Mathematics of Kalman-Bucy filtering:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1988
|
| Edition: | 2. ed. |
| Series: | Springer series in information sciences
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 170 S. |
| ISBN: | 3540187812 0387187812 3540135081 0387135081 |
Staff View
MARC
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| 100 | 1 | |a Ruymgaart, Peter A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics of Kalman-Bucy filtering |c P. A. Ruymgaart ; T. T. Soong |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1988 | |
| 300 | |a X, 170 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Springer series in information sciences |v 14 | |
| 650 | 7 | |a Ciência da informação |2 larpcal | |
| 650 | 4 | |a Cálculo | |
| 650 | 4 | |a Probabilidades | |
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Hilbert space | |
| 650 | 4 | |a Kalman filtering | |
| 650 | 4 | |a Probabilities | |
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| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text |
Contents
1. Elements of Probability Theory 1
1.1 Probability and Probability Spaces 1
1.1.1 Measurable Spaces, Measurable Mappings and Measure
Spaces 1
1.1.2 Probability Spaces 3
1.2 Random Variables and "Almost Sure" Properties 3
1.2.1 Mathematical Expectations 5
1.2.2 Probability Distribution and Density Functions 7
1.2.3 Characteristic Function 9
1.2.4 Examples 9
1.3 Random Vectors 11
1.3.1 Stochastic Independence 13
1.3.2 The Gaussian N Vector and Gaussian Manifolds 16
1.4 Stochastic Processes 18
1.4.1 The Hilbert Space L2(Q) 21
1.4.2 Second Order Processes 24
1.4.3 The Gaussian Process 26
1.4.4 Brownian Motion, the Wiener Levy Process and White
Noise 27
2. Calculus in Mean Square 30
2.1 Convergence in Mean Square 30
2.2 Continuity in Mean Square 33
2.3 Differentiability in Mean Square 35
2.3.1 Supplementary Exercises 39
2.4 Integration in Mean Square 40
2.4.1 Some Elementary Properties 42
2.4.2 A Condition for Existence 46
2.4.3 A Strong Condition for Existence 52
2.4.4 A Weak Condition for Existence 54
2.4.5 Supplementary Exercises 63
2.5 Mean Square Calculus of Random iV Vectors 65
2.5.1 Conditions for Existence 67
XII Contents
2.6 The Wiener Levy Process 68
2.6.1 The General Wiener Levy N Vector 70
2.6.2 Supplementary Exercises 75
2.7 Mean Square Calculus and Gaussian Distributions 76
2.8 Mean Square Calculus and Sample Calculus 76
2.8.1 Supplementary Exercise 79
3. The Stochastic Dynamic System 80
3.1 System Description 80
3.2 Uniqueness and Existence of m.s. Solution to (3.3) 81
3.2.1 The Banach Space I^(fi) 81
3.2.2 Uniqueness 83
3.2.3 The Homogeneous System 84
3.2.4 The Inhomogeneous System 89
3.2.5 Supplementary Exercises 93
3.3 A Discussion of System Representation 94
4. The Kalman Bucy Filter 100
4.1 Some Preliminaries 101
4.1.1 Supplementary Exercise 102
4.2 Some Aspects of L2 {[a,b]) 103
4.2.1 Supplementary Exercise 106
4.3 Mean Square Integrals Continued 106
4.4 Least Squares Approximation in Euclidean Space 114
4.4.1 Supplementary Exercises 116
4.5 A Representation of Elements of H{Z,t) 116
4.5.1 Supplementary Exercises 128
4.6 The Wiener Hopf Equation 128
4.6.1 The Integral Equation (4.106) 134
4.7 Kalman Bucy Filter and the Riccati Equation 146
4.7.1 Recursion Formula and the Riccati Equation 148
4.7.2 Supplementary Exercise 153
5. A Theorem by Liptser and Shiryayev 154
5.1 Discussion on Observation Noise 154
5.2 A Theorem of Liptser and Shiryayev 155
Appendix: Solutions to Selected Exercises 158
References 167
Subject Index 169 |
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| author_facet | Ruymgaart, Peter A. Soong, Tsu T. |
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| dewey-tens | 510 - Mathematics |
| discipline | Elektrotechnik Mathematik |
| edition | 2. ed. |
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| isbn | 3540187812 0387187812 3540135081 0387135081 |
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| physical | X, 170 S. |
| publishDate | 1988 |
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| publisher | Springer |
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| series | Springer series in information sciences |
| series2 | Springer series in information sciences |
| spelling | Ruymgaart, Peter A. Verfasser aut Mathematics of Kalman-Bucy filtering P. A. Ruymgaart ; T. T. Soong 2. ed. Berlin u.a. Springer 1988 X, 170 S. txt rdacontent n rdamedia nc rdacarrier Springer series in information sciences 14 Ciência da informação larpcal Cálculo Probabilidades Calculus Hilbert space Kalman filtering Probabilities Kalman-Filter (DE-588)4130759-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Kalman-Filter (DE-588)4130759-8 s DE-604 Mathematik (DE-588)4037944-9 s 1\p DE-604 Soong, Tsu T. Verfasser aut Springer series in information sciences 14 (DE-604)BV000008063 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001565812&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 |
| spellingShingle | Ruymgaart, Peter A. Soong, Tsu T. Mathematics of Kalman-Bucy filtering Springer series in information sciences Ciência da informação larpcal Cálculo Probabilidades Calculus Hilbert space Kalman filtering Probabilities Kalman-Filter (DE-588)4130759-8 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4130759-8 (DE-588)4037944-9 |
| title | Mathematics of Kalman-Bucy filtering |
| title_auth | Mathematics of Kalman-Bucy filtering |
| title_exact_search | Mathematics of Kalman-Bucy filtering |
| title_full | Mathematics of Kalman-Bucy filtering P. A. Ruymgaart ; T. T. Soong |
| title_fullStr | Mathematics of Kalman-Bucy filtering P. A. Ruymgaart ; T. T. Soong |
| title_full_unstemmed | Mathematics of Kalman-Bucy filtering P. A. Ruymgaart ; T. T. Soong |
| title_short | Mathematics of Kalman-Bucy filtering |
| title_sort | mathematics of kalman bucy filtering |
| topic | Ciência da informação larpcal Cálculo Probabilidades Calculus Hilbert space Kalman filtering Probabilities Kalman-Filter (DE-588)4130759-8 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Ciência da informação Cálculo Probabilidades Calculus Hilbert space Kalman filtering Probabilities Kalman-Filter Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001565812&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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