Stochastic processes and filtering theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Pr.
1974
|
| Edition: | 3. print. |
| Series: | Mathematics in science and engineering
64 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 376 S. Ill. |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
Acknowledgments ix
1. Introduction
1. Introduction 1
2. Scope and Objectives 2
3. A Guided Tour 4
References 6
2. Probability Theory and Random Variables
1. Introduction 8
2. Probability Axioms 10
3. Random Variables 13
4. Jointly Distributed Random Variables 24
5. Conditional Probabilities and Expectations 36
6. Properties of Gaussian Random Variables 42
References 46
3. Stochastic Processes
1. Introduction 47
2. Probability Law of a Stochastic Process 50
xi
xii CONTENTS
3. Convergence of Random Sequences 56
4. Mean Square Calculus 60
5. Independence, Conditioning, the Brownian Motion Process 70
6. Gaussian Processes 74
7. Markov Processes 77
8. White Noise 81
9. Stochastic Difference Equations 85
References 92
4. Stochastic Differential Equations
1. Introduction 93
2. Modeling the Process ePt 95
3. Ito Stochastic Integral 97
4. Stochastic Differential Equations 105
5. Ito Stochastic Calculus 112
6. Stochastic Integral of Stratonovich 116
7. Evaluation of Stochastic (Ito) Integrals 120
8. More on Modeling 121
9. Kolmogorov s Equations 126
10. Discussion 139
References 140
5. Introduction to Filtering Theory
1. Introduction 142
2. Probabilistic Approach 145
3. Statistical Methods 150
4. Foreword and Discussion 158
References 159
6. Nonlinear Filtering Theory
1. Introduction 162
2. Continuous Discrete Filtering 163
3. Evolution of the Conditional Density (Continuous Discrete) 164
4. Evolution of Moments (Continuous Discrete) 166
5. Evolution of the Mode (Continuous Discrete) 169
6. Discrete Filtering 174
7. Continuous Filtering 175
8. Evolution of the Conditional Density (Continuous) 178
9. Evolution of Moments (Continuous) 182
10. Evolution of the Mode (Continuous) 184
11. Limited Memory Filter 189
References 193
CONTENTS Xlii
7. Linear Filtering Theory
1. Introduction 194
2. Continuous Discrete Filter 195
3. Discrete Filter 200
4. Continuous Filter 218
5. Observability and Information 231
6. Bounds and Stability—Discrete Filter 234
7. Bounds and Stability—Continuous Filter 243
8. Error Sensitivity—Discrete Filter 244
9. Error Sensitivity—Continuous Filter 251
10. Linear Limited Memory Filter 255
Appendix 7A Classical Parameter Estimation 259
Appendix 7B Some Matrix Equalities 261
References 262
8. Applications of Linear Theory
1. Introduction 266
2. Review of the Discrete Filter 269
3. Extension to Nonlinear Problems 272
4. Uncertain Parameters 281
5. A Simple Example 287
6. Applications in Orbit Determination 292
7. Applications in Reentry 297
8. Filter Divergence and Error Compensation Techniques 301
9. Fictitious Noise Inputs and Parameter Uncertainties 305
10. Overweighting the Most Recent Data 307
11. Adaptive Noise Estimation 311
12. Limited Memory Filtering 318
13. Miscellaneous Topics 323
Appendix 8A Orbit Mechanics 324
Appendix 8B Reentry Mechanics 328
References 329
9. Approximate Nonlinear Filters
1. Introduction 332
2. Approximation Techniques: Parametrization of Density Functions 333
3. Nonlinear Filter Approximations: Continuous Filter 336
4. Nonlinear Filter Approximations: Continuous Discrete Filter 340
5. Nonlinear Filter Approximations: Discrete Filter 346
6. Discussion of Nonlinear Effects 347
7. Local Iterations 349
8. A Nonlinear Example 351
9. Applications in Orbit Determination 358
xiv CONTENTS
10. Applications in Reentry 359
11. Summary 360
Appendix 9A Approximate Continuous Filters: Vector Case 361
Appendix 9B Approximate Continuous Discrete Filters: Vector Case 362
References 365
Author Index 367
Subject Index 371
|
| adam_txt |
Contents
Preface vii
Acknowledgments ix
1. Introduction
1. Introduction 1
2. Scope and Objectives 2
3. A Guided Tour 4
References 6
2. Probability Theory and Random Variables
1. Introduction 8
2. Probability Axioms 10
3. Random Variables 13
4. Jointly Distributed Random Variables 24
5. Conditional Probabilities and Expectations 36
6. Properties of Gaussian Random Variables 42
References 46
3. Stochastic Processes
1. Introduction 47
2. Probability Law of a Stochastic Process 50
xi
xii CONTENTS
3. Convergence of Random Sequences 56
4. Mean Square Calculus 60
5. Independence, Conditioning, the Brownian Motion Process 70
6. Gaussian Processes 74
7. Markov Processes 77
8. White Noise 81
9. Stochastic Difference Equations 85
References 92
4. Stochastic Differential Equations
1. Introduction 93
2. Modeling the Process ePt 95
3. Ito Stochastic Integral 97
4. Stochastic Differential Equations 105
5. Ito Stochastic Calculus 112
6. Stochastic Integral of Stratonovich 116
7. Evaluation of Stochastic (Ito) Integrals 120
8. More on Modeling 121
9. Kolmogorov's Equations 126
10. Discussion 139
References 140
5. Introduction to Filtering Theory
1. Introduction 142
2. Probabilistic Approach 145
3. Statistical Methods 150
4. Foreword and Discussion 158
References 159
6. Nonlinear Filtering Theory
