Bayesian filtering and smoothing:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Schriftenreihe: | Textbooks / Institute of Mathematical Statistics
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXII, 232 S. graph. Darst. |
| ISBN: | 9781107619289 9781107030657 |
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Datensatz im Suchindex
| _version_ | 1804150633275588608 |
|---|---|
| adam_text | Titel: Bayesian filtering and smoothing
Autor: Särkkä, Simo
Jahr: 2013
Contents
Preface ix
Symbols and abbreviations xiii
1 What are Bayesian filtering and smoothing? 1
1.1 Applications of Bayesian filtering and smoothing 1
1.2 Origins of Bayesian filtering and smoothing 7
1.3 Optimal filtering and smoothing as Bayesian inference 8
1.4 Algorithms for Bayesian filtering and smoothing 12
1.5 Parameter estimation 14
1.6 Exercises 15
2 Bayesian inference 17
2.1 Philosophy of Bayesian inference 17
2.2 Connection to maximum likelihood estimation 17
2.3 The building blocks of Bayesian models 19
2.4 Bayesian point estimates 20
2.5 Numerical methods 22
2.6 Exercises 24
3 Batch and recursive Bayesian estimation 27
3.1 Batch linear regression 27
3.2 Recursive linear regression 29
3.3 Batch versus recursive estimation 31
3.4 Drift model for linear regression 33
3.5 State space model for linear regression with drift 36
3.6 Examples of state space models 39
3.7 Exercises 46
4 Bayesian filtering equations and exact solutions 51
4.1 Probabilistic state space models 51
4.2 Bayesian filtering equations 54
4.3 Kaiman filter 56
vi Contents
4.4 Exercises 62
5 Extended and unscented Kaiman filtering 64
5.1 Taylor series expansions 64
5.2 Extended Kaiman filter 69
5.3 Statistical linearization 75
5.4 Statistically linearized filter 77
5.5 Unscented transform 81
5.6 Unscented Kaiman filter 86
5.7 Exercises 92
6 General Gaussian filtering 96
6.1 Gaussian moment matching 96
6.2 Gaussian filter 97
6.3 Gauss-Hermite integration 99
6.4 Gauss-Hermite Kaiman filter 103
6.5 Spherical cubature integration 106
6.6 Cubature Kaiman filter 110
6.7 Exercises 114
7 Particle filtering 116
7.1 Monte Carlo approximations in Bayesian inference 116
7.2 Importance sampling 117
7.3 Sequential importance sampling 120
7.4 Sequential importance resampling 123
7.5 Rao-Blackwellized particle filter 129
7.6 Exercises 132
8 Bayesian smoothing equations and exact solutions 134
8.1 Bayesian smoothing equations 134
8.2 Rauch-Tung-Striebel smoother 135
8.3 Two-filter smoothing 139
8.4 Exercises 142
9 Extended and unscented smoothing 144
9.1 Extended Rauch-Tung-Striebel smoother 144
9.2 Statistically linearized Rauch-Tung-Striebel smoother 146
9.3 Unscented Rauch-Tung-Striebel smoother 148
9.4 Exercises 152
10 General Gaussian smoothing 154
10.1 General Gaussian Rauch-Tung-Striebel smoother 154
10.2 Gauss-Hermite Rauch-Tung-Striebel smoother 155
Contents vii
10.3 Cubature Rauch-Tung-Striebel smoother 156
10.4 General fixed-point smoother equations 159
10.5 General fixed-lag smoother equations 162
10.6 Exercises 164
11 Particle smoothing 165
11.1 SIR particle smoother 165
11.2 Backward-simulation particle smoother 167
11.3 Reweighting particle smoother 169
11.4 Rao-Blackwellized particle smoothers 171
11.5 Exercises 173
12 Parameter estimation 174
12.1 Bayesian estimation of parameters in state space models 174
12.2 Computational methods for parameter estimation 177
12.3 Practical parameter estimation in state space models 185
12.4 Exercises 202
13 Epilogue 204
13.1 Which method should I choose? 204
13.2 Further topics 206
Appendix Additional material 209
A.l Properties of Gaussian distribution 209
A.2 Cholesky factorization and its derivative 210
A.3 Parameter derivatives for the Kaiman filter 212
A.4 Parameter derivatives for the Gaussian filter 214
References 219
Index 229
|
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| spelling | Särkkä, Simo Verfasser aut Bayesian filtering and smoothing Simo Särkkä Cambridge [u.a.] Cambridge Univ. Press 2013 XXII, 232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Textbooks / Institute of Mathematical Statistics 3 Hier auch später erschienene, unveränderte Nachdrucke Bayes-Inferenz (DE-588)4648118-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Bayes-Inferenz (DE-588)4648118-7 s DE-604 Institute of Mathematical Statistics Textbooks 3 (DE-604)BV036598560 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026179601&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Bayesian filtering and smoothing |
| title_auth | Bayesian filtering and smoothing |
| title_exact_search | Bayesian filtering and smoothing |
| title_full | Bayesian filtering and smoothing Simo Särkkä |
| title_fullStr | Bayesian filtering and smoothing Simo Särkkä |
| title_full_unstemmed | Bayesian filtering and smoothing Simo Särkkä |
| title_short | Bayesian filtering and smoothing |
| title_sort | bayesian filtering and smoothing |
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