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Filtering and System Identification: A Least Squares Approach Book

Filtering and System Identification: A Least Squares Approach
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Filtering and System Identification: A Least Squares Approach, Filtering and system identification are powerful techniques for building models of complex systems in communications, signal processing, control, and other engineering disciplines. This book discusses the design of reliable numerical methods to retrieve m, Filtering and System Identification: A Least Squares Approach
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  • Filtering and System Identification: A Least Squares Approach
  • Written by author Michel Verhaegen
  • Published by Cambridge University Press, 7/19/2012
  • Filtering and system identification are powerful techniques for building models of complex systems in communications, signal processing, control, and other engineering disciplines. This book discusses the design of reliable numerical methods to retrieve m
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Authors

Preface     xi
Notation and symbols     xiii
List of abbreviations     xv
Introduction     1
Linear algebra     8
Introduction     8
Vectors     9
Matrices     13
Square matrices     18
Matrix decompositions     25
Linear least-squares problems     28
Solution if the matrix F has full column rank     32
Solutions if the matrix F does not have full column rank     33
Weighted linear least-squares problems     35
Summary     37
Discrete-time signals and systems     42
Introduction     42
Signals     43
Signal transforms     47
The z-transform     47
The discrete-time Fourier transform     50
Linear systems     55
Linearization     58
System response and stability     59
Controllability and observability     64
Input-output descriptions     69
Interaction between systems     78
Summary     82
Random variables and signals     87
Introduction     87
Description of arandom variable     88
Experiments and events     90
The probability model     90
Linear functions of a random variable     95
The expected value of a random variable     95
Gaussian random variables     96
Multiple random variables     97
Random signals     100
Expectations of random signals     100
Important classes of random signals     101
Stationary random signals     102
Ergodicity and time averages of random signals     104
Power spectra     105
Properties of least-squares estimates     108
The linear least-squares problem     109
The weighted linear least-squares problem     112
The stochastic linear least-squares problem     113
A square-root solution to the stochastic linear least-squares problem     115
Maximum-likelihood interpretation of the weighted linear least-squares problem     120
Summary     121
Kalman filtering     126
Introduction     127
The asymptotic observer     128
The Kalman-filter problem     133
The Kalman filter and stochastic least squares     135
The Kalman filter and weighted least squares     141
A weighted least-squares problem formulation     141
The measurement update     142
The time update     146
The combined measurement-time update     150
The innovation form representation     152
Fixed-interval smoothing     159
The Kalman filter for LTI systems     162
The Kalman filter for estimating unknown inputs     166
Summary     171
Estimation of spectra and frequency-response functions     178
Introduction     178
The discrete Fourier transform     180
Spectral leakage     185
The FFT algorithm     188
Estimation of signal spectra     191
Estimation of FRFs and disturbance spectra     195
Periodic input sequences     196
General input sequences     198
Estimating the disturbance spectrum     200
Summary     203
Output-error parametric model estimation     207
Introduction     207
Problems in estimating parameters of an LTI state-space model     209
Parameterizing a MIMO LTI state-space model     213
The output normal form     219
The tridiagonal form     226
The output-error cost function     227
Numerical parameter estimation     231
The Gauss-Newton method     233
Regularization in the Gauss-Newton method     237
The steepest descent method     237
Gradient projection     239
Analyzing the accuracy of the estimates     242
Dealing with colored measurement noise     245
Weighted least squares     247
Prediction-error methods     248
Summary     248
Prediction-error parametric model estimation     254
Introduction     254
Prediction-error methods for estimating state-space models     256
Parameterizing an innovation state-space model     257
The prediction-error cost function     259
Numerical parameter estimation     263
Analyzing the accuracy of the estimates     264
Specific model parameterizations for SISO systems     265
The ARMAX and ARX model structures     266
The Box-Jenkins and output-error model structures     271
Qualitative analysis of the model bias for SISO systems     275
Estimation problems in closed-loop systems     283
Summary      286
Subspace model identification     292
Introduction     292
Subspace model identification for deterministic systems     294
The data equation     294
Identification for autonomous systems     297
Identification using impulse input sequences     299
Identification using general input sequences     301
Subspace identification with white measurement noise     307
The use of instrumental variables     312
Subspace identification with colored measurement noise     315
Subspace identification with process and measurement noise     321
The PO-MOESP method     326
Subspace identification as a least-squares problem     329
Estimating the Kalman gain K[subscript T]     333
Relations among different subspace identification methods     334
Using subspace identification with closed-loop data     336
Summary     338
The system-identification cycle     345
Introduction     346
Experiment design     349
Choice of sampling frequency     349
Transient-response analysis     352
Experiment duration     355
Persistency of excitation of the input sequence      356
Types of input sequence     366
Data pre-processing     369
Decimation     369
Detrending the data     370
Pre-filtering the data     372
Concatenating data sequences     373
Selection of the model structure     373
Delay estimation     373
Model-structure selection in ARMAX model estimation     376
Model-structure selection in subspace identification     382
Model validation     387
The auto-correlation test     388
The cross-correlation test     388
The cross-validation test     390
Summary     390
References     395
Index     401


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Filtering and System Identification: A Least Squares Approach, Filtering and system identification are powerful techniques for building models of complex systems in communications, signal processing, control, and other engineering disciplines. This book discusses the design of reliable numerical methods to retrieve m, Filtering and System Identification: A Least Squares Approach

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Filtering and System Identification: A Least Squares Approach, Filtering and system identification are powerful techniques for building models of complex systems in communications, signal processing, control, and other engineering disciplines. This book discusses the design of reliable numerical methods to retrieve m, Filtering and System Identification: A Least Squares Approach

Filtering and System Identification: A Least Squares Approach

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Filtering and System Identification: A Least Squares Approach, Filtering and system identification are powerful techniques for building models of complex systems in communications, signal processing, control, and other engineering disciplines. This book discusses the design of reliable numerical methods to retrieve m, Filtering and System Identification: A Least Squares Approach

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