Model-Based Processing

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.

• Preface xiiiAcknowledgements xxiGlossary xxiii1 Introduction 11.1 Background 11.2 Signal Estimation 21.3 Model-Based Processing 81.4 Model-Based Identification 161.5 Subspace Identification 201.6 Notation and Terminology 221.7 Summary 24MATLAB Notes 25References 25Problems 262 Random Signals and Systems 292.1 Introduction 292.2 Discrete Random Signals 322.3 Spectral Representation of Random Signals 362.4 Discrete Systems with Random Inputs 402.4.1 Spectral Theorems 412.4.2 ARMAX Modeling 422.5 Spectral Estimation 442.5.1 Classical (Nonparametric) Spectral Estimation 442.5.1.1 Correlation Method (Blackman–Tukey) 452.5.1.2 Average Periodogram Method (Welch) 462.5.2 Modern (Parametric) Spectral Estimation 472.5.2.1 Autoregressive (All-Pole) Spectral Estimation 482.5.2.2 Autoregressive Moving Average Spectral Estimation 512.5.2.3 Minimum Variance Distortionless Response (MVDR) Spectral Estimation 522.5.2.4 Multiple Signal Classification (MUSIC) Spectral Estimation 552.6 Case Study: Spectral Estimation of Bandpass Sinusoids 592.7 Summary 61MATLAB Notes 61References 62Problems 643 State-Space Models for Identification 693.1 Introduction 693.2 Continuous-Time State-Space Models 693.3 Sampled-Data State-Space Models 733.4 Discrete-Time State-Space Models 743.4.1 Linear Discrete Time-Invariant Systems 773.4.2 Discrete Systems Theory 783.4.3 Equivalent Linear Systems 823.4.4 Stable Linear Systems 833.5 Gauss–Markov State-Space Models 833.5.1 Discrete-Time Gauss–Markov Models 833.6 Innovations Model 893.7 State-Space Model Structures 903.7.1 Time-Series Models 913.7.2 State-Space and Time-Series Equivalence Models 913.8 Nonlinear (Approximate) Gauss–Markov State-Space Models 973.9 Summary 101MATLAB Notes 102References 102Problems 1034 Model-Based Processors 1074.1 Introduction 1074.2 Linear Model-Based Processor: Kalman Filter 1084.2.1 Innovations Approach 1104.2.2 Bayesian Approach 1144.2.3 Innovations Sequence 1164.2.4 Practical Linear Kalman Filter Design: Performance Analysis 1174.2.5 Steady-State Kalman Filter 1254.2.6 Kalman Filter/Wiener Filter Equivalence 1284.3 Nonlinear State-Space Model-Based Processors 1294.3.1 Nonlinear Model-Based Processor: Linearized Kalman Filter 1304.3.2 Nonlinear Model-Based Processor: Extended Kalman Filter 1334.3.3 Nonlinear Model-Based Processor: Iterated–Extended Kalman Filter 1384.3.4 Nonlinear Model-Based Processor: Unscented Kalman Filter 1414.3.5 Practical Nonlinear Model-Based Processor Design: Performance Analysis 1484.3.6 Nonlinear Model-Based Processor: Particle Filter 1514.3.7 Practical Bayesian Model-Based Design: Performance Analysis 1604.4 Case Study: 2D-Tracking Problem 1664.5 Summary 173MATLAB Notes 173References 174Problems 1775 Parametrically Adaptive Processors 1855.1 Introduction 1855.2 Parametrically Adaptive Processors: Bayesian Approach 1865.3 Parametrically Adaptive Processors: Nonlinear Kalman Filters 1875.3.1 Parametric Models 1885.3.2 Classical Joint State/Parametric Processors: Augmented Extended Kalman Filter 1905.3.3 Modern Joint State/Parametric Processor: Augmented Unscented Kalman Filter 1985.4 Parametrically Adaptive Processors: Particle Filter 2015.4.1 Joint State/Parameter Estimation: Particle Filter 2015.5 Parametrically Adaptive Processors: Linear Kalman Filter 2085.6 Case Study: Random Target Tracking 2145.7 Summary 222MATLAB Notes 223References 223Problems 2266 Deterministic Subspace Identification 2316.1 Introduction 2316.2 Deterministic Realization Problem 2326.2.1 Realization Theory 2336.2.2 Balanced Realizations 2386.2.3 Systems Theory Summary 2396.3 Classical Realization 2416.3.1 Ho–Kalman Realization Algorithm 2416.3.2 SVD Realization Algorithm 2436.3.2.1 Realization: Linear Time-Invariant Mechanical Systems 2466.3.3 Canonical Realization 2516.3.3.1 Invariant System Descriptions 2516.3.3.2 Canonical Realization Algorithm 2576.4 Deterministic Subspace Realization: Orthogonal Projections 2646.4.1 Subspace Realization: Orthogonal Projections 2666.4.2 Multivariable Output Error State-Space (MOESP) Algorithm 2716.5 Deterministic Subspace Realization: Oblique Projections 2746.5.1 Subspace Realization: Oblique Projections 