Contents 1 Introduction 1 1.1 Examples of the Blind System Identification 1 1.2 Optimization Based Blind System Identification 4 1.3 Blind Identification of Various System Models 5 1.4 Organization of This Book 6 References 8 Part I Preliminaries 2 Linear Algebra and Polynomial Matrices 11 2.1 Vector Space and Basis 11 2.2 Eigenvalue Decomposition 13 2.3 Singular Value Decomposition 15 2.4 Orthogonal Projection and Oblique Projection 16 2.5 Sum and Intersection of Subspaces 18 2.6 Angles Between Subspaces 19 2.7 Polynomial Matrices and Polynomial Bases 20 2.8 Summary 24 References 24 3 Representation of Linear System Models 25 3.1 Transfer Functions 25 3.1.1 Properties of Coprime Matrix Fraction 26 3.1.2 Verification and Computation of Coprime Matrix Fraction 28 3.2 State Space Models 31 3.3 State Space Realization 38 3.4 HankelMatrix Interpretation 40 3.5 Structured State-Space Models 41 3.5.1 Graph Theory 42 3.5.2 Structured Algebraic System Theory 44 3.6 Summary 47 Reference 48 4 Identification of LTI Systems 49 4.1 Least-Squares Identification 50 4.1.1 Identifiability of a Rational Transfer Function Matrix 50 4.1.2 Least-Squares Identification Method 51 4.2 Subspace Identification 53 4.2.1 Subspace Identification via Orthogonal Projection 55 4.2.2 Subspace Identification via State Estimation 56 4.2.3 Subspace Identification via State Compensation 59 4.2.4 Subspace Identification via Markov Parameter Estimation 61 4.3 Parameterized State-Space Identification 62 4.3.1 Gradient-BasedMethod 63 4.3.2 Difference-of-Convex Programming Method 64 4.4 Summary 69 References 70 Part II Blind System Identification with a Single Unknown Input 5 Blind Identification of SIMO FIR Systems 73 5.1 Structured Subspace Factorization 74 5.1.1 Blind Identification of FIR Filters 75 5.1.2 Blind Identification of a Source Signal 78 5.2 Cross RelationMethod 80 5.3 Least-Squares Smoothing Method 83 5.3.1 Blind FIR Filter Identification 84 5.3.2 Blind Source Signal Estimation 85 5.4 Blind Identification of Time-Varying FIR Systems 86 5.4.1 Input Signal Estimation 87 5.4.2 Time-Varying Filter Identification 88 5.5 Blind Identification of Nonlinear SIMO Systems 90 5.5.1 SIMO-Wiener System Identification 91 5.5.2 Hammerstein-Wiener System Identification 93 5.6 Summary 94 References 95 6 Blind Identification of SISO IIR Systems via Oversampling 97 6.1 Oversampling of FIR and IIR Systems 98 6.1.1 Multirate Identities 98 6.1.2 Multirate Transfer Functions 99 6.1.3 Multirate State-Space Models 103 6.2 Coprime Conditions for Lifted SIMO Systems 104 6.3 Blind Identification of Non-minimum Phase Systems 108 6.4 Blind Identification of Hammerstein Systems 110 6.4.1 Blind Identifiability 111 6.4.2 Blind Identification Approach 112 6.5 Blind Identification of Output Switching Systems 114 6.6 Summary 125 References 126 7 Distributed Blind Identification of Networked FIR Systems 127 7.1 Motivation for the Distributed Blind Identification 127 7.2 Distributed Blind System Identification Using Noise-Free Data 128 7.2.1 Distributed Blind Identification Algorithm 129 7.2.2 Convergence Analysis 131 7.2.3 Numerical Simulation 136 7.3 Distributed Blind System Identification Using Noisy Data 138 7.3.1 Distributed Blind Identification Algorithm 139 7.3.2 Convergence Analysis 140 7.3.3 Numerical Simulation 147 7.4 Recursive Blind Source Equalization Using Noisy Data 148 7.4.1 Direct Distributed Equalization 149 7.4.2 Indirect Distributed Equalization 151 7.4.3 Distributed Blind Equalization with Noise-Free Measurements 152 7.4.4 Distributed Blind Equalization with Noisy Measurements 156 7.4.5 Blind Equalization with a Time-Varying Topology 157 7.4.6 Numerical Simulation 159 7.5 Summary 162 References 163 Part III Blind System Identification with Multiple Unknown Inputs 8 Blind Identification of MIMO Systems 167 8.1 Blind Identification ofMIMO FIR Systems 167 8.1.1 Identifiability Analysis 169 8.1.2 Subspace Blind Identification Method 171 8.2 Blind Identification of Multivariable State-Space Models 173 8.2.1 Identifiability of Two Channel Systems 174 8.2.2 Blind Identification of Characteristic Polynomials 179 8.2.3 Blind Identification of Numerator Polynomial Matrices 183 8.2.4 Numerical Simulation 192 8.3 Summary 197 References 198 9 Blind Identification of Structured State-Space Models 199 9.1 Strong Observability of Structured State-Space Models 199 9.1.1 Maximum Unobservable Subspace 200 9.1.2 State Estimation with Unknown Inputs 202 9.2 Blind Identification of Multivariable State-Space Models 204 9.2.1 Identifiability Analysis 206 9.2.2 Subspace-Based Blind Identification Method 215 9.2.3 Numerical Simulations 220 9.3
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