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