Identification of time-varying processes / Maciej Niedźwiecki.

By:

Niedźwiecki, Maciej

Material type: Text

text

Media type:

unmediated

Carrier type:

volume

ISBN:

0471986291 (acidfree paper)

Subject(s):

DDC classification:

621.3822 21 N.M.I

Online resources:

Contents:

1 Modeling Essentials 1 -- 1.1 Physical and instrumental approaches to modeling 1 -- 1.2 Titius--Bode law and the method of least sqares 7 -- 1.3 Principle of parsimony 8 -- 1.4 Mathematical models of stationary processes 9 -- 1.4.1 Autoregressive model 10 -- 1.4.2 Moving average model 18 -- 1.4.3 Equivalence of autoregressive and moving average models 24 -- 1.4.4 Mixed autoregressive moving average model 27 -- 1.4.5 A bridge to continuous-time processes 28 -- 1.4.6 Models with exogenous inputs 31 -- 1.4.7 Shorthand notation 31 -- 1.5 Model-based approach to adaptive signal processing and control 32 -- 1.5.1 Prediction 33 -- 1.5.2 Predictive coding of signals 34 -- 1.5.3 Detection and elimination of outliers 36 -- 1.5.4 Equalization of communication channels 40 -- 1.5.5 Spectrum estimation 42 -- 1.5.6 Adaptive control 47 -- 2 Models of Nonstationary Processes 51 -- 2.1 Origins of time dependence 51 -- 2.2 Characteristics of nonstationary processes 52 -- 2.3 Irreducible nonstationary processes and parameter tracking 55 -- 2.4 Measures of tracking ability 56 -- 2.5 Prior knowledge in identification of nonstationary processes 60 -- 2.5.1 Events and auxiliary measurements 61 -- 2.5.2 Probabilistic models 61 -- 2.5.3 Deterministic models 63 -- 2.6 Slowly varying systems and the concept of local stationarity 64 -- 2.7 Rate of process time variation 66 -- 2.7.1 Speed of variation and sampling frequency 66 -- 2.7.2 Nonstationarity degree 67 -- 2.8 Assumptions 70 -- 2.8.1 Dependence among regressors 70 -- 2.8.2 Dependence between system variables 71 -- 2.8.3 Persistence of excitation 71 -- 2.8.4 Boundedness of system variables 72 -- 2.8.5 Variation of system parameters 73 -- 2.9 About computer simulations 74 -- 3 Process Segmentation 79 -- 3.1 Nonadaptive segmentation 79 -- 3.1.1 Conditions of identifiability 80 -- 3.1.2 Recursive least squares algorithm 82 -- 3.2 Adaptive segmentation 86 -- 3.2.1 Segmentation based on the Akaike criterion 86 -- 3.2.2 Segmentation based on the generalized likelihood ratio test 93 -- 3.3 Extension to ARMAX processes 95 -- 3.3.1 Iterative estimation algorithms 95 -- 3.3.2 Recursive estimation algorithms 98 -- 3.3.3 Conditions of identifiability 100 -- 3.3.4 Adaptive segmentation 100 -- 4 Weighted Least Squares 103 -- 4.1 Estimation principles 103 -- 4.2 Estimation windows 104 -- 4.3 Static characteristics of WLS estimators 105 -- 4.3.1 Effective window width 106 -- 4.3.2 Equivalent window width 106 -- 4.3.3 Degree of window concentration 108 -- 4.4 Dynamic time-domain characteristics of WLS estimators 108 -- 4.4.1 Impulse response associated with WLS estimators 109 -- 4.4.2 Variability of WLS estimators 111 -- 4.5 Dynamic frequency-domain characteristics of WLS estimators 112 -- 4.5.1 Frequency characteristics associated with WLS estimators 112 -- 4.5.2 Properties of associated frequency characteristics 113 -- 4.5.3 Estimation delay of WLS estimators 115 -- 4.5.4 Matching characteristics of WLS estimators 117 -- 4.6 Principle of uncertainty 118 -- 4.7 Comparison of the EWLS and SWLS approaches 119 -- 4.8 Technical issues 122 -- 4.9 Computer simulations 125 -- 4.10 Extension to ARMAX processes 136 -- 5 Least Mean Squares 139 -- 5.1 Estimation principles 139 -- 5.2 Convergence and stability of LMS algorithms 141 -- 5.2.1 Analysis for independent regressors 143 -- 5.2.2 Analysis for dependent regressors 146 -- 5.3 Static characteristics of LMS estimators 148 -- 5.3.1 Equivalent memory of LMS estimators 149 -- 5.3.2 Normalized LMS estimators 153 -- 5.4 Dynamic characteristics of LMS estimators 154 -- 5.4.1 Impulse response associated with LMS estimators 154 -- 5.4.2 Frequency response associated with LMS estimators 155 -- 5.5 Comparison of the EWLS and LMS. estimators 156 -- 5.5.1 Initial convergence 156 -- 5.5.2 Tracking performance 159 -- 5.6 Computer simulations 166 -- 5.7 Extension to ARMAX processes 177 --

