Bayesian filtering and smoothing.pdf

发布时间：2022-06-08 发布人：admin 分类：说明书资料大小：2.27M 资料格式：pdf 举报版权申诉

flyboyee2019-10957760-4744302543456867867.pdf-第1页.png

第1页 / 共256页

flyboyee2019-10957760-4744302543456867867.pdf-第2页.png

第2页 / 共256页

flyboyee2019-10957760-4744302543456867867.pdf-第3页.png

第3页 / 共256页

flyboyee2019-10957760-4744302543456867867.pdf-第4页.png

第4页 / 共256页

flyboyee2019-10957760-4744302543456867867.pdf-第5页.png

第5页 / 共256页

flyboyee2019-10957760-4744302543456867867.pdf-第6页.png

第6页 / 共256页

flyboyee2019-10957760-4744302543456867867.pdf-第7页.png

第7页 / 共256页

flyboyee2019-10957760-4744302543456867867.pdf-第8页.png

第8页 / 共256页

Bayesian Filtering and Smoothing

Contents

Preface

Symbols and abbreviations

1 What are Bayesian filtering and smoothing?

1.1 Applications of Bayesian filtering and smoothing

1.2 Origins of Bayesian filtering and smoothing

1.3 Optimal filtering and smoothing as Bayesian inference

1.4 Algorithms for Bayesian filtering and smoothing

1.5 Parameter estimation

1.6 Exercises

2 Bayesian inference

2.1 Philosophy of Bayesian inference

2.2 Connection to maximum likelihood estimation

2.3 The building blocks of Bayesian models

2.4 Bayesian point estimates

2.5 Numerical methods

2.6 Exercises

3 Batch and recursive Bayesian estimation

3.1 Batch linear regression

3.2 Recursive linear regression

3.3 Batch versus recursive estimation

3.4 Drift model for linear regression

3.5 State space model for linear regression with drift

3.6 Examples of state space models

3.7 Exercises

4 Bayesian filtering equations and exact solutions

4.1 Probabilistic state space models

4.2 Bayesian filtering equations

4.3 Kalman filter

4.4 Exercises

5 Extended and unscented Kalman filtering

5.1 Taylor series expansions

5.2 Extended Kalman filter

5.3 Statistical linearization

5.4 Statistically linearized filter

5.5 Unscented transform

5.6 Unscented Kalman filter

5.7 Exercises

6 General Gaussian filtering

6.1 Gaussian moment matching

6.2 Gaussian filter

6.3 Gauss–Hermite integration

6.4 Gauss–Hermite Kalman filter

6.5 Spherical cubature integration

6.6 Cubature Kalman filter

6.7 Exercises

7 Particle filtering

7.1 Monte Carlo approximations in Bayesian inference

7.2 Importance sampling

7.3 Sequential importance sampling

7.4 Sequential importance resampling

7.5 Rao–Blackwellized particle filter

7.6 Exercises

8 Bayesian smoothing equations and exact solutions

8.1 Bayesian smoothing equations

8.2 Rauch–Tung–Striebel smoother

8.3 Two-filter smoothing

8.4 Exercises

9 Extended and unscented smoothing

9.1 Extended Rauch–Tung–Striebel smoother

9.2 Statistically linearized Rauch–Tung–Striebel smoother

9.3 Unscented Rauch–Tung–Striebel smoother

9.4 Exercises

10 General Gaussian smoothing

10.1 General Gaussian Rauch–Tung–Striebel smoother

10.2 Gauss–Hermite Rauch–Tung–Striebel smoother

10.3 Cubature Rauch–Tung–Striebel smoother

10.4 General fixed-point smoother equations

10.5 General fixed-lag smoother equations

10.6 Exercises

11 Particle smoothing

11.1 SIR particle smoother

11.2 Backward-simulation particle smoother

11.3 Reweighting particle smoother

11.4 Rao–Blackwellized particle smoothers

11.5 Exercises

12 Parameter estimation

12.1 Bayesian estimation of parameters in state space models

12.2 Computational methods for parameter estimation

12.3 Practical parameter estimation in state space models

12.4 Exercises

13 Epilogue

13.1 Which method should I choose?

13.2 Further topics

Appendix Additional material

A.1 Properties of Gaussian distribution

A.2 Cholesky factorization and its derivative

A.3 Parameter derivatives for the Kalman filter

A.4 Parameter derivatives for the Gaussian filter

References

Index

more information - www.cambridge.org/9781107030657

Bayesian Filtering and Smoothing Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in ﬁelds such as navigation, aerospace engineering, telecommunications, and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art ﬁltering and smoothing methods in a uniﬁed Bayesian framework. Readers learn what non-linear Kalman ﬁlters and particle ﬁlters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art ﬁltering and smoothing algorithms. The book’s practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods. s i m o s ¨arkk¨a worked, from 2000 to 2010, with Nokia Ltd., Indagon Ltd., and the Nalco Company in various industrial research projects related to telecommunications, positioning