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020 _a9783031776847
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024 7 _a10.1007/978-3-031-77684-7
_2doi
050 4 _aQA274-274.9
072 7 _aPBT
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072 7 _aPBWL
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072 7 _aMAT029040
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072 7 _aPBT
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072 7 _aPBWL
_2thema
100 1 _aYau, Stephen S.-T.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_989083
245 1 0 _aPrinciples of Nonlinear Filtering Theory
_h[electronic resource] /
_cby Stephen S.-T. Yau, Xiuqiong Chen, Xiaopei Jiao, Jiayi Kang, Zeju Sun, Yangtianze Tao.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVII, 470 p. 28 illus., 25 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAlgorithms and Computation in Mathematics,
_x2512-3254 ;
_v33
505 0 _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.
520 _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.
650 0 _aStochastic processes.
_976770
650 0 _aControl engineering.
650 0 _aDifferential equations.
650 1 4 _aStochastic Processes.
_976770
650 2 4 _aControl and Systems Theory.
_965868
650 2 4 _aDifferential Equations.
700 1 _aChen, Xiuqiong.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_989084
700 1 _aJiao, Xiaopei.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_989085
700 1 _aKang, Jiayi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_989086
700 1 _aSun, Zeju.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_989087
700 1 _aTao, Yangtianze.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_989088
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031776830
776 0 8 _iPrinted edition:
_z9783031776854
776 0 8 _iPrinted edition:
_z9783031776861
830 0 _aAlgorithms and Computation in Mathematics,
_x2512-3254 ;
_v33
_973956
856 4 0 _uhttps://doi.org/10.1007/978-3-031-77684-7
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c65794
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