LEADER 05120nam 22007215 450 001 9910917797503321 005 20250526171211.0 010 $a9783031776847 010 $a3031776844 024 7 $a10.1007/978-3-031-77684-7 035 $a(CKB)37037090600041 035 $a(MiAaPQ)EBC31850030 035 $a(Au-PeEL)EBL31850030 035 $a(DE-He213)978-3-031-77684-7 035 $a(EXLCZ)9937037090600041 100 $a20241218d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPrinciples of Nonlinear Filtering Theory /$fby Stephen S.-T. Yau, Xiuqiong Chen, Xiaopei Jiao, Jiayi Kang, Zeju Sun, Yangtianze Tao 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (477 pages) 225 1 $aAlgorithms and Computation in Mathematics,$x2512-3254 ;$v33 311 08$a9783031776830 311 08$a3031776836 327 $aPreface -- 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. 330 $aThis 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. 410 0$aAlgorithms and Computation in Mathematics,$x2512-3254 ;$v33 606 $aStochastic processes 606 $aAutomatic control 606 $aDifferential equations 606 $aEquacions diferencials$2thub 606 $aProcessos estocāstics$2thub 606 $aStochastic Processes 606 $aControl and Systems Theory 606 $aDifferential Equations 608 $aLlibres electrōnics.$2thub 615 0$aStochastic processes. 615 0$aAutomatic control. 615 0$aDifferential equations. 615 7$aEquacions diferencials. 615 7$aProcessos estocāstics 615 14$aStochastic Processes. 615 24$aControl and Systems Theory. 615 24$aDifferential Equations. 676 $a519.23 700 $aYau$b Stephen S. T$01587106 701 $aChen$b Xiuqiong$01780666 701 $aJiao$b Xiaopei$01780667 701 $aKang$b Jiayi$01780668 701 $aSun$b Zeju$01780669 701 $aTao$b Yangtianze$01780670 701 $aYau$b Stephen S. T$01587106 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910917797503321 996 $aPrinciples of Nonlinear Filtering Theory$94304998 997 $aUNINA