Lessons in digital estimation theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice-Hall
1987
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| Series: | Prentice-Hall signal processing series.
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 304 S. graph. Darst. |
| ISBN: | 0135308097 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lessons in digital estimation theory |
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Record in the Search Index
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| adam_text | Contents
PREFACE xiii
LESSON 1 INTRODUCTION, COVERAGE, AND PHILOSOPHY 1
Introduction 1
Coverage 2
Philosophy 5
LESSON 2 THE LINEAR MODEL 7
Introduction 7
Examples 7
Notational Preliminaries 14
Problems 15
LESSON 3 LEAST SQUARES ESTIMATION: BATCH PROCESSING 17
Introduction 17
Number of Measurements 18
Objective Function and Problem Statement 18
Derivation of Estimator 19
Fixed and Expanding Memory Estimators 23
Scale Changes 23
Problems 25
v
Vl Contents
LESSON 4 LEAST SQUARES ESTIMATION:
RECURSIVE PROCESSING 26
Introduction 26
Recursive Least Squares: Information Form 27
Matrix Inversion Lemma 30
Recursive Least Squares: Covariance Form 30
Which Form to Use 31
Problems 32
LESSON 5 LEAST SQUARES ESTIMATION:
RECURSIVE PROCESSING (continued) 35
Generalization to Vector Measurements 36
Cross Sectional Processing 37
Multistage Least Squares Estimators 38
Problems 42
LESSON 6 SMALL SAMPLE PROPERTIES OF ESTIMATORS 43
Introduction 43
Unbiasedness 44
Efficiency 46
Problems 52
LESSON 7 LARGE SAMPLE PROPERTIES OF ESTIMATORS 54
Introduction 54
Asymptotic Distributions 54
Asymptotic Unbiasedness 57
Consistency 57
Asymptotic Efficiency 60
Problems 61
LESSON 8 PROPERTIES OF LEAST SQUARES ESTIMATORS 63
Introduction 63
Small Sample Properties of Least Squares
Estimators 63
Large Sample Properties of Least Squares
Estimators 68
Problems 70
Contents vii
LESSON 9 BEST LINEAR UNBIASED ESTIMATION 71
Introduction 71
Problem Statement and Objective Function 72
Derivation of Estimator 73
Comparison of 6Blu( ) and 6WLS(A:) 74
Some Properties of §Blu( ) 75
Recursive BLUEs 78
Problems 79
LESSON 10 LIKELIHOOD 81
Introduction 81
Likelihood Defined 81
Likelihood Ratio 84
Results Described by Continuous Distributions 85
Multiple Hypotheses 85
Problems 87
LESSON 11 MAXIMUM LIKELIHOOD ESTIMATION 88
Likelihood 88
Maximum Likelihood Method and Estimates 89
Properties of Maximum Likelihood Estimates 91
The Linear Model (H€(k) deterministic) 92
A Log Likelihood Function for an Important
Dynamical System 94
Problems 97
LESSON 12 ELEMENTS OF MULTIVARIATE GAUSSIAN
RANDOM VARIABLES 100
Introduction 100
Univariate Gaussian Density Function 100
Multivariate Gaussian Density Function 101
Jointly Gaussian Random Vectors 101
The Conditional Density Function 102
Properties of Multivariate Gaussian Random
Variables 104
Properties of Conditional Mean 104
Problems 106
viii Contents
LESSON 13 ESTIMATION OF RANDOM PARAMETERS:
GENERAL RESULTS 108
Introduction 108
Mean Squared Estimation 109
Maximum a Posteriori Estimation 114
Problems 116
LESSON 14 ESTIMATION OF RANDOM PARAMETERS:
THE LINEAR AND GAUSSIAN MODEL 118
Introduction 118
Mean Squared Estimator 118
Best Linear Unbiased Estimation,
Revisited 121
Maximum a Posteriori Estimator 123
Problems 126
LESSON 15 ELEMENTS OF DISCRETE TIME GAUSS MARKOV
RANDOM PROCESSES 128
Introduction 128
Definitions and Properties of Discrete Time
Gauss Markov Random Processes 128
A Basic State Variable Model 131
Properties of the Basic State Variable
Model 133
Signal to Noise Ratio 137
Problems 138
LESSON 16 STATE ESTIMATION: PREDICTION 140
Introduction 140
Single Stage Predictor 140
A General State Predictor 142
The Innovations Process 146
Problems 147
Contents ix
LESSON 17 STATE ESTIMATION: FILTERING
(THE KALMAN FILTER) 149
Introduction 149
A Preliminary Result 150
The Kalman Filter 151
Observations About the Kalman Filter 153
Problems 158
LESSON 18 STATE ESTIMATION: FILTERING EXAMPLES 160
Introduction 160
Examples 160
Problems 169
LESSON 19 STATE ESTIMATION: STEADY STATE KALMAN
FILTER AND ITS RELATIONSHIP TO A DIGITAL
WIENER FILTER 170
Introduction 170
Steady State Kalman Filter 170
Single Channel Steady State Kalman Filter 173
Relationships Between the Steady State
Kalman Filter and a Finite Impulse
Response Digital Wiener Filter 176
Comparisons of Kalman and Wiener Filters 181
Problems 182
