TY - BOOK AU - Niedźwiecki,Maciej TI - Identification of time-varying processes SN - 0471986291 (acidfree paper) U1 - 621.3822 21 PY - 2000///] CY - Chichester, New York PB - Wiley KW - Adaptive signal processing KW - Signal processing KW - Digital techniques KW - Time-series analysis N1 - 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 UR - http://www.loc.gov/catdir/description/wiley036/00033019.html UR - http://www.loc.gov/catdir/toc/onix07/00033019.html ER -