ontents

Preface / 3
Contents / 5

Chapter One: Introduction to Filtering and Smoothing 9
1.1  Introduction 10
1.2  Background 12
1.3  Application Areas 15
1.4  Organization and Content 16
References 20

Chapter Two: Statistic Control and Filter Problems 27
2.1  Introduction 28
2.2  Control Problems with Perfect Information 28
2.3  Control and Estimation with Imperfect Information 30
2.4  Best Liner Estimates 39
2.5  Linearized Applications 43
2.6  Partial Optimization 46
References 48

Chapter Three : Stationary Processes 49
3.1  Introduction 50
3.2  Unbiased Linear Filters 51
3.3  Biased Linear Filters 57
3.4  Reduced Order Modeling 66
3.5  Stochastic Control 80
3.6  Controls Which Make Use of Estimates and Observations 90
3.7  A Discrete Control Problem 93
References 102

Chapter Four : Estimation over Finite Time Intervals 103
4.1  Introduction 104
4.2  Optimal Unbiased Estimators of Fixed Order 105
4.3  Partial Optimization of Fixed Order Estimators 117
4.4  Joint Optimization of Both Filter Matrices 126
4.5  Reduced Order Modeling as a Design Aid 129
4.6  Generalized Reduced Order Modeling and Filtering 142
References 154

Chapter Five : Smoothing 157
5.1  Introduction 158
5.2  The Reduced?Order Smoothing Problem 159
5.3  The Backward Filter 160
5.4  The Optimal Reduced?Order Smoother 163
5.5  Example of Reduced?Order Smoother 165
5.6  Summary 168
References 169

Chapter Six : Stochastic Filtering and Control 171
6.1  Introduction 172
6.2  The Basic Stochastic Control Problem 172
6.3  Stochastic Control in the presence of Measurement Noise 177
References 185

Chapter Seven : Linear Two?Point Boundary Value
                 Processes 187
7.1  Introduction 188
7.2  Problem Statement 189
7.3  Least?Square Approach to Smoothing 195
7.4  Reduced?Order Smoother 202
7.5  Two?Filter Form 207
7.6  Smoothing Error 211
7.7  Special Cases 215
   7.7.1  Full order TPBVP Smoother 216
   7.7.2  Reduced Order Separable Systems 217
7.8  Summary 220
References 221

Chapter Eight : Reduced?Order Filtering for Flexible
                Space Structure 223
8.1  Introduction 224
8.2  The Mathematical Model 225
8.3  The Reduced?Order Filtering Problem 228
8.4  The Solution 230
8.5  Velocity Estimation 234
8.6  Biased Reduced?Order Filters 239
8.7  Comments 243
References 244

Chapter Nine : Robust Reduced?Order Filtering 245
9.1  Introduction 246
9.2  Full Order Filtering In an H∞ Setting 246
9.3  Reduced?Order Filtering in an H∞ Setting 255
9.4  Full?Order Discrete filtering in an H∞ Setting 262
9.5  Reduced?Order Discrete Filtering in an H∞ Setting 270
9.6  Reduced?Order Filters for State Dependent Noise 274
9.7  Summary 280
References 283

Chapter Ten : A Reduced?Order H∞ Deconvolution Filter                    Using Bounded Real Lemma 285
10.1  Introduction 286
10.2  Weighted Bounded Real Lemma 287
10.3  Main Results 289
10.4  Special Case of the Reduced?Order H∞ Deconvolution Filter 295
10.5  Examples 297
10.6  Conclusion 305
Appendix 310
References 317

Index / 319