Identification of Time-Varying Processes
Identification of Time-Varying Processes offers a comprehensive treatment of the key issue in adaptive systems: tracking of time-varying system parameters. Time-varying identification techniques facilitate many challenging applications in different areas including telecommunications (channel equalization, predictive coding of signals, adaptive noise reduction and echo cancellation) and automatic control (adaptive control and failure detection). The processes also assist signal processing in areas such as adaptive noise reduction, prediction of time series, restoration of archive audio recordings and spectrum estimation. Includes: All three major approaches to time-varying identification: local estimation, the basis functions approach and the method based on Kalman filtering/smoothing. Analysis and comparison of tracking capabilities of different time-varying identification schemes. Discussion of all aspects of time-varying identification such as assessment of the estimation memory, estimation bandwidth and numerical stability of different identification algorithms and optimization of adaptive filters. Presentation of selected practical applications of time-varying process identification. Essential reading for adaptive signal processing engineers, researchers, lecturers and senior electrical engineering and computer science students in telecommunications and signal processing.
Why Read This Book
You should read this book if you need a focused, methodical treatment of how to track nonstationary systems and estimate time-varying parameters in practice. It gives you workable algorithms (local estimators, basis-function expansions, and Kalman-based filtering/smoothing) together with analysis and application examples relevant to communications, audio restoration, and control.
Who Will Benefit
Practicing engineers and graduate students working on adaptive filters, channel tracking, time-varying spectral estimation, or adaptive control who need practical identification techniques for nonstationary systems.
Level: Advanced — Prerequisites: Linear algebra, basic estimation theory and stochastic processes, familiarity with state-space models/Kalman filtering, and basic DSP concepts; MATLAB exposure will help follow examples.
Key Takeaways
- Understand the formulation and challenges of identifying time-varying systems and parameter tracking metrics.
- Implement local estimation techniques for slowly varying parameters (windowed/weighted least squares and recursive forms).
- Apply basis-function approaches (polynomial, spline, orthogonal basis expansions) to represent and estimate time variation.
- Use Kalman filtering and smoothing for recursive tracking and evaluate their advantages and limitations in nonstationary settings.
- Compare and choose among algorithms based on tracking ability, noise sensitivity, and computational cost.
- Adapt identification methods to practical applications such as channel equalization, predictive coding, and adaptive noise reduction.
Topics Covered
- 1. Introduction: Time-Varying Processes and Identification Challenges
- 2. Problem Formulation and Performance Measures for Tracking
- 3. Local Estimation Methods: Windowing and Recursive Least Squares
- 4. Basis-Function Approaches: Polynomials, Splines, and Orthogonal Bases
- 5. State-Space Modeling of Time-Varying Systems
- 6. Kalman Filtering for Time-Varying Parameter Estimation
- 7. Smoothing and Fixed-Interval Estimation Techniques
- 8. Recursive Implementations and Numerical Issues
- 9. Performance Analysis: Bias, Variance, and Tracking Ability
- 10. Applications: Channel Tracking, Predictive Coding, Echo Cancellation, Audio Restoration
- 11. Case Studies and Simulation Examples
- 12. Practical Considerations and Implementation Tips
- Appendices: Mathematical Background and Useful Identities
Languages, Platforms & Tools
How It Compares
Compared to Ljung's System Identification (broad and theory-oriented), this book is narrower and more focused on practical time-varying methods; compared to Haykin's Adaptive Filter Theory, it emphasizes identification and Kalman/smoothing approaches rather than extensive adaptive-algorithm derivations.
