Main Topics: System Identification - Optimal Estimation
| 1. Part1- Basics:
Realization theory: Impulse response matrices. Hankel
matrices. Observability and controllability matrices.
Singular Value Decomposition (SVD). Ordinary Least Squares
(OLS) regression. PCA, PCR and PLS.
2. Part2- Subspace System
Identification: Linear systems. Autonomous systems.
Deterministic systems. Combined stochastic and
deterministic systems (the general case). The Kalman
filter on innovations form. Subspace ID of the complete
Kalman filter. Open and closed loop system identification.
The D-SR Toolbox for MATLAB. Input Experiment design,
3. Part3- The Kalman filter: Linear
systems. Innovations form. Apriori and aposteriori form.
Prediction form. Non-linear systems and the Extended
Kalman Filter (EKF).
4. Part4- Prediction Error Methods
(PEM) for System Identification. Prediction form of the
Kalman filter. Optimal prediction of the output.
Prediction error. Prediction error criterion. Optimization
methods. ARX, ARMAX model structures etc. Model
validation. Recursive system identification and
Recursive Ordinary Least Squares (ROLS).
References: The figures on this page are
and Ruscio (2015)