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, PRBS.

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 from Dalen and Ruscio (2015)

Teacher:  Dr. ing., 1. amanuensis David Di Ruscio                          


Updated 2018