Blind Identification of Structured Dynamic Systems. A Deterministic Perspective

Preface
Contents
Notations
Abbreviations
1 Introduction
	1.1 Examples of the Blind System Identification
	1.2 Optimization Based Blind System Identification
	1.3 Blind Identification of Various System Models
	1.4 Organization of This Book
	References
Part I Preliminaries
2 Linear Algebra and Polynomial Matrices
	2.1 Vector Space and Basis
	2.2 Eigenvalue Decomposition
	2.3 Singular Value Decomposition
	2.4 Orthogonal Projection and Oblique Projection
	2.5 Sum and Intersection of Subspaces
	2.6 Angles Between Subspaces
	2.7 Polynomial Matrices and Polynomial Bases
	2.8 Summary
	References
3 Representation of Linear System Models
	3.1 Transfer Functions
		3.1.1 Properties of Coprime Matrix Fraction
		3.1.2 Verification and Computation of Coprime Matrix Fraction
	3.2 State Space Models
	3.3 State Space Realization
	3.4 Hankel Matrix Interpretation
	3.5 Structured State-Space Models
		3.5.1 Graph Theory
		3.5.2 Structured Algebraic System Theory
	3.6 Summary
	Reference
4 Identification of LTI Systems
	4.1 Least-Squares Identification
		4.1.1 Identifiability of a Rational Transfer Function Matrix
		4.1.2 Least-Squares Identification Method
	4.2 Subspace Identification
		4.2.1 Subspace Identification via Orthogonal Projection
		4.2.2 Subspace Identification via State Estimation
		4.2.3 Subspace Identification via State Compensation
		4.2.4 Subspace Identification via Markov Parameter Estimation
	4.3 Parameterized State-Space Identification
		4.3.1 Gradient-Based Method
		4.3.2 Difference-of-Convex Programming Method
	4.4 Summary
	References
Part II Blind System Identification with a Single Unknown Input
5 Blind Identification of SIMO FIR Systems
	5.1 Structured Subspace Factorization
		5.1.1 Blind Identification of FIR Filters
		5.1.2 Blind Identification of a Source Signal
	5.2 Cross Relation Method
	5.3 Least-Squares Smoothing Method
		5.3.1 Blind FIR Filter Identification
		5.3.2 Blind Source Signal Estimation
	5.4 Blind Identification of Time-Varying FIR Systems
		5.4.1 Input Signal Estimation
		5.4.2 Time-Varying Filter Identification
	5.5 Blind Identification of Nonlinear SIMO Systems
		5.5.1 SIMO-Wiener System Identification
		5.5.2 Hammerstein-Wiener System Identification
	5.6 Summary
	References
6 Blind Identification of SISO IIR Systems via Oversampling
	6.1 Oversampling of FIR and IIR Systems
		6.1.1 Multirate Identities
		6.1.2 Multirate Transfer Functions
		6.1.3 Multirate State-Space Models
	6.2 Coprime Conditions for Lifted SIMO Systems
	6.3 Blind Identification of Non-minimum Phase Systems
	6.4 Blind Identification of Hammerstein Systems
		6.4.1 Blind Identifiability
		6.4.2 Blind Identification Approach
	6.5 Blind Identification of Output Switching Systems
	6.6 Summary
	References
7 Distributed Blind Identification of Networked FIR Systems
	7.1 Motivation for the Distributed Blind Identification
	7.2 Distributed Blind System Identification Using Noise-Free Data
		7.2.1 Distributed Blind Identification Algorithm
		7.2.2 Convergence Analysis
		7.2.3 Numerical Simulation
	7.3 Distributed Blind System Identification Using Noisy Data
		7.3.1 Distributed Blind Identification Algorithm
		7.3.2 Convergence Analysis
		7.3.3 Numerical Simulation
	7.4 Recursive Blind Source Equalization Using Noisy Data
		7.4.1 Direct Distributed Equalization
		7.4.2 Indirect Distributed Equalization
		7.4.3 Distributed Blind Equalization with Noise-Free Measurements
		7.4.4 Distributed Blind Equalization with Noisy Measurements
		7.4.5 Blind Equalization with a Time-Varying Topology
		7.4.6 Numerical Simulation
	7.5 Summary
	References
Part III Blind System Identification with Multiple Unknown Inputs
8 Blind Identification of MIMO Systems
	8.1 Blind Identification of MIMO FIR Systems
		8.1.1 Identifiability Analysis
		8.1.2 Subspace Blind Identification Method
	8.2 Blind Identification of Multivariable State-Space Models
		8.2.1 Identifiability of Two Channel Systems
		8.2.2 Blind Identification of Characteristic Polynomials
		8.2.3 Blind Identification of Numerator Polynomial Matrices
		8.2.4 Numerical Simulation
	8.3 Summary
	References
9 Blind Identification of Structured State-Space Models
	9.1 Strong Observability of Structured State-Space Models
		9.1.1 Maximum Unobservable Subspace
		9.1.2 State Estimation with Unknown Inputs
	9.2 Blind Identification of Multivariable State-Space Models
		9.2.1 Identifiability Analysis
		9.2.2 Subspace-Based Blind Identification Method
		9.2.3 Numerical Simulations
	9.3 Blind System Identification Excited by Different Unknown Inputs
		9.3.1 Identifiability Analysis
		9.3.2 Subspace Identification Method
	9.4 Summary
	References
10 Blind Local Identification of Large-Scale Networked Systems
	10.1 Local Network Identification
	10.2 Subspace Identification Approach
	10.3 Subspace Identification of Unknown Inputs
		10.3.1 Estimation of Completely Unmeasurable Inputs
	10.4 Numerical Simulations
	10.5 Summary
	References
11 Conclusions
	11.1 About the Identification Object
	11.2 About the Identifiability Analysis
	11.3 About the Identification Method
	11.4 Artificial Intelligence Driven Blind System Identification
	References
Index