Schedule

Preliminary schedule

Homeworks within parentheses are additional problems for FEL3202.

1. Introduction. Updated slides (Friday 15/5, 15-17) . Chapter 1-2 in Lecture Notes (LN). Chapter 1-2 in Ljung 
• Signals and systems
• The basic problem
• Some examples
• Introduction to parameter estimation
• Some pitfalls
• HW: 1.1 a-d  (1.1e). 2.1 (2.2, 2.5) ) Deadline Tuesday 26/5.
2. Probabilistic models Updated slides (Tuesday 19/5, 10-12). Chapter 3 in LN. Chapter 4 in Ljung. 
   • Models and model structures
   • Estimators
   • A probabilistic toolshed
   • HW: 3.3 a-f (g,h), 3.4 a (b,c) . Deadline: Friday 29/5.
3. Probabilistic models continued, and estimation theory (Tuesday 26/5, 10-12). Sections 3.4.7-4.2 in LN. Chapter 3 in Ljung 
   • A probabilistic toolshed continued
     • Stationary processes
     • Wide-sense stationarity
     • Quasi-stationarity
     • Frequency domain characterization
     • A swatch of building blocks
   • Estimation theory
     • Information contents in random variables
     • Estimation of random variables
   • HW 4.1, 4.3, 4.7f,h (3.6,4.5,4.7g). Deadline: Friday 5/6.
4. Wold decomposition and unbiased parameter estimation (Friday 29/5, 15-17). Sections 4.3-5.9 in LN. Chapter 7 in Ljung.
   • Wold decomposition
     • Linearly regular processes
     • Wold decomposition
     • Multivariable considerations
     • Spectral distribution function
     • Spectral factorization
     • Full rank processes
   • Unbiased parameter estimation
     • The Cramér-Rao lower bound
     • Efficient estimators
     • The maximum likelihood estimator
     • Data compression
     • Uniform minimum variance unbiased estimators
     • Best linear unbiased estimator (BLUE)
   • HW: 5.1, 5.5, 5.7 (4.7,5.3)
5. Biased parameter estimation (Tuesday 2/6, 10-12) . Chapter 6 in LN.
   • The bias-variance trade-off
   • The Cramér-Rao lower bound
   • Average risk minimization
   • Minimax estimation
   • Pointwise risk minimization
   • HW: 6.2a,b (6.2c, 6.3)
6. Asymptotic theory (Friday 5/6, 15-17). Chapter 7 in L.N. Chapter 8 in Ljung
   • Limits of random variables
   • Large sample properties of estimators
   • Large sample properties of biased estimators
7. Computational aspects (Tuesday 9/6, 08-10). Chapter 10 in Ljung.
   • Gradient based optimization
   • Convex relaxations
   • Integration by Markov Chain Monte Carlo (MCMC) methods
8. Case studies I (Friday 12/6, 10-12) 
   • Parametric LTI models
   • Impulse response models
9. Case studies II (Tuesday 16/6, 10-12) 
   • Uncertain input models
   • Nonlinear stochastic state-space models
10. Model accuracy (Friday 19/6, 15-17)  Chapter 9 in Ljung.
11. Model structure selection and model validation  (Tuesday 23/6, 10-12). Chapter 16 in Ljung
12. Experiment design (Tuesday 25/8, 10-12) . Chapter 13 in Ljung.
13. Continuous time identification (Friday 28/8, 15-17)