Schedule

Preliminary schedule

Homeworks within parentheses are additional problems for FEL3202.

* 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.
* 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.

* 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: See excel file

* 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)

* 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)

* Estimating LTI models (Friday 5/6, 15-17). Chapter 7 in LN, Chapter 7 in Ljung.
* LTI models
* Maximum likelihood estimation
* Prediction error methods
* HW: C.7.1, C.7.2, 7.1a-e (7.1f-g, 7.2, the remaining problems are also very illuminating for the intricacies of filtering, if you have time do more)

* Asymptotic theory (Tuesday 9/6, 08-10). Chapter 8 in L.N. Chapters 8-9 in Ljung (we will cover these chapters in Lecture 9 though)
* Limits of random variables
* Large sample properties of estimators
* Large sample properties of biased estimators
* HW: 8.1 (8.2)

* Modeling and estimation using Gaussian Processes (Friday 12/6, 15-17) Guest lecture by Dr Riccardo Sven Risuleo, Klarna AB
* Basics, including Mercers theorem
* Impulse response estimation
* Estimation of nonlinear systems, including Hammerstein and Wiener models
* Modeling and estimation of uncertain input systems

* Asymptotic theory for the PEM (Friday 26/6, 10-12) Chapter 8 in L.N. Chapter 8, Sections 13.2, 13.4 and 13.5 in Ljung
* Identifiability
* Informative experiments
* Persistence of excitation
* Consistency
* Closed loop identification
* HW: 9.2, 9.4, C.9.1, (9.1, 9.3)

* Asymptotic theory for the PEM (Friday 28/8, 15-17) Section 9.5 in L.N. Chapter 9 in Ljung
* Estimation criteria and the corresponding asymptotic covariance matrices
* Geometric analysis
* Reproducing kernel approach
* SISO LTI systems
* HW: 9.7, 9.8 C.9.2a-d, (9.5, 9.6, C.9.2e-g)

* Experiment design (Wednesday 2/9). Slides + Chapter 13 in Ljung.
* Model structure selection and model validation (Friday 4/9). Slides + Chapter 16 in Ljung
* HW: C.9.3, C.9.4, C.9.6d-f, C.9.7, C.9.8 (C.9.6.a-c). Data can be found here. These exercises do not have to be corrected. Just make sure you understand what is going on.

* Computational aspects. Chapter 10 in Ljung.
* Gradient based optimization
* Convex relaxations
* Integration by Markov Chain Monte Carlo (MCMC) methods

* Additional methods
* Correlation based methods
* Subspace identification
* Nonlinear stochastic state-space models
* Continuous time identification