrand, South Africa till her relocation to Portugal in 2009, where she held a six-year full-time researcher position (2010-2015) granted by the Portuguese Research Fund (FCT). Since 2016 she has been an integrated research member at Centro de Matemática Computacional e Estocástica (CEMAT), Instituto Superior Técnico, Universidade de Lisboa, Portugal. In 2022, M. V. Kulikova became a full-time researcher at the mentioned institution.
Her main research interests include Kalman filtering and nonlinear Bayesian filtering methods, numerical stability and robust estimation with applications in target tracking, econometrics and mathematical neuroscience. She has published widely in national and international peer-reviewed journals and has received individual research grants from the University of the Witwatersrand (South Africa), CEMAT (Portugal) as well as from the FCT (Portugal). She has served as a referee for various international peer reviewed journals and as a reviewer for the Mathematical Reviews of the American Mathematical Society (AMS). In addition, M. V. Kulikova has an experience to be a part of evaluation panels of the higher degrees committees and she is a research associate of the "African Collaboration for Quantitative Finance & Risk Research" (ACQuFRR). Dr. Kulikova has contributed to teaching undergraduate and graduate courses in computational mathematics and numerical methods in finance. She has also supervised a number of M.Sc. students in the area of her expertise. In recent years, M. V. Kulikova has been recognized as a TOP 2% cited researcher in the world according to Scopus' data.
作者簡介(中文翻譯)
Gennady Yu. Kulikov於1988年畢業於莫斯科國立大學機械與數學系，獲得數學學位（優等畢業），並於1994年在俄羅斯科學院計算機工程中心獲得計算數學的博士學位（俄羅斯學位「物理與數學科學候選人」）。他於2002年獲得Habilitation（俄羅斯學位「物理與數學科學博士」）。G. Yu. Kulikov自1993年起在俄羅斯烏里揚諾夫斯克國立大學機械與數學系工作，直到2004年移居南非，並在威特沃特斯蘭大學擔任高級講師，隨後成為讀者。2009年，他移民到葡萄牙，成為里斯本大學高等技術學院計算數學與隨機數學中心（CEMAT）的全職研究員。
Kulikov的研究興趣主要有兩個方面。首先，他專注於微分方程的數值方法，特別強調全局誤差估計和控制策略。其次，他的研究主題包括這些方法在流體力學、非線性卡爾曼濾波和數學神經科學中的應用。他在高品質的同行評審期刊上發表了大量文章（約150篇期刊文章、書籍章節和會議論文），並獲得了16項研究資助。此外，G. Yu. Kulikov還擔任各種國內外同行評審出版物的審稿人，以及美國數學學會（AMS）數學評論的審查員。多年來，他教授了多門本科和研究生課程，包括計算數學、微分方程的數值方法、計算線性代數，並指導了多名碩士和博士生，還監督了他專業領域的博士後研究項目。近年來，根據Scopus的數據，G. Yu. Kulikov被認定為全球前2%被引用的研究人員。
Maria V. Kulikova於2001年畢業於烏里揚諾夫斯克國立大學機械與數學系，並於2006年獲得應用數學的博士學位（學位「物理與數學科學候選人」）。她於2007年至2009年在南非威特沃特斯蘭大學擔任博士後研究員，直到2009年移居葡萄牙，並在2010年至2015年期間獲得葡萄牙研究基金（FCT）授予的六年全職研究員職位。自2016年以來，她一直是里斯本大學高等技術學院計算數學與隨機數學中心（CEMAT）的整合研究成員。2022年，M. V. Kulikova成為該機構的全職研究員。
她的主要研究興趣包括卡爾曼濾波和非線性貝葉斯濾波方法、數值穩定性和穩健估計，並應用於目標追蹤、計量經濟學和數學神經科學。她在國內外同行評審期刊上發表了大量文章，並獲得了來自南非威特沃特斯蘭大學、CEMAT（葡萄牙）以及FCT（葡萄牙）的個人研究資助。她擔任過各種國際同行評審期刊的審稿人，以及美國數學學會（AMS）數學評論的審查員。此外，M. V. Kulikova還參與了高等學位委員會的評估小組，並且是「非洲定量金融與風險研究合作」（ACQuFRR）的研究助理。Kulikova博士對本科和研究生的計算數學和金融數值方法課程的教學做出了貢獻，並指導了多名碩士生。近年來，M. V. Kulikova被認定為前2%被引用的研究人員。
