CH5230 – System Identification
The main objective of this course is to teach fundamental aspects of system identification, which is all about estimating dynamic models from measured data. Through a proper study of this course, the student would obtain an insightful overview of this subject and learn various aspects of identification, specifically: (i) estimation of non-parametric and parametric models, (ii) notions of model quality (bias, variance, etc.) (iii) choosing model structures, (iv) methods for estimation of input-output models (v) sub-space identification (vii) design of inputs (probe signals) for identification and (v) data pre-processing for identification. While the lectures are designed to impart the theoretical foundations, the assignments and computer-based exercises provide ample opportunity to implement and learn the practical aspects. The course primarily deals with estimation of black-box input-output and state-space (non-parametric as well as parametric) with glimpses of grey-box models. We shall also learn to obtain frequency-domain interpretations of the model quality and parameter estimates, which throw light on the design choices in identification.
- Background: overview, systematic procedure, motivation with a case study.
- Models of deterministic LTI systems: discrete-time convolution models, response-based models, difference equation descriptions, transfer function and state-space models, discretization.
- Stochastic processes: Review (auto- and cross-correlation functions, white- noise process and ARMA models).
- Basics of estimation theory: estimators, bias and variance, convergence, consistency, asymptotic distribution of parameter estimates.
- Generic estimation methods: Ordinary least squares, Variants of LS methods, Maximum Likelihood Estimation.
- Input-output models for Identification: non-parametric (step, impulse and frequency response) and parametric models (ARX, ARMAX, OE, B-J).
- Prediction: one-step ahead prediction, k-step ahead predictors, simulation.
- Identification of non-parametric and parametric models: estimation of impulse response and frequency response functions; prediction-error minimization (PEM) methods, correlation methods, instrumental variable (IV) methods.
- Statistical and Practical Aspects: time-delay estimation, diagnostics for model quality checks, residual analysis, model validation, handling drifts, outliers and missing data; input design.
- Identification of State-Space Models: Kalman filter, subspace identifica- tion methods, Grey-box modelling.
- Advanced topics: Recursive and closed-loop identification.