Principles of System Identification: Theory and Practice
Master Techniques and Successfully Build Models Using a Single Resource
Vital to all data-driven or measurement-based process operations, system identification is an interface that is based on observational science, and centers on developing mathematical models from observed data. Principles of System Identification: Theory and Practice is an introductory-level book that presents the basic foundations and underlying methods relevant to system identification. The overall scope of the book focuses on system identification with an emphasis on practice, and concentrates most specifically on discrete-time linear system identification.
Useful for Both Theory and Practice
The book presents the foundational pillars of identification, namely, the theory of discrete-time LTI systems, the basics of signal processing, the theory of random processes, and estimation theory. It explains the core theoretical concepts of building (linear) dynamic models from experimental data, as well as the experimental and practical aspects of identification. The author offers glimpses of modern developments in this area, and provides numerical and simulation-based examples, case studies, end-of-chapter problems, and other ample references to code for illustration and training.
Comprising 26 chapters, and ideal for coursework and self-study, this extensive text:
- Provides the essential concepts of identification
- Lays down the foundations of mathematical descriptions of systems, random processes, and estimation in the context of identification
- Discusses the theory pertaining to non-parametric and parametric models for deterministic-plus-stochastic LTI systems in detail
- Demonstrates the concepts and methods of identification on different case-studies
- Presents a gradual development of state-space identification and grey-box modeling
- Offers an overview of advanced topics of identification namely the linear time-varying (LTV), non-linear, and closed-loop identification
- Discusses a multivariable approach to identification using the iterative principal component analysis
- Embeds MATLAB® codes for illustrated examples in the text at the respective points
Principles of System Identification: Theory and Practice
presents a formal base in LTI deterministic and stochastic systems modeling and estimation theory; it is a one-stop reference for introductory to moderately advanced courses on system identification, as well as introductory courses on stochastic signal processing or time-series analysis.Why Read This Book
You will learn how to turn measured data into reliable mathematical models using a single, practice-oriented resource that emphasizes discrete-time linear system identification. The book balances statistical foundations with hands-on estimation, model selection, and validation techniques so you can build, validate, and deploy models for control, signal processing, and diagnostics.
Who Will Benefit
Graduate students and practicing engineers in control, signal processing, communications, or related fields who need to build, validate, and apply data-driven dynamic models from measurements.
Level: Intermediate — Prerequisites: Undergraduate calculus and linear algebra, basic probability and stochastic processes, signals and systems fundamentals, and basic familiarity with numerical computing (e.g., MATLAB or Python).
Key Takeaways
- Formulate system identification problems for discrete-time linear systems and choose appropriate model structures (ARX, ARMAX, Box–Jenkins, state-space).
- Apply least-squares, prediction error methods, and instrumental-variable techniques to estimate parameters from noisy data.
- Implement model order selection and validation procedures (residual analysis, cross-validation, information criteria) to avoid overfitting.
- Use subspace and state-space identification approaches to derive reduced-order models suitable for control and estimation.
- Analyze the effect of noise and experiment design on estimator bias/variance and improve estimates through preprocessing and experiment planning.
- Deploy recursive/adaptive identification algorithms for online parameter tracking and time-varying system modeling.
Topics Covered
- 1. Introduction to System Identification: Objectives and Examples
- 2. Statistical and Probabilistic Preliminaries
- 3. Parametric Model Structures: ARX, ARMAX, OE, Box–Jenkins, State‑Space
- 4. Least Squares and Prediction Error Methods
- 5. Instrumental Variables and Bias-Reducing Estimators
- 6. Maximum Likelihood and Asymptotic Properties
- 7. Subspace and State‑Space Identification Methods
- 8. Frequency-Domain Methods and Spectral Analysis
- 9. Model Order Selection and Complexity Control
- 10. Model Validation, Residual Analysis, and Diagnostics
- 11. Recursive Identification and Adaptive Filtering
- 12. Practical Issues: Experiment Design, Preprocessing, and Numerical Implementation
- 13. Case Studies and Applications (control, audio/speech, communications)
- Appendices: Numerical Recipes, Matrix Algebra, Probability Results
Languages, Platforms & Tools
How It Compares
Tangirala provides a concise, practice-oriented introduction focused on discrete-time linear methods, whereas Ljung's 'System Identification: Theory for the User' is more comprehensive and theory-heavy, and Pintelon & Schoukens emphasize frequency-domain identification.
