Content - State and Parameter Estimation

Information Organizational structure of the course

In the summer of 2022, the course will most likely be held in face-to-face sessions again and is structured as follows:
 
Lecture: Thu. 08:30 - 10:00 a.m.
(starting 07.04.2022)
BC 003
Exercise: Thu. 10:15 - 11:00 a.m.
(starting 14.04.2022)
BC 003

 

In addition, the recordings of each lecture from the previous year will be made available on moodle for one week at a time.
Further details can be found in the organizing issues (pdf) or in the linked moodle course.

 

 

As of summer semester 2022

further links State and Parameter Estimation

    Organising issues (pdf,
login with Uni-ID)
Icons8-moodle-48 State and Parameter estimation
  

Keys (Login mit Uni-Kennung)

 LSF Course details in the LSF

 

Responsible: Prof. Ding (Lecture), N.N. (Exercise)
L/E, 3 SWS
 
(2. FS, WP) 15 M.Sc.; (2. FS, PV) 15 M.Sc.; (2. FS, PV) EIT MA AT;
(WP) M-EIT(AT)-19
Wahlpflichtfach / Elective M-ACE_PO15
VO/ÜB

Information Lecture content

After a short summary of scalar and vector random variables, the description of scalar and vector stochastic processes by probability distribution and density functions, expectations like correlation and covariance functions/matrices are considered. For stationary processes, further subjects are ergodicity, time averages, spectral density and correlation matrices.

The next chapter deals with some rule for matrices: Derivation to vectors and matrices, the pseudoinverse for solution or least-squares estimation of consistent or inconsistent linear equations, matrix inversion lemma.

A chapter on estimation theory deals with the methods of Bayes estimation (includig minimum variance, maximum a posteriori), maximum likelihood, and least-squares.

Based on these fundamentals, the equations of the time-discrete optimal filter (Kalman filter) for linear systems with normally distributed disturbances are derived (resp. optimal linear filter for arbitrary distribution). Numerical variants of the algorithm, as well as extensions (correlated system and measurement noise, coloured noise, continuous Kalman Bucy filter) are presented. For linear time-invariant systems, the relations between Kalman filter, Wiener filter, ans classic state observers are shown.

A short outlook deals with prediction, smoothing, and nonlinear filtering, followed by parameter estimation for linear system identification.

Finally, various application examples are presented.