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More About This Title Model-Based Processing: An Applied Subspace Identification Approach
English
A bridge between the application of subspace-based methods for parameter estimation in signal processing and subspace-based system identification in control systems
Model-Based Processing: An Applied Subspace Identification Approach provides expert insight on developing models for designing model-based signal processors (MBSP) employing subspace identification techniques to achieve model-based identification (MBID) and enables readers to evaluate overall performance using validation and statistical analysis methods. Focusing on subspace approaches to system identification problems, this book teaches readers to identify models quickly and incorporate them into various processing problems including state estimation, tracking, detection, classification, controls, communications, and other applications that require reliable models that can be adapted to dynamic environments.
The extraction of a model from data is vital to numerous applications, from the detection of submarines to determining the epicenter of an earthquake to controlling an autonomous vehicles—all requiring a fundamental understanding of their underlying processes and measurement instrumentation. Emphasizing real-world solutions to a variety of model development problems, this text demonstrates how model-based subspace identification system identification enables the extraction of a model from measured data sequences from simple time series polynomials to complex constructs of parametrically adaptive, nonlinear distributed systems. In addition, this resource features:
- Kalman filtering for linear, linearized, and nonlinear systems; modern unscented Kalman filters; as well as Bayesian particle filters
- Practical processor designs including comprehensive methods of performance analysis
- Provides a link between model development and practical applications in model-based signal processing
- Offers in-depth examination of the subspace approach that applies subspace algorithms to synthesized examples and actual applications
- Enables readers to bridge the gap from statistical signal processing to subspace identification
- Includes appendices, problem sets, case studies, examples, and notes for MATLAB
Model-Based Processing: An Applied Subspace Identification Approach is essential reading for advanced undergraduate and graduate students of engineering and science as well as engineers working in industry and academia.
English
JAMES V. CANDY, PHD, is Chief Scientist for Engineering, Distinguished Member of the Technical Staff, and founder of the Center for Advanced Signal & Image Sciences (CASIS), Lawrence Livermore National Laboratory, Livermore, California. Dr. Candy is also Adjunct Full-Professor, University of California, Santa Barbara, a Fellow of the IEEE, and a Fellow of the Acoustical Society of America. He is author of Bayesian Signal Processing: Classical, Modern, and Particle Filtering Methods and Model-Based Signal Processing(John Wiley & Sons, Inc., 2006) and Bayesian Signal Processing: Classical, Modern and Particle Filtering Methods, Second Edition(John Wiley & Sons, Inc., 2016). Dr. Candy was awarded the IEEE Distinguished Technical Achievement Award for his development of model-based signal processing and the Acoustical Society of America Helmholtz-Rayleigh Interdisciplinary Silver Medal for his contributions to acoustical signal processing and underwater acoustics.
English
Preface v
References x
Acknowledgments xiii
Glossary xxiii
1 Introduction 1
1.1 Background 1
1.2 Signal Estimation 2
1.3 Model-based Processing 9
1.4 Model-based Identification 18
