Rajamani Doraiswami, Professor Emeritus, Electrical and Computer Engineering Department, University of New Brunswick, USARajamani Doraiswami is Professor Emeritus in the Department of Electrical and Computer Engineering at the University of New Brunswick.Dr. Doraiswami is known internationally as an excellent researcher, has held an NSERC operating grant continually since 1981 and has published more than 60 papers in refereed journals and 90 conference papers.

Identification of a physical system deals with the problem ofidentifying its mathematical model using the measured input andoutput data. As the physical system is generally complex,nonlinear, and its input-output data is corrupted noise,there are fundamental theoretical and practical issues that need tobe considered.

Preface xv
 
Nomenclature xxi
 
1 Modeling of Signals and Systems 1
 
1.1 Introduction 1
 
1.2 Classification of Signals 2
 
1.3 Model of Systems and Signals 5
 
1.4 Equivalence of Input-Output and State-Space Models 8
 
1.5 Deterministic Signals 11
 
1.6 Introduction to Random Signals 23
 
1.7 Model of Random Signals 28
 
1.8 Model of a System with Disturbance and Measurement Noise 41
 
1.9 Summary 50
 
References 54
 
Further Readings 54
 
2 Characterization of Signals: Correlation and Spectral Density 57
 
2.1 Introduction 57
 
2.2 Definitions of Auto- and Cross-Correlation (and Covariance) 58
 
2.3 Spectral Density: Correlation in the Frequency Domain 67
 
2.4 Coherence Spectrum 74
 
2.5 Illustrative Examples in Correlation and Spectral Density 76
 
2.6 Input-Output Correlation and Spectral Density 91
 
2.7 Illustrative Examples: Modeling and Identification 98
 
2.8 Summary 109
 
2.9 Appendix 112
 
References 116
 
3 Estimation Theory 117
 
3.1 Overview 117
 
3.2 Map Relating Measurement and the Parameter 119
 
3.3 Properties of Estimators 123
 
3.4 Cramér-Rao Inequality 127
 
3.5 Maximum Likelihood Estimation 139
 
3.6 Summary 154
 
3.7 Appendix: Cauchy-Schwarz Inequality 157
 
3.8 Appendix: Cram´er-Rao Lower Bound 157
 
3.9 Appendix: Fisher Information: Cauchy PDF 161
 
3.10 Appendix: Fisher Information for i.i.d. PDF 161
 
3.11 Appendix: Projection Operator 162
 
3.12 Appendix: Fisher Information: Part Gauss-Part Laplace 164
 
Problem 165
 
References 165
 
Further Readings 165
 
4 Estimation of Random Parameter 167
 
4.1 Overview 167
 
4.2 Minimum Mean-Squares Estimator (MMSE): Scalar Case 167
 
4.3 MMSE Estimator: Vector Case 169
 
4.4 Expression for Conditional Mean 172
 
4.5 Summary 183
 
4.6 Appendix: Non-Gaussian Measurement PDF 184
 
References 188
 
Further Readings 188
 
5 Linear Least-Squares Estimation 189
 
5.1 Overview 189
 
5.2 Linear Least-Squares Approach 189
 
5.3 Performance of the Least-Squares Estimator 195
 
5.4 Illustrative Examples 205
 
5.5 Cram´er-Rao Lower Bound 209
 
5.6 Maximum Likelihood Estimation 210
 
5.7 Least-Squares Solution of Under-Determined System 212
 
5.8 Singular Value Decomposition 213
 
5.9 Summary 218
 
5.10 Appendix: Properties of the Pseudo-Inverse and the Projection Operator 221
 
5.11 Appendix: Positive Definite Matrices 222
 
5.12 Appendix: Singular Value Decomposition of a Matrix 223
 
5.13 Appendix: Least-Squares Solution for Under-Determined System 228
 
5.14 Appendix: Computation of Least-Squares Estimate Using the SVD 229
 
References 229
 
Further Readings 230
 
6 Kalman Filter 231
 
6.1 Overview 231
 
6.2 Mathematical Model of the System 233
 
6.3 Internal Model Principle 236
 
6.4 Duality Between Controller and an Estimator Design 244
 
6.5 Observer: Estimator for the States of a System 246
 
6.6 Kalman Filter: Estimator of the States of a Stochastic System 250
 
6.7 The Residual of the Kalman Filter with Model Mismatch and Non-Optimal Gain 267
 
6.8 Summary 274
 
6.9 Appendix: Estimation Error Covariance and the Kalman Gain 277
 
6.10 Appendix: The Role of the Ratio of Plant and the Measurement Noise Variances 279
 
6.11

Identification of a physical system deals with the problem of identifying its mathematical model using the measured input and output data. As the physical system is generally complex, nonlinear, and its input-output data is corrupted noise, there are fundamental theoretical and practical issues that need to be considered.
 
Identification of Physical Systems addresses this need, presenting a systematic, unified approach to the problem of physical system identification and its practical applications. Starting with a least-squares method, the authors develop various schemes to address the issues of accuracy, variation in the operating regimes, closed loop, and interconnected subsystems. Also presented is a non-parametric signal or data-based scheme to identify a means to provide a quick macroscopic picture of the system to complement the precise microscopic picture given by the parametric model-based scheme. Finally, a sequential integration of totally different schemes, such as non-parametric, Kalman filter, and parametric model, is developed to meet the speed and accuracy requirement of mission-critical systems.
 

Key features:
* Provides a clear understanding of theoretical and practical issues in identification and its applications, enabling the reader to grasp a clear understanding of the theory and apply it to practical problems
* Offers a self-contained guide by including the background necessary to understand this interdisciplinary subject
* Includes case studies for the application of identification on physical laboratory scale systems, as well as number of illustrative examples throughout the book
 
Identification of Physical Systems is a comprehensive reference for researchers and practitioners working in this field and is also a useful source of information for graduate students in electrical, computer, biomedical, chemical, and mechanical engineering.