6.1 Approach based on process segmentation 179 -- 6.1.1 Estimation principles 179 -- 6.1.2 Invariance under the change of coordinates 183 -- 6.1.3 Static characteristics of BF estimators 186 -- 6.1.4 Dynamic characteristics of BF estimators 188 -- 6.1.5 Impulse response associated with BF estimators 190 -- 6.1.6 Frequency response associated with BF estimators 191 -- 6.1.7 Properties of the associated frequency characteristics 193 -- 6.1.8 Comparing the matching properties of different BF estimators 196 -- 6.2 Weighted basis function estimation 199 -- 6.2.1 Estimation principles 199 -- 6.2.2 Recursive WBF estimators 203 -- 6.2.3 Static characteristics of WBF estimators 205 -- 6.2.4 Impulse response associated with WBF estimators 209 -- 6.2.5 Frequency response associated with WBF estimators 210 -- 6.3 Computer simulations 215 -- 6.4 Method of basis functions: good news or bad news? 215 -- 7 Kalman Filtering 229 -- 7.1 Estimation principles 229 -- 7.2 Estimation based on the random walk model 231 -- 7.3 Estimation based on the integrated random walk models 234 -- 7.4 Stability and convergence of the RWKF algorithm 236 -- 7.5 Estimation memory of the RWKF algorithm 237 -- 7.6 Dynamic characteristics of RWKF estimators 242 -- 7.6.1 Impulse response associated with RWKF estimators 242 -- 7.6.2 Frequency response associated with RWKF estimators 243 -- 7.7 Convergence and tracking performance of RWKF estimators 244 -- 7.7.1 Initial convergence 244 -- 7.7.2 Tracking performance 244 -- 7.8 Parameter matching using the Kalman smoothing approach 247 -- 7.8.1 Fixed interval smoothing 248 -- 7.8.2 Fixed lag smoothing 249 -- 7.9 Computer simulations 250 -- 7.10 Extension to ARMAX processes 261 -- 8 Practical Issues 265 -- 8.1 Numerical safeguards 265 -- 8.1.1 Least squares algorithms 265 -- 8.1.2 Gradient algorithms 281 -- 8.1.3 Kalman filter algorithms 284 -- 8.2 Optimization 287 -- 8.2.1 Memory optimization 287 -- 8.2.2 Other optimization issues 297.

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Item type	Current library	Collection	Call number	Status	Date due	Barcode
Books	Main library B3	Faculty of Engineering & Technology (Electrical)	621.3822 N.M.I (Browse shelf(Opens below))	Available		00002936
Books	Main library B3	Faculty of Engineering & Technology (Electrical)	621.3822 N.M.I (Browse shelf(Opens below))	Available		00002935

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Includes bibliographical references (pages [309]-320) and index.