1. Introduction 162
2. Continuous Discrete Filtering 163
3. Evolution of the Conditional Density (Continuous Discrete) 164
4. Evolution of Moments (Continuous Discrete) 166
5. Evolution of the Mode (Continuous Discrete) 169
6. Discrete Filtering 174
7. Continuous Filtering 175
8. Evolution of the Conditional Density (Continuous) 178
9. Evolution of Moments (Continuous) 182
10. Evolution of the Mode (Continuous) 184
11. Limited Memory Filter 189
References 193
CONTENTS Xlii
7. Linear Filtering Theory
1. Introduction 194
2. Continuous Discrete Filter 195
3. Discrete Filter 200
4. Continuous Filter 218
5. Observability and Information 231
6. Bounds and Stability—Discrete Filter 234
7. Bounds and Stability—Continuous Filter 243
8. Error Sensitivity—Discrete Filter 244
9. Error Sensitivity—Continuous Filter 251
10. Linear Limited Memory Filter 255
Appendix 7A Classical Parameter Estimation 259
Appendix 7B Some Matrix Equalities 261
References 262
8. Applications of Linear Theory
1. Introduction 266
2. Review of the Discrete Filter 269
3. Extension to Nonlinear Problems 272
4. Uncertain Parameters 281
5. A Simple Example 287
6. Applications in Orbit Determination 292
7. Applications in Reentry 297
8. Filter Divergence and Error Compensation Techniques 301
9. Fictitious Noise Inputs and Parameter Uncertainties 305
10. Overweighting the Most Recent Data 307
11. Adaptive Noise Estimation 311
12. Limited Memory Filtering 318
13. Miscellaneous Topics 323
Appendix 8A Orbit Mechanics 324
Appendix 8B Reentry Mechanics 328
References 329
9. Approximate Nonlinear Filters
1. Introduction 332
2. Approximation Techniques: Parametrization of Density Functions 333
3. Nonlinear Filter Approximations: Continuous Filter 336
4. Nonlinear Filter Approximations: Continuous Discrete Filter 340
5. Nonlinear Filter Approximations: Discrete Filter 346
6. Discussion of Nonlinear Effects 347
7. Local Iterations 349
8. A Nonlinear Example 351
9. Applications in Orbit Determination 358
xiv CONTENTS
10. Applications in Reentry 359
11. Summary 360
Appendix 9A Approximate Continuous Filters: Vector Case 361
Appendix 9B Approximate Continuous Discrete Filters: Vector Case 362
References 365
Author Index 367
Subject Index 371 |
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| id | DE-604.BV022112308 |
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| index_date | 2024-07-02T16:15:47Z |
| indexdate | 2024-07-09T20:50:49Z |
| institution | BVB |
| language | English |
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| physical | XIV, 376 S. Ill. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
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| publisher | Acad. Pr. |
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| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Jazwinski, Andrew H. Verfasser aut Stochastic processes and filtering theory Anrew H. Jazwinski 3. print. New York [u.a.] Acad. Pr. 1974 XIV, 376 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 64 Filtertheorie (DE-588)4154392-0 gnd rswk-swf Filterung Stochastik (DE-588)4121267-8 gnd rswk-swf Filter Stochastik (DE-588)4128590-6 gnd rswk-swf Filter Mathematik (DE-588)4154388-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Filter Mathematik (DE-588)4154388-9 s Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Filtertheorie (DE-588)4154392-0 s 2\p DE-604 Filter Stochastik (DE-588)4128590-6 s 3\p DE-604 Filterung Stochastik (DE-588)4121267-8 s 4\p DE-604 Mathematics in science and engineering 64 (DE-604)BV000001196 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015327183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jazwinski, Andrew H. Stochastic processes and filtering theory Mathematics in science and engineering Filtertheorie (DE-588)4154392-0 gnd Filterung Stochastik (DE-588)4121267-8 gnd Filter Stochastik (DE-588)4128590-6 gnd Filter Mathematik (DE-588)4154388-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4154392-0 (DE-588)4121267-8 (DE-588)4128590-6 (DE-588)4154388-9 (DE-588)4057630-9 |
| title | Stochastic processes and filtering theory |
| title_auth | Stochastic processes and filtering theory |
| title_exact_search | Stochastic processes and filtering theory |
| title_exact_search_txtP | Stochastic processes and filtering theory |
| title_full | Stochastic processes and filtering theory Anrew H. Jazwinski |
| title_fullStr | Stochastic processes and filtering theory Anrew H. Jazwinski |
| title_full_unstemmed | Stochastic processes and filtering theory Anrew H. Jazwinski |
| title_short | Stochastic processes and filtering theory |
| title_sort | stochastic processes and filtering theory |
| topic | Filtertheorie (DE-588)4154392-0 gnd Filterung Stochastik (DE-588)4121267-8 gnd Filter Stochastik (DE-588)4128590-6 gnd Filter Mathematik (DE-588)4154388-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Filtertheorie Filterung Stochastik Filter Stochastik Filter Mathematik Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015327183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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