Identification of Time-varying Processes

by Maciej Niedź wiecki (Technical Univ. of Gda)

• ISBN13: 9780471986294
• ISBN10: 0471986291
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-08-22
• Publisher: WILEY

Summary

Essential reading for adaptive signal processing engineers, researchers, lecturers and senior electrical engineering and computer science students in telecommunications and signal processing.

Author Biography

Maciej Niedzwiecki was born in Poznan, Poland in 1953. He received the M.Sc. and Ph.D. degrees from the Gdansk University of Technology, Gdansk, Poland, and the Dr.Hab. - D.Sc. - degree from the Technical University of Warsaw, Warsaw, Poland, in 1977, 1981 and 1991, respectively.

Table of Contents

Preface	xi
Acknowledgments	xv
Modeling Essentials	1	(50)
Physical and instrumental approaches to modeling	1	(6)
The Titius-Bode law and the method of least sqares	7	(1)
The principle of parsimony	8	(1)
Mathematical models of stationary processes	9	(23)
Autoregressive model	10	(8)
Moving average model	18	(6)
Equivalence of autoregressive and moving average models	24	(3)
Mixed autoregressive moving average model	27	(1)
A bridge to continuous-time processes	28	(3)
Models with exogenous inputs	31	(1)
The shorthand notation	31	(1)
The model-based approach to adaptive signal processing and control	32	(19)
Prediction	33	(1)
Predictive coding of signals	34	(2)
Detection and elimination of outliers	36	(4)
Equalization of communication channels	40	(2)
Spectrum estimation	42	(5)
Adaptive control	47	(4)
Models of Nonstationary Processes	51	(28)
The origins of time dependence	51	(1)
Characteristics of nonstationary processes	52	(3)
Irreducible nonstationary processes and parameter tracking	55	(1)
Measures of tracking ability	56	(4)
Prior knowledge in identification of nonstationary processes	60	(4)
Events and auxiliary measurements	61	(1)
Probabilistic models	61	(2)
Deterministic models	63	(1)
Slowly varying systems and the concept of local stationarity	64	(2)
Rate of process time variation	66	(4)
Speed of variation and sampling frequency	66	(1)
Nonstationarity degree	67	(3)
Assumptions	70	(4)
Dependence among regressors	70	(1)
Dependence between system variables	71	(1)
Persistence of excitation	71	(1)
Boundedness of system variables	72	(1)
Variation of system parameters	73	(1)
About computer simulations	74	(5)
Process Segmentation	79	(24)
Nonadaptive segmentation	79	(7)
Conditions of identifiability	80	(2)
Recursive least squares algorithm	82	(4)
Adaptive segmentation	86	(9)
Segmentation based on the Akaike criterion	86	(7)
Segmentation based on the generalized likelihood ratio test	93	(2)
Extension to ARMAX processes	95	(8)
Iterative estimation algorithms	95	(3)
Recursive estimation algorithms	98	(2)
Conditions of identifiability	100	(1)
Adaptive segmentation	100	(1)
Comments and extensions	101	(2)
Weighted Least Squares	103	(36)
Estimation principles	103	(1)
Estimation windows	104	(1)
Static characteristics of WLS estimators	105	(3)
Effective window width	106	(1)
Equivalent window width	106	(2)
Degree of window concentration	108	(1)
Dynamic time-domain characteristics of WLS estimators	108	(4)
Impulse response associated with WLS estimators	109	(2)
Variability of WLS estimators	111	(1)
Dynamic frequency-domain characteristics of WLS estimators	112	(6)
Frequency characteristics associated with WLS estimators	112	(1)
Properties of associated frequency characteristics	113	(2)
Estimation delay of WLS estimators	115	(2)
Matching characteristics of WLS estimators	117	(1)
The principle of uncertainty	118	(1)
Comparison of the EWLS and SWLS approaches	119	(3)
Technical issues	122	(3)
Computer simulations	125	(11)
Extension to ARMAX processes	136	(3)
Comments and extensions	137	(2)
Least Mean Squares	139	(40)
Estimation principles	139	(2)
Convergence and stability of LMS algorithms	141	(7)
Analysis for independent regressors	143	(3)
Analysis for dependent regressors	146	(2)
Static characteristics of LMS estimators	148	(6)
Equivalent memory of LMS estimators	149	(4)
Normalized LMS estimators	153	(1)
Dynamic characteristics of LMS estimators	154	(2)
Impulse response associated with LMS estimators	154	(1)
Frequency response associated with LMS estimators	155	(1)
Comparison of the EWLS and LMS estimators	156	(10)
Initial convergence	156	(3)
Tracking performance	159	(7)
Computer simulations	166	(11)
Extension to ARMAX processes	177	(2)
Comments and extensions	177	(2)
Basis Functions	179	(50)
Approach based on process segmentation	179	(20)
Estimation principles	179	(4)
Invariance under the change of coordinates	183	(3)
Static characteristics of BF estimators	186	(2)
Dynamic characteristics of BF estimators	188	(2)
Impulse response associated with BF estimators	190	(1)
Frequency response associated with BF estimators	191	(2)
Properties of the associated frequency characteristics	193	(3)
Comparing the matching properties of different BF estimators	196	(3)
Weighted basis function estimation	199	(16)
Estimation principles	199	(4)
Recursive WBF estimators	203	(2)
Static characteristics of WBF estimators	205	(4)
Impulse response associated with WBF estimators	209	(1)
Frequency response associated with WBF estimators	210	(5)
Computer simulations	215	(1)
The method of basis functions: good news or bad news?	215	(14)
Comments and extensions	227	(2)
Kalman Filtering	229	(36)
Estimation principles	229	(2)
Estimation based on the random walk model	231	(3)
Estimation based on the integrated random walk models	234	(2)
Stability and convergence of the RWKF algorithm	236	(1)
Estimation memory of the RWKF algorithm	237	(5)
Dynamic characteristics of RWKF estimators	242	(2)
Impulse response associated with RWKF estimators	242	(1)
Frequency response associated with RWKF estimators	243	(1)
Convergence and tracking performance of RWKF estimators	244	(3)
Initial convergence	244	(1)
Tracking performance	244	(3)
Parameter matching using the Kalman smoothing approach	247	(3)
Fixed interval smoothing	248	(1)
Fixed lag smoothing	249	(1)
Computer simulations	250	(11)
Extension to ARMAX processes	261	(4)
Comments and extensions	263	(2)
Practical Issues	265	(42)
Numerical safeguards	265	(22)
Least squares algorithms	265	(16)
Gradient algorithms	281	(3)
Kalman filter algorithms	284	(3)
Optimization	287	(20)
Memory optimization	287	(10)
Other optimization issues	297	(7)
Comments and extensions	304	(3)
Epilogue	307	(2)
References	309	(12)
Index	321