LESSON 20 STATE ESTIMATION: SMOOTHING 183
Three Types of Smoothers 183
Approaches for Deriving Smoothers 184
A Summary of Important Formulas 184
Single Stage Smoother 184
Double Stage Smoother 187
Single and Double Stage Smoothers
as General Smoothers 189
Problems 192
x Contents
LESSON 21 STATE ESTIMATION: SMOOTHING
(GENERAL RESULTS) 193
Introduction 193
Fixed Interval Smoothers 193
Fixed Point Smoothing 199
Fixed Lag Smoothing 201
Problems 202
LESSON 22 STATE ESTIMATION: SMOOTHING APPLICATIONS 204
Introduction 204
Minimum Variance Deconvolution (MVD) 204
Steady State MVD Filter 207
Relationship Between Steady State MVD
Filter and an Infinite Impulse Response
Digital Wiener Deconvolution Filter 213
Maximum Likelihood Deconvolution 215
Recursive Waveshaping 216
Problems 222
LESSON 23 STATE ESTIMATION FOR THE NOT SO BASIC
STATE VARIABLE MODEL 223
Introduction 223
Biases 224
Correlated Noises 225
Colored Noises 227
Perfect Measurements: Reduced Order
Estimators 230
Final Remark 233
Problems 233
LESSON 24 LINEARIZATION AND DISCRETIZATION OF
NONLINEAR SYSTEMS 236
Introduction 236
A Dynamical Model 237
Linear Perturbation Equations 239
Contents xi
Discretization of a Linear Time Varying
State Variable Model 242
Discretized Perturbation State Variable
Model 245
Problems 246
LESSON 25 ITERATED LEAST SQUARES AND EXTENDED
KALMAN FILTERING 248
Introduction 248
Iterated Least Squares 248
Extended Kalman Filter 249
Application to Parameter Estimation 255
Problems 256
LESSON 26 MAXIMUM LIKELIHOOD STATE AND PARAMETER
ESTIMATION 258
Introduction 258
A Log Likelihood Function for the Basic
State Variable Model 259
On Computing §ml 261
A Steady State Approximation 264
Problems 269
LESSON 27 KALMAN BUCY FILTERING 270
Introduction 270
System Description 271
Notation and Problem Statement 271
The Kalman Bucy Filter 272
Derivation of KBF Using a Formal Limiting
Procedure 273
Derivation of KBF When Structure of the
Filter Is Prespecified 275
Steady State KBF 278
An Important Application for the KBF 280
Problems 281
xii Contents
LESSON A SUFFICIENT STATISTICS AND STATISTICAL
ESTIMATION OF PARAMETERS 282
Introduction 282
Concept of Sufficient Statistics 282
Exponential Families of Distributions 284
Exponential Families and Maximum
Likelihood Estimation 287
Sufficient Statistics and Uniformly Minimum
Variance Unbiased Estimation 290
Problems 294
APPENDIX A GLOSSARY OF MAJOR RESULTS 295
REFERENCES 300
INDEX 305
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:48Z |
| institution | BVB |
| isbn | 0135308097 |
| language | English |
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| physical | XIV, 304 S. graph. Darst. |
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| publisher | Prentice-Hall |
| record_format | marc |
| series2 | Prentice-Hall signal processing series. |
| spelling | Mendel, Jerry M. 1938- Verfasser (DE-588)134275918 aut Lessons in digital estimation theory Englewood Cliffs, NJ Prentice-Hall 1987 XIV, 304 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Prentice-Hall signal processing series. Estimation, théorie de l' ram estimation statistique inriac modèle linéaire inriac théorie estimation inriac Estimation theory Schätztheorie (DE-588)4121608-8 gnd rswk-swf Schätztheorie (DE-588)4121608-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001396241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mendel, Jerry M. 1938- Lessons in digital estimation theory Estimation, théorie de l' ram estimation statistique inriac modèle linéaire inriac théorie estimation inriac Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4121608-8 |
| title | Lessons in digital estimation theory |
| title_auth | Lessons in digital estimation theory |
| title_exact_search | Lessons in digital estimation theory |
| title_full | Lessons in digital estimation theory |
| title_fullStr | Lessons in digital estimation theory |
| title_full_unstemmed | Lessons in digital estimation theory |
| title_short | Lessons in digital estimation theory |
| title_sort | lessons in digital estimation theory |
| topic | Estimation, théorie de l' ram estimation statistique inriac modèle linéaire inriac théorie estimation inriac Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Estimation, théorie de l' estimation statistique modèle linéaire théorie estimation Estimation theory Schätztheorie |
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