2786.5.2 Numerical Algorithms for Subspace State-Space System Identification (N4SID) Algorithm 2806.6 Model Order Estimation and Validation 2856.6.1 Order Estimation: SVD Approach 2866.6.2 Model Validation 2896.7 Case Study: Structural Vibration Response 2956.8 Summary 299MATLAB Notes 300References 300Problems 3037 Stochastic Subspace Identification 3097.1 Introduction 3097.2 Stochastic Realization Problem 3127.2.1 Correlated Gauss–Markov Model 3127.2.2 Gauss–Markov Power Spectrum 3137.2.3 Gauss–Markov Measurement Covariance 3147.2.4 Stochastic Realization Theory 3157.3 Classical Stochastic Realization via the Riccati Equation 3177.4 Classical Stochastic Realization via Kalman Filter 3217.4.1 Innovations Model 3217.4.2 Innovations Power Spectrum 3227.4.3 Innovations Measurement Covariance 3237.4.4 Stochastic Realization: Innovations Model 3257.5 Stochastic Subspace Realization: Orthogonal Projections 3307.5.1 Multivariable Output Error State-SPace (MOESP) Algorithm 3347.6 Stochastic Subspace Realization: Oblique Projections 3427.6.1 Numerical Algorithms for Subspace State-Space System Identification (N4SID) Algorithm 3467.6.2 Relationship: Oblique (N4SID) and Orthogonal (MOESP) Algorithms 3517.7 Model Order Estimation and Validation 3537.7.1 Order Estimation: Stochastic Realization Problem 3547.7.1.1 Order Estimation: Statistical Methods 3567.7.2 Model Validation 3627.7.2.1 Residual Testing 3637.8 Case Study: Vibration Response of a Cylinder: Identification and Tracking 3697.9 Summary 378MATLAB NOTES 378References 379Problems 3828 Subspace Processors for Physics-Based Application 3918.1 Subspace Identification of a Structural Device 3918.1.1 State-Space Vibrational Systems 3928.1.1.1 State-Space Realization 3948.1.2 Deterministic State-Space Realizations 3968.1.2.1 Subspace Approach 3968.1.3 Vibrational System Processing 3988.1.4 Application: Vibrating Structural Device 4008.1.5 Summary 4048.2 MBID for Scintillator System Characterization 4058.2.1 Scintillation Pulse Shape Model 4078.2.2 Scintillator State-Space Model 4098.2.3 Scintillator Sampled-Data State-Space Model 4108.2.4 Gauss–Markov State-Space Model 4118.2.5 Identification of the Scintillator Pulse Shape Model 4128.2.6 Kalman Filter Design: Scintillation/Photomultiplier System 4148.2.6.1 Kalman Filter Design: Scintillation/Photomultiplier Data 4168.2.7 Summary 4178.3 Parametrically Adaptive Detection of Fission Processes 4188.3.1 Fission-Based Processing Model 4198.3.2 Interarrival Distribution 4208.3.3 Sequential Detection 4228.3.4 Sequential Processor 4228.3.5 Sequential Detection for Fission Processes 4248.3.6 Bayesian Parameter Estimation 4268.3.7 Sequential Bayesian Processor 4278.3.8 Particle Filter for Fission Processes 4298.3.9 SNM Detection and Estimation: Synthesized Data 4308.3.10 Summary 4338.4 Parametrically Adaptive Processing for Shallow Ocean Application 4358.4.1 State-Space Propagator 4368.4.2 State-Space Model 4368.4.2.1 Augmented State-Space Models 4388.4.3 Processors 4418.4.4 Model-Based Ocean Acoustic Processing 4448.4.4.1 Adaptive PF Design: Modal Coefficients 4458.4.4.2 Adaptive PF Design: Wavenumbers 4478.4.5 Summary 4508.5 MBID for Chirp Signal Extraction 4528.5.1 Chirp-like Signals 4538.5.1.1 Linear Chirp 4538.5.1.2 Frequency-Shift Key (FSK) Signal 4558.5.2 Model-Based Identification: Linear Chirp Signals 4578.5.2.1 Gauss–Markov State-Space Model: Linear Chirp 4578.5.3 Model-Based Identification: FSK Signals 4598.5.3.1 Gauss–Markov State-Space Model: FSK Signals 4608.5.4 Summary 462References 462Appendix A Probability and Statistics Overview 467A.1 Probability Theory 467A.2 Gaussian Random Vectors 473A.3 Uncorrelated Transformation: Gaussian Random Vectors 473A.4 Toeplitz Correlation Matrices 474A.5 Important Processes 474References 476Appendix B Projection Theory 477B.1 Projections: Deterministic Spaces 477B.2 Projections: Random Spaces 478B.3 Projection: Operators 479B.3.1 Orthogonal (Perpendicular) Projections 479B.3.2 Oblique (Parallel) Projections 481References 483Appendix C Matrix Decompositions 485C.1 Singular-Value Decomposition 485C.2 QR-Decomposition 487C.3 LQ-Decomposition 487References 488Appendix D Output-Only Subspace Identification 489References 492Index 495