Identification of time-varying processes /
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| Author / Creator: | Niedźwiecki, Maciej. |
|---|---|
| Imprint: | Chichester ; New York : Wiley, c2000. |
| Description: | xiii, 324 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7367338 |
Table of Contents:
- Preface
- Acknowledgments
- 1. Modeling Essentials
- 1.1. Physical and instrumental approaches to modeling
- 1.2. The Titius--Bode law and the method of least sqares
- 1.3. The principle of parsimony
- 1.4. Mathematical models of stationary processes
- 1.4.1. Autoregressive model
- 1.4.2. Moving average model
- 1.4.3. Equivalence of autoregressive and moving average models
- 1.4.4. Mixed autoregressive moving average model
- 1.4.5. A bridge to continuous-time processes
- 1.4.6. Models with exogenous inputs
- 1.4.7. The shorthand notation
- 1.5. The model-based approach to adaptive signal processing and control
- 1.5.1. Prediction
- 1.5.2. Predictive coding of signals
- 1.5.3. Detection and elimination of outliers
- 1.5.4. Equalization of communication channels
- 1.5.5. Spectrum estimation
- 1.5.6. Adaptive control
- 2. Models of Nonstationary Processes
- 2.1. The origins of time dependence
- 2.2. Characteristics of nonstationary processes
- 2.3. Irreducible nonstationary processes and parameter tracking
- 2.4. Measures of tracking ability
- 2.5. Prior knowledge in identification of nonstationary processes
- 2.5.1. Events and auxiliary measurements
- 2.5.2. Probabilistic models
- 2.5.3. Deterministic models
- 2.6. Slowly varying systems and the concept of local stationarity
- 2.7. Rate of process time variation
- 2.7.1. Speed of variation and sampling frequency
- 2.7.2. Nonstationarity degree
- 2.8. Assumptions
- 2.8.1. Dependence among regressors
- 2.8.2. Dependence between system variables
- 2.8.3. Persistence of excitation
- 2.8.4. Boundedness of system variables
- 2.8.5. Variation of system parameters
- 2.9. About computer simulations
- 3. Process Segmentation
- 3.1. Nonadaptive segmentation
- 3.1.1. Conditions of identifiability
- 3.1.2. Recursive least squares algorithm
- 3.2. Adaptive segmentation
- 3.2.1. Segmentation based on the Akaike criterion
- 3.2.2. Segmentation based on the generalized likelihood ratio test
- 3.3. Extension to ARMAX processes
- 3.3.1. Iterative estimation algorithms
- 3.3.2. Recursive estimation algorithms
- 3.3.3. Conditions of identifiability
- 3.3.4. Adaptive segmentation
- Comments and extensions
- 4. Weighted Least Squares
- 4.1. Estimation principles
- 4.2. Estimation windows
- 4.3. Static characteristics of WLS estimators
- 4.3.1. Effective window width
- 4.3.2. Equivalent window width
- 4.3.3. Degree of window concentration
- 4.4. Dynamic time-domain characteristics of WLS estimators
- 4.4.1. Impulse response associated with WLS estimators
- 4.4.2. Variability of WLS estimators
- 4.5. Dynamic frequency-domain characteristics of WLS estimators
- 4.5.1. Frequency characteristics associated with WLS estimators
- 4.5.2. Properties of associated frequency characteristics
- 4.5.3. Estimation delay of WLS estimators
- 4.5.4. Matching characteristics of WLS estimators
- 4.6. The principle of uncertainty
- 4.7. Comparison of the EWLS and SWLS approaches
- 4.8. Technical issues
- 4.9. Computer simulations
- 4.10. Extension to ARMAX processes
- Comments and extensions
- 5. Least Mean Squares
- 5.1. Estimation principles
- 5.2. Convergence and stability of LMS algorithms
- 5.2.1. Analysis for independent regressors
- 5.2.2. Analysis for dependent regressors
- 5.3. Static characteristics of LMS estimators
- 5.3.1. Equivalent memory of LMS estimators
- 5.3.2. Normalized LMS estimators
- 5.4. Dynamic characteristics of LMS estimators
- 5.4.1. Impulse response associated with LMS estimators
- 5.4.2. Frequency response associated with LMS estimators
- 5.5. Comparison of the EWLS and LMS estimators
- 5.5.1. Initial convergence
- 5.5.2. Tracking performance
- 5.6. Computer simulations
- 5.7. Extension to ARMAX processes
- Comments and extensions
- 6. Basis Functions
- 6.1. Approach based on process segmentation
- 6.1.1. Estimation principles
- 6.1.2. Invariance under the change of coordinates
- 6.1.3. Static characteristics of BF estimators
- 6.1.4. Dynamic characteristics of BF estimators
- 6.1.5. Impulse response associated with BF estimators
- 6.1.6. Frequency response associated with BF estimators
- 6.1.7. Properties of the associated frequency characteristics
- 6.1.8. Comparing the matching properties of different BF estimators
- 6.2. Weighted basis function estimation
- 6.2.1. Estimation principles
- 6.2.2. Recursive WBF estimators
- 6.2.3. Static characteristics of WBF estimators
- 6.2.4. Impulse response associated with WBF estimators
- 6.2.5. Frequency response associated with WBF estimators
- 6.3. Computer simulations
- 6.4. The method of basis functions: good news or bad news?
- Comments and extensions
- 7. Kalman Filtering
- 7.1. Estimation principles
- 7.2. Estimation based on the random walk model
- 7.3. Estimation based on the integrated random walk models
- 7.4. Stability and convergence of the RWKF algorithm
- 7.5. Estimation memory of the RWKF algorithm
- 7.6. Dynamic characteristics of RWKF estimators
- 7.6.1. Impulse response associated with RWKF estimators
- 7.6.2. Frequency response associated with RWKF estimators
- 7.7. Convergence and tracking performance of RWKF estimators
- 7.7.1. Initial convergence
- 7.7.2. Tracking performance
- 7.8. Parameter matching using the Kalman smoothing approach
- 7.8.1. Fixed interval smoothing
- 7.8.2. Fixed lag smoothing
- 7.9. Computer simulations
- 7.10. Extension to ARMAX processes
- Comments and extensions
- 8. Practical Issues
- 8.1. Numerical safeguards
- 8.1.1. Least squares algorithms
- 8.1.2. Gradient algorithms
- 8.1.3. Kalman filter algorithms
- 8.2. Optimization
- 8.2.1. Memory optimization
- 8.2.2. Other optimization issues
- Comments and extensions
- Epilogue
- References
- Index
