Hidden Markov Processes and Adaptive Filtering
This book is devoted to the problem of adaptive filtering for partially observed systems depending on unknown parameters. Adaptive filters are proposed for a wide variety of models: Gaussian and conditionally Gaussian linear models of diffusion processes; some nonlinear models; telegraph signals in...
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| Format: | Electrònic eBook |
| Idioma: | anglès |
| Publicat: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Edició: | 1st ed. 2025. |
| Col·lecció: | Springer Series in Statistics,
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| Matèries: | |
| Accés en línia: | https://doi.org/10.1007/978-3-032-00052-1 |
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| 100 | 1 | |a Kutoyants, Yury A. |e author. |0 (orcid)0000-0003-0464-3380 |1 https://orcid.org/0000-0003-0464-3380 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Hidden Markov Processes and Adaptive Filtering |h [electronic resource] / |c by Yury A. Kutoyants. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XXI, 654 p. 5 illus.). | ||
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| 505 | 0 | |a 1 Auxiliary Result -- 2 Small Noise in Both Equations -- 3 Small Noise in Observations -- 4 Hidden Ergodic O-U process -- 5 Hidden Telegraph Process -- 6 Hidden AR Process -- 7 Source Localization. | |
| 520 | |a This book is devoted to the problem of adaptive filtering for partially observed systems depending on unknown parameters. Adaptive filters are proposed for a wide variety of models: Gaussian and conditionally Gaussian linear models of diffusion processes; some nonlinear models; telegraph signals in white Gaussian noise (all in continuous time); and autoregressive processes observed in white noise (discrete time). The properties of the estimators and adaptive filters are described in the asymptotics of small noise or large samples. The parameter estimators and adaptive filters have a recursive structure which makes their numerical realization relatively simple. The question of the asymptotic efficiency of the adaptive filters is also discussed. Readers will learn how to construct Le Cam’s One-step MLE for all these models and how this estimator can be transformed into an asymptotically efficient estimator process which has a recursive structure. The last chapter covers several applications of the developed method to such problems as localization of fixed and moving sources on the plane by observations registered by K detectors, estimation of a signal in noise, identification of a security price process, change point problems for partially observed systems, and approximation of the solution of BSDEs. Adaptive filters are presented for the simplest one-dimensional observations and state equations, known initial values, non-correlated noises, etc. However, the proposed constructions can be extended to a wider class of models, and the One-step MLE-processes can be used in many other problems where the recursive evolution of estimators is an important property. The book will be useful for students of filtering theory, both undergraduates (discrete time models) and postgraduates (continuous time models). The method described, preliminary estimator + One-step MLE-process + adaptive filter, will also be of interest to engineers and researchers working with partially observed models. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Markov processes. | |
| 650 | 0 | |a Stochastic models. | |
| 650 | 0 | |a Statistics . | |
| 650 | 0 | |a Probabilities. | |
| 650 | 1 | 4 | |a Markov Process. |
| 650 | 2 | 4 | |a Stochastic Modelling in Statistics. |
| 650 | 2 | 4 | |a Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. |
| 650 | 2 | 4 | |a Probability Theory. |
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| 830 | 0 | |a Springer Series in Statistics, |x 2197-568X | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-032-00052-1 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||
| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||