19208111 Masterseminar Stochastics "Stochastische Filtertheorie"
- FU-Students only need to register via Campus Management.
- Non-FU-students are required to register via MyCampus/Whiteboard.
Winter semester 2021/2022
Lecturer: Prof. Dr. Nicolas Perkowski and Prof. Dr. Péter Koltai
- Time and place: Monday, 2pm--4pm, online
If you want to participate, please write an email to email@example.com
Prerequisites: Stochastics I und II.
Target group: BMS students, Master students and advanced Bachelor students.
Contents: The seminar covers advanced topics of stochastics.
The goal in filtering is to estimate the current state of a (possibly random) dynamical system given dynamic, noisy measurements, i.e. to filter out the observation noise. We will discuss classical and modern mathematical methods, starting with the Kalman filter that was used in the Apollo missions of the 1960s. In particular, we will put special emphasis on challenges and properties of different filters. Among others, we will treat the following subjects:
- Kalman filter
- Extended / ensemble Kalman filter
- Particle filters & Markov chain Monte Carlo
- Curse of dimension
- Robustness of filters
- Ergodic filters, long-time stability
|25.10.||-||First meeting, discussion of subjects|
Among others the following. Further literature will be made available during the seminar.
Kalman filter (classical, linear problem, discrete time):
- I. Reid: Estimation II. Lecture Notes 2 (2001)
Extended Kalman filter (local linearisation in every step):
- B.D.O. Anderson and J.B. Moore: Optimal Filtering. Dover Publications (1979)
Unscented Kalman filter (approximate moments by sample points — „sigma points“):
- Julier, Uhlmann: Unscented Filtering and Nonlinear Estimation
- Menegaz, et.al.: A Systematization of the Unscented Kalman Filter Theory
Ensemble Kalman filter (approximate distributions by particles):
- Evensen: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophysical Res., Vol.99, NO. C5, pages 10,143-10,162, May 15, 1994.
- Evensen: The Ensemble Kalman Filter: theoretical formulation and practical implementation. Ocean Dynamics 53: 343–367 (2003)
- Houtekamer & Mitchell 1998: Data Assimilation Using an Ensemble Kalman Filter Technique. Monthly Weather Rev., Vol.126: issue 3, p.796-811, (1998)
Large-sample asymptotics of EnKF:
- E. Kwiatkowski and J. Mandel: Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit. 2015
- F. Le Gland, V. Monbet and V.D. Tran: Large sample asymptotics for the ensemble Kalman filter. Chapter 22 in The Oxford Handbook of Nonlinear Filtering. pp. 598–631 (2011)
- J. Mandel, L. Cobb, and J.D. Beezley: On the convergence of the ensemble Kalman filter. Applications of Mathematics. vol. 56, no. 6. pp. 533–541 (2011)
- Doucet, Johansen: A Tutorial on Particle Filtering and Smoothing: Fifteen years later
- van Leeuwen: Nonlinear data assimilation in geosciences: an extremely efficient particle filter. Quarterly J. Royal Meteorological Society, Vol.136, Issue 653, p.1991-1999 (2010)
Curse of dimensionality:
- Snyder, Bengtsson, Bickel, Anderson: Obstacles to High-Dimensional Particle Filtering. Monthly Weather Review, Vol.135: Issue 12, p.4629-4640 (2008)
- Rebeschini, van Handel: Can local particle filters beat the curse of dimensionality? Ann. Appl. Probab. 