1 Modeling Essentials 1 --
1.1 Physical and instrumental approaches to modeling 1 --
1.2 Titius--Bode law and the method of least sqares 7 --
1.3 Principle of parsimony 8 --
1.4 Mathematical models of stationary processes 9 --
1.4.1 Autoregressive model 10 --
1.4.2 Moving average model 18 --
1.4.3 Equivalence of autoregressive and moving average models 24 --
1.4.4 Mixed autoregressive moving average model 27 --
1.4.5 A bridge to continuous-time processes 28 --
1.4.6 Models with exogenous inputs 31 --
1.4.7 Shorthand notation 31 --
1.5 Model-based approach to adaptive signal processing and control 32 --
1.5.1 Prediction 33 --
1.5.2 Predictive coding of signals 34 --
1.5.3 Detection and elimination of outliers 36 --
1.5.4 Equalization of communication channels 40 --
1.5.5 Spectrum estimation 42 --
1.5.6 Adaptive control 47 --
2 Models of Nonstationary Processes 51 --
2.1 Origins of time dependence 51 --
2.2 Characteristics of nonstationary processes 52 --
2.3 Irreducible nonstationary processes and parameter tracking 55 --
2.4 Measures of tracking ability 56 --
2.5 Prior knowledge in identification of nonstationary processes 60 --
2.5.1 Events and auxiliary measurements 61 --
2.5.2 Probabilistic models 61 --
2.5.3 Deterministic models 63 --
2.6 Slowly varying systems and the concept of local stationarity 64 --
2.7 Rate of process time variation 66 --
2.7.1 Speed of variation and sampling frequency 66 --
2.7.2 Nonstationarity degree 67 --
2.8 Assumptions 70 --
2.8.1 Dependence among regressors 70 --
2.8.2 Dependence between system variables 71 --
2.8.3 Persistence of excitation 71 --
2.8.4 Boundedness of system variables 72 --
2.8.5 Variation of system parameters 73 --
2.9 About computer simulations 74 --
3 Process Segmentation 79 --
3.1 Nonadaptive segmentation 79 --
3.1.1 Conditions of identifiability 80 --
3.1.2 Recursive least squares algorithm 82 --
3.2 Adaptive segmentation 86 --
3.2.1 Segmentation based on the Akaike criterion 86 --
3.2.2 Segmentation based on the generalized likelihood ratio test 93 --
3.3 Extension to ARMAX processes 95 --
3.3.1 Iterative estimation algorithms 95 --
3.3.2 Recursive estimation algorithms 98 --
3.3.3 Conditions of identifiability 100 --
3.3.4 Adaptive segmentation 100 --
4 Weighted Least Squares 103 --
4.1 Estimation principles 103 --
4.2 Estimation windows 104 --
4.3 Static characteristics of WLS estimators 105 --
4.3.1 Effective window width 106 --
4.3.2 Equivalent window width 106 --
4.3.3 Degree of window concentration 108 --
4.4 Dynamic time-domain characteristics of WLS estimators 108 --
4.4.1 Impulse response associated with WLS estimators 109 --
4.4.2 Variability of WLS estimators 111 --
4.5 Dynamic frequency-domain characteristics of WLS estimators 112 --
4.5.1 Frequency characteristics associated with WLS estimators 112 --
4.5.2 Properties of associated frequency characteristics 113 --
4.5.3 Estimation delay of WLS estimators 115 --
4.5.4 Matching characteristics of WLS estimators 117 --
4.6 Principle of uncertainty 118 --
4.7 Comparison of the EWLS and SWLS approaches 119 --
4.8 Technical issues 122 --
4.9 Computer simulations 125 --
4.10 Extension to ARMAX processes 136 --
5 Least Mean Squares 139 --
5.1 Estimation principles 139 --
5.2 Convergence and stability of LMS algorithms 141 --
5.2.1 Analysis for independent regressors 143 --
5.2.2 Analysis for dependent regressors 146 --
5.3 Static characteristics of LMS estimators 148 --
5.3.1 Equivalent memory of LMS estimators 149 --
5.3.2 Normalized LMS estimators 153 --
5.4 Dynamic characteristics of LMS estimators 154 --
5.4.1 Impulse response associated with LMS estimators 154 --
5.4.2 Frequency response associated with LMS estimators 155 --
5.5 Comparison of the EWLS and LMS. estimators 156 --
5.5.1 Initial convergence 156 --
5.5.2 Tracking performance 159 --
5.6 Computer simulations 166 --
5.7 Extension to ARMAX processes 177 --

6.1 Approach based on process segmentation 179 --
6.1.1 Estimation principles 179 --
6.1.2 Invariance under the change of coordinates 183 --
6.1.3 Static characteristics of BF estimators 186 --
6.1.4 Dynamic characteristics of BF estimators 188 --
6.1.5 Impulse response associated with BF estimators 190 --
6.1.6 Frequency response associated with BF estimators 191 --
6.1.7 Properties of the associated frequency characteristics 193 --
6.1.8 Comparing the matching properties of different BF estimators 196 --
6.2 Weighted basis function estimation 199 --
6.2.1 Estimation principles 199 --
6.2.2 Recursive WBF estimators 203 --
6.2.3 Static characteristics of WBF estimators 205 --
6.2.4 Impulse response associated with WBF estimators 209 --
6.2.5 Frequency response associated with WBF estimators 210 --
6.3 Computer simulations 215 --
6.4 Method of basis functions: good news or bad news? 215 --
7 Kalman Filtering 229 --
7.1 Estimation principles 229 --
7.2 Estimation based on the random walk model 231 --
7.3 Estimation based on the integrated random walk models 234 --
7.4 Stability and convergence of the RWKF algorithm 236 --
7.5 Estimation memory of the RWKF algorithm 237 --
7.6 Dynamic characteristics of RWKF estimators 242 --
7.6.1 Impulse response associated with RWKF estimators 242 --
7.6.2 Frequency response associated with RWKF estimators 243 --
7.7 Convergence and tracking performance of RWKF estimators 244 --
7.7.1 Initial convergence 244 --
7.7.2 Tracking performance 244 --
7.8 Parameter matching using the Kalman smoothing approach 247 --
7.8.1 Fixed interval smoothing 248 --
7.8.2 Fixed lag smoothing 249 --
7.9 Computer simulations 250 --
7.10 Extension to ARMAX processes 261 --
8 Practical Issues 265 --
8.1 Numerical safeguards 265 --
8.1.1 Least squares algorithms 265 --
8.1.2 Gradient algorithms 281 --
8.1.3 Kalman filter algorithms 284 --
8.2 Optimization 287 --
8.2.1 Memory optimization 287 --
8.2.2 Other optimization issues 297.

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