1.5 Subspace Identification 22
1.6 Notation and Terminology 25
1.7 Summary 26
References 27
Problems 28
2 Random Signals and Systems 31
2.1 Introduction 31
2.2 Discrete Random Signals 34
2.3 Spectral Representation of Random Signals 41
2.4 Discrete Systems with Random Inputs 45
2.4.1 Spectral Theorems 45
2.4.2 ARMAX Modeling 47
2.5 Spectral Estimation 49
2.5.1 Classical (Nonparametric) Spectral Estimation 50
2.5.1.1 Correlation Method (Blackman-Tukey) 50
2.5.1.2 Average Periodogram Method (Welch) 51
2.5.2 Modern (Parametric) Spectral Estimation 53
2.5.2.1 Autoregressive (All Pole) Spectral Estimation 54
2.5.2.2 Autoregressive Moving Average Spectral Estimation 56
2.5.2.3 Minimum Variance Distortionless Response Spectral Estimation 58
2.5.2.4 Multiple Signal Classification (MUSIC) Spectral Estimation 60
2.6 Case Study: Spectral Estimation of Bandpass Sinusoids 65
2.7 Summary 66
References 68
Problems 70
3 State-Space Models for Identification 75
3.1 Introduction 76
3.2 Continuous-time State-space Models 76
3.3 Sampled-data State-space Models 79
3.4 Discrete-time State-space Models 81
3.4.1 Linear Discrete Time-Invariant Systems 83
3.4.2 Discrete Systems Theory 85
3.4.3 Equivalent Linear Systems 89
3.4.4 Stable Linear Systems 90
3.5 Gauss-Markova State-space Models 90
3.5.1 Discrete-Time Gauss-Markov Models 90
3.6 Innovations Model 97
3.7 State-space Model Structures 98
3.7.1 Time Series Models 98
3.7.2 State-Space and Time-Series Equivalence Models 99
3.8 Nonlinear (Approximate) Gauss-Markova State-space Models 106
3.9 Summary 110
References 112
Problems 113
4 Model-based Processors 119
4.1 Introduction 120
4.2 Linear Model-based Processor: Kalman Filter 120
4.2.1 Innovations Approach 123
4.2.2 Bayesian Approach 128
4.2.3 Innovations Sequence 130
4.2.4 Practical Linear Kalman Filter Design: Performance Analysis 131
4.2.5 Steady-State Kalman Filter 138
4.2.6 Kalman Filter/Wiener Filter Equivalence 142
4.3 Nonlinear State-space Model-based Processors 143
4.3.1 Nonlinear Model-Based Processor: Linearized Kalman Filter 144
4.3.2 Nonlinear Model-Based Processor: Extended Kalman Filter 148
4.3.3 Nonlinear Model-Based Processor: IteratedExtended Kalman Filter 152
4.3.4 Nonlinear Model-Based Processor: Unscented Kalman Filter 158
4.3.5 Practical Nonlinear Model-Based Processor Design: Performance Analysis 164
4.3.6 Nonlinear Model-Based Processor: Particle Filter 167
4.3.7 Practical Bayesian Model-Based Design: Performance Analysis 178
4.4 Case Study: 2dtrackingproblem 183
4.5 Summary 190
References 191
Problems 193
5 Parametrically Adaptive Processors 201
5.1 Introduction 202
5.2 Parametrically Adaptive Processors: Bayesian Approach 202
5.3 Parametrically Adaptive Processors: Nonlinear Kalman Filters 203
5.3.1 Parametric Models 205
5.3.2 Classical Joint State/Parametric Processors: Augmented Extended Kalman Filter 207
5.3.3 Modern Joint State/Parametric Processor: Augmented Unscented Kalman Filter 216
5.4 Parametrically Adaptive Processors: Particle Filter 218
5.4.1 Joint State/Parameter Estimation: Particle Filter 218
5.5 Parametrically Adaptive Processors: Linear Kalman Filter 223
5.6 Case Study: Random Target Tracking 232
5.7 Summary 236
References 241
Problems 244
6 Deterministic Subspace Identification 249
6.1 Introduction 250
6.2 Deterministic Realization Problem 250
6.2.1 Realization Theory 251
6.2.2 Balanced Realizations 256
6.2.3 Systems Theory Summary 257
6.3 Classical Realization 259
6.3.1 Ho-kalman Realization Algorithm 259
6.3.2 SVD Realization Algorithm 261
6.3.2.1 Realization: Linear Time Invariant Mechanical Systems 266
6.3.3 Canonical Realization 268
6.3.3.1 Invariant System Descriptions 271
6.3.3.2 Canonical Realization Algorithm 277
6.4.1 Subspace Realization: Orthogonal Projections 288
