02MIJLG - System Identification, Estimation and Filtering

(II level Specializing Master in Automatica and Control Technologies)

Lecture Notes / Slides

Estimation problem; Estimator probabilistic characteristics; Cramér-Rao inequality; Estimation methods: Least-Squares,Weighted Least-Squares, Maximum Likelihood, Bayesian, Recursive Bayesian

2. Set Membership estimation theory (PDF file)

Unknown but bounded errors; Estimate Uncertainty Set (EUS) and Intervals (EUI); Feasible Parameter Set (FPS) and Parameter Uncertainty Intervals (PUI); Optimal estimates

3. Kalman filter theory (PDF file)

Filtering problem; One-step and Multi-step Kalman predictor; Kalman filter; Steady-state Kalman predictor; Nonlinear Kalman filtering: Linearized and Extended Kalman predictor

4. System identification (PDF file)

Model classes; Prediction-Error method (PEM): Least-Squares and Recursive Least-Squares; Anderson's whiteness test; Model stucture selection and validation criteria: FPE, AIC, MDL

5. Nonlinear system identification (PDF file)

Parametric approach; Fized and tunable basis functions; Parametric models; Nonlinear regression systems

6. Essentials of probability theory (PDF file)

Random experiment; Scalar random variables; Vector random variables; Normal random variables

Laboratory Lecture Notes / Slides and Auxiliary Lectures

Lab #1: parametric estimation from data of a position transducer model (PDF file)

MATLAB data file sensor.mat
Proposed solution under MATLAB using the statistical approach (file sensor.m )
Proposed solution under MATLAB using the Set Membership approach (file sensor_sm.m ), requiring the function plot_dx.m