简介
Grewal (California State U. at Fullerton) and Andrews, retired from the Rockwell Science Center, explain the theoretical and practical aspects of Kalman filtering through practice and real world examples, and in this edition include important developments in applications of filtering over the past several years, including adaptations for nonlinear filtering, more robust methods of assessment, and new applications in navigation. They cover linear dynamics systems, random processes and stochastic systems, linear filters and predictors, optimal smoothers, implementation methods, nonlinear filtering, practical considerations, and applications, and include an appendix on matrices. The authors provide all necessary software, making this a text suitable for first year graduate courses on common filtering theory and application, or in a basic course in digital estimation theory and application. This is so well-written it can be used as a self-study guide. Annotation 漏2008 Book News, Inc., Portland, OR (booknews.com)
目录
Preface p. ix
Acknowledgments p. xiii
List of Abbreviations p. xv
General Information p. 1
On Kalman Filtering p. 1
On Optimal Estimation Methods p. 5
On the Notation Used In This Book p. 23
Summary p. 25
Problems p. 26
Linear Dynamic Systems p. 31
Chapter Focus p. 31
Dynamic System Models p. 36
Continuous Linear Systems and Their Solutions p. 40
Discrete Linear Systems and Their Solutions p. 53
Observability of Linear Dynamic System Models p. 55
Summary p. 61
Problems p. 64
Random Processes and Stochastic Systems p. 67
Chapter Focus p. 67
Probability and Random Variables (RVs) p. 70
Statistical Properties of RVs p. 78
Statistical Properties of Random Processes (RPs) p. 80
Linear RP Models p. 88
Shaping Filters and State Augmentation p. 95
Mean and Covariance Propagation p. 99
Relationships Between Model Parameters p. 105
Orthogonality Principle p. 114
Summary p. 118
Problems p. 121
Linear Optimal Filters and Predictors p. 131
Chapter Focus p. 131
Kalman Filter p. 133
Kalman-Bucy Filter p. 144
Optimal Linear Predictors p. 146
Correlated Noise Sources p. 147
Relationships Between Kalman-Bucy and Wiener Filters p. 148
Quadratic Loss Functions p. 149
Matrix Riccati Differential Equation p. 151
Matrix Riccati Equation In Discrete Time p. 165
Model Equations for Transformed State Variables p. 170
Application of Kalman Filters p. 172
Summary p. 177
Problems p. 179
Optimal Smoothers p. 183
Chapter Focus p. 183
Fixed-Interval Smoothing p. 189
Fixed-Lag Smoothing p. 200
Fixed-Point Smoothing p. 213
Summary p. 220
Problems p. 221
Implementation Methods p. 225
Chapter Focus p. 225
Computer Roundoff p. 227
Effects of Roundoff Errors on Kalman Filters p. 232
Factorization Methods for Square-Root Filtering p. 238
Square-Root and UD Filters p. 261
Other Implementation Methods p. 275
Summary p. 288
Problems p. 289
Nonlinear Filtering p. 293
Chapter Focus p. 293
Quasilinear Filtering p. 296
Sampling Methods for Nonlinear Filtering p. 330
Summary p. 345
Problems p. 350
Practical Considerations p. 355
Chapter Focus p. 355
Detecting and Correcting Anomalous Behavior p. 356
Prefiltering and Data Rejection Methods p. 379
Stability of Kalman Filters p. 382
Suboptimal and Reduced-Order Filters p. 383
Schmidt-Kalman Filtering p. 393
Memory, Throughput, and Wordlength Requirements p. 403
Ways to Reduce Computational Requirements p. 409
Error Budgets and Sensitivity Analysis p. 414
Optimizing Measurement Selection Policies p. 419
Innovations Analysis p. 424
Summary p. 425
Problems p. 426
Applications to Navigation p. 427
Chapter Focus p. 427
Host Vehicle Dynamics p. 431
Inertial Navigation Systems (INS) p. 435
Global Navigation Satellite Systems (GNSS) p. 465
Kalman Filters for GNSS p. 470
Loosely Coupled GNSS/INS Integration p. 488
Tightly Coupled GNSS/INS Integration p. 491
Summary p. 507
Problems p. 508
MATLAB Software p. 511
Notice p. 511
General System Requirements p. 511
CD Directory Structure p. 512
MATLAB Software for Chapter 2 p. 512
MATLAB Software for Chapter 3 p. 512
MATLAB Software for Chapter 4 p. 512
MATLAB Software for Chapter 5 p. 513
MATLAB Software for Chapter 6 p. 513
MATLAB Software for Chapter 7 p. 514
MATLAB Software for Chapter 8 p. 515
MATLAB Software for Chapter 9 p. 515
Other Sources of Software p. 516
A Matrix Refresher p. 519
Matrix Forms p. 519
Matrix Operations p. 523
Block Matrix Formulas p. 527
Functions of Square Matrices p. 531
Norms p. 538
Cholesky Decomposition p. 541
Orthogonal Decompositions of Matrices p. 543
Quadratic Forms p. 545
Derivatives of Matrices p. 546
Bibliography p. 549
Index p. 565
Acknowledgments p. xiii
List of Abbreviations p. xv
General Information p. 1
On Kalman Filtering p. 1
On Optimal Estimation Methods p. 5
On the Notation Used In This Book p. 23
Summary p. 25
Problems p. 26
Linear Dynamic Systems p. 31
Chapter Focus p. 31
Dynamic System Models p. 36
Continuous Linear Systems and Their Solutions p. 40
Discrete Linear Systems and Their Solutions p. 53
Observability of Linear Dynamic System Models p. 55
Summary p. 61
Problems p. 64
Random Processes and Stochastic Systems p. 67
Chapter Focus p. 67
Probability and Random Variables (RVs) p. 70
Statistical Properties of RVs p. 78
Statistical Properties of Random Processes (RPs) p. 80
Linear RP Models p. 88
Shaping Filters and State Augmentation p. 95
Mean and Covariance Propagation p. 99
Relationships Between Model Parameters p. 105
Orthogonality Principle p. 114
Summary p. 118
Problems p. 121
Linear Optimal Filters and Predictors p. 131
Chapter Focus p. 131
Kalman Filter p. 133
Kalman-Bucy Filter p. 144
Optimal Linear Predictors p. 146
Correlated Noise Sources p. 147
Relationships Between Kalman-Bucy and Wiener Filters p. 148
Quadratic Loss Functions p. 149
Matrix Riccati Differential Equation p. 151
Matrix Riccati Equation In Discrete Time p. 165
Model Equations for Transformed State Variables p. 170
Application of Kalman Filters p. 172
Summary p. 177
Problems p. 179
Optimal Smoothers p. 183
Chapter Focus p. 183
Fixed-Interval Smoothing p. 189
Fixed-Lag Smoothing p. 200
Fixed-Point Smoothing p. 213
Summary p. 220
Problems p. 221
Implementation Methods p. 225
Chapter Focus p. 225
Computer Roundoff p. 227
Effects of Roundoff Errors on Kalman Filters p. 232
Factorization Methods for Square-Root Filtering p. 238
Square-Root and UD Filters p. 261
Other Implementation Methods p. 275
Summary p. 288
Problems p. 289
Nonlinear Filtering p. 293
Chapter Focus p. 293
Quasilinear Filtering p. 296
Sampling Methods for Nonlinear Filtering p. 330
Summary p. 345
Problems p. 350
Practical Considerations p. 355
Chapter Focus p. 355
Detecting and Correcting Anomalous Behavior p. 356
Prefiltering and Data Rejection Methods p. 379
Stability of Kalman Filters p. 382
Suboptimal and Reduced-Order Filters p. 383
Schmidt-Kalman Filtering p. 393
Memory, Throughput, and Wordlength Requirements p. 403
Ways to Reduce Computational Requirements p. 409
Error Budgets and Sensitivity Analysis p. 414
Optimizing Measurement Selection Policies p. 419
Innovations Analysis p. 424
Summary p. 425
Problems p. 426
Applications to Navigation p. 427
Chapter Focus p. 427
Host Vehicle Dynamics p. 431
Inertial Navigation Systems (INS) p. 435
Global Navigation Satellite Systems (GNSS) p. 465
Kalman Filters for GNSS p. 470
Loosely Coupled GNSS/INS Integration p. 488
Tightly Coupled GNSS/INS Integration p. 491
Summary p. 507
Problems p. 508
MATLAB Software p. 511
Notice p. 511
General System Requirements p. 511
CD Directory Structure p. 512
MATLAB Software for Chapter 2 p. 512
MATLAB Software for Chapter 3 p. 512
MATLAB Software for Chapter 4 p. 512
MATLAB Software for Chapter 5 p. 513
MATLAB Software for Chapter 6 p. 513
MATLAB Software for Chapter 7 p. 514
MATLAB Software for Chapter 8 p. 515
MATLAB Software for Chapter 9 p. 515
Other Sources of Software p. 516
A Matrix Refresher p. 519
Matrix Forms p. 519
Matrix Operations p. 523
Block Matrix Formulas p. 527
Functions of Square Matrices p. 531
Norms p. 538
Cholesky Decomposition p. 541
Orthogonal Decompositions of Matrices p. 543
Quadratic Forms p. 545
Derivatives of Matrices p. 546
Bibliography p. 549
Index p. 565
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