6.4.2 Multivariable Output Error State-space (MOESP) Algorithm 293
6.5.1 Subspace Realization: Oblique Projections 301
6.5.2 Numerical Algorithms for Subspace State-space System Identification (N4SID) 303
6.6 Model Order Estimation and Validation 310
6.6.1 Order Estimation: SVD Approach 310
6.6.2 Model Validation 313
6.7 Case Study: Structural Vibration Response 319
6.8 Summary 321
References 324
Problems 328
7 STOCHASTIC SUBSPACE IDENTIFICATION 333
7.1 Introduction 334
7.2 Stochastic Realization Problem 335
7.2.1 Correlated Gauss-Markov Model 335
7.2.2 Gauss-Markov Power Spectrum 337
7.2.3 Gauss-Markov Measurement Covariance 338
7.2.4 Stochastic Realization Theory 339
7.3 Classical Stochastic Realization via the Riccati Equation 341
7.4 Classical Stochastic Realization via Kalman Filter 347
7.4.1 Innovations Model 347
7.4.2 Innovations Power Spectrum 348
7.4.3 Innovations Measurement Covariance 349
7.4.4 Stochastic Realization: Innovations Model 352
7.5 Stochastic Subspace Realization: Orthogonal Projections 357
7.5.1 Multivariable Output Error State-space (MOESP) Algorithm 363
7.6 Stochastic Subspace Realization: Oblique Projections 371
7.6.1 Numerical Algorithms for Subspace State-space System Identification (N4SID) 376
7.6.2 Relationship: Oblique (N4SID) and Orthogonal (MOESP) 383
7.7 Model Order Estimation and Validation 384
7.7.1 Order Estimation: Stochastic Realization Problem 384
7.7.1.1 Order Estimation: Statistical Methods 387
7.7.2 Model Validation 393
7.7.2.1 Residual Testing 394
7.8 Case Study: Vibration Response of a Cylinder: Identification and Tracking 397
7.9 Summary 406
References 410
Problems 413
8 Subspace Processors for Physics-based Application421
8.1 Subspace Identification of a Structural Device 421
8.1.1 State-space Vibrational Systems 422
8.1.2 Deterministic State-space Realizations 426
8.1.3 Vibrational System Processing 429
8.1.4 Application: Vibrating Structural Device 431
8.1.5 Summary 434
8.2 MBID for Scintillator System Characterization436
8.2.1 Gauss-Markov State-space Model 440
8.2.2 Identification of the Scintillator Pulse Shape Model 442
8.2.3 Kalman Filter Design: Scintillation/Photomultiplier System 444
8.2.4 Summary 446
8.3 Parametrically Adaptive Detection of Fission Processes 449
8.3.1 Fission-Based Processing Model 449
8.3.2 Inter-arrival Distribution 450
8.3.3 Sequential Detection 452
8.3.4 Sequential Processor 452
8.3.5 Sequential Detection for Fission Processes 455
8.3.6 Bayesian Parameter Estimation 457
8.3.7 Sequential Bayesian Processor 458
8.3.8 Particle Filter for Fission Processes 460
8.3.9 SNM Detection and Estimation: Synthesized Data 461
8.3.10 Summary 465
8.4 Parametrically Adaptive Processing for Shallow Ocean Application 466
8.4.1 State-space Propagator 467
8.4.1.1 Augmented State-space Models 470
8.4.2 Processors 473
8.4.3 Model-Based Ocean Acoustic Processing 476
8.4.4 Summary 482
8.5 MBID for Chirp Signal Extraction 484
8.5.1 CHIRP-like Signals 484
8.5.2 Model-Based Identification: Linear Chirp Signals 487
8.5.3 Model-Based Identification: FSK Signals 489
8.5.4 Summary 492
References 492
A Probability & Statistics Overview 497
A.1 Probability Theory 497
A.2 Gaussian Random Vectors 503
A.3 Uncorrelated Transformation: Gaussian Random Vectors 504
A.4 Toeplitz Correlation Matrices 505
A.5 Important Processes 505
References 507
B Projection Theory 509
B.1 Projections: Deterministic Spaces 509
B.2 Projections: Random Spaces 510
B.3 Projection: Operators 511
B.3.1 Orthogonal (Perpendicular) Projections 512
B.3.2 Oblique (Parallel) Projections 514
References 515
C Matrix Decompositions 517
C.1 Singular Value Decomposition 517
C.2 QR-Decomposition 519
C.3 LQ-Decomposition 520
References 520
Index 523