systems, and industrial process control. Currently, he is a Senior Researcher with the Department of Biomedical Engineering and Computational Science at Aalto University, Finland, and Adjunct Professor with Tampere University of Technology and Lappeenranta University of Technology. In 2011 he was a visiting scholar with the Signal Processing and Communications Laboratory of the Department of Engineering at the University of Cambridge. His research interests are in state and parameter estimation in stochastic dynamic systems and, in particular, Bayesian methods in signal processing, machine learning, and inverse problems with applications to brain imaging, positioning systems, computer vision, and audio signal processing. He is a Senior Member of the IEEE.

INSTITUTE OF MATHEMATICAL STATISTICS TEXTBOOKS Editorial Board D. R. Cox (University of Oxford) A. Agresti (University of Florida) B. Hambly (University of Oxford) S. Holmes (Stanford University) X.-L. Meng (Harvard University) IMS Textbooks give introductory accounts of topics of current concern suitable for advanced courses at master’s level, for doctoral students and for individual study. They are typically shorter than a fully developed textbook, often arising from material created for a topical course. Lengths of 100–290 pages are envisaged. The books typically contain exercises.

Bayesian Filtering and Smoothing SIMO S ¨ARKK ¨A Aalto University, Finland

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York Information on this title: www.cambridge.org/9781107030657 www.cambridge.org C Simo S¨arkk¨a 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2013 Printed and bound in the United Kingdom by the MPG Books Group A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data ISBN 978-1-107-03065-7 Hardback ISBN 978-1-107-61928-9 Paperback Additional resources for this publication at www.cambridge.org/sarkka Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

Contents 1 2 3 4 Preface Symbols and abbreviations What are Bayesian ﬁltering and smoothing? 1.1 1.2 1.3 1.4 1.5 1.6 Applications of Bayesian ﬁltering and smoothing Origins of Bayesian ﬁltering and smoothing Optimal ﬁltering and smoothing as Bayesian inference Algorithms for Bayesian ﬁltering and smoothing Parameter estimation Exercises Bayesian inference 2.1 2.2 2.3 2.4 2.5 2.6 Philosophy of Bayesian inference Connection to maximum likelihood estimation The building blocks of Bayesian models Bayesian point estimates Numerical methods Exercises Batch and recursive Bayesian estimation 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Batch linear regression Recursive linear regression Batch versus recursive estimation Drift model for linear regression State space model for linear regression with drift Examples of state space models Exercises Bayesian ﬁltering equations and exact solutions 4.1 4.2 4.3 Probabilistic state space models Bayesian ﬁltering equations Kalman ﬁlter v ix xiii 1 1 7 8 12 14 15 17 17 17 19 20 22 24 27 27 29 31 33 36 39 46 51 51 54 56

vi 5 6 7 8 9 Contents 4.4 Exercises Extended and unscented Kalman ﬁltering 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Taylor series expansions Extended Kalman ﬁlter Statistical linearization Statistically linearized ﬁlter Unscented transform Unscented Kalman ﬁlter Exercises General Gaussian ﬁltering 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Gaussian moment matching Gaussian ﬁlter Gauss–Hermite integration Gauss–Hermite Kalman ﬁlter Spherical cubature integration Cubature Kalman ﬁlter Exercises Particle ﬁltering 7.1 Monte Carlo approximations in Bayesian inference 7.2 7.3 7.4 7.5 7.6 Importance sampling Sequential importance sampling Sequential importance resampling Rao–Blackwellized particle ﬁlter Exercises Bayesian smoothing equations and exact solutions 8.1 8.2 8.3 8.4 Bayesian smoothing equations Rauch–Tung–Striebel smoother Two-ﬁlter smoothing Exercises Extended and unscented smoothing 9.1 9.2 9.3 9.4 Extended Rauch–Tung–Striebel smoother Statistically linearized Rauch–Tung–Striebel smoother Unscented Rauch–Tung–Striebel smoother Exercises 10 General Gaussian smoothing 10.1 General Gaussian Rauch–Tung–Striebel smoother 10.2 Gauss–Hermite Rauch–Tung–Striebel smoother 62 64 64 69 75 77 81 86 92 96 96 97 99 103 106 110 114 116 116 117 120 123 129 132 134 134 135 139 142 144 144 146 148 152 154 154 155

分享到：

赞收藏

资料库

Bayesian filtering and smoothing.pdf

相关推荐

课程资源

热门标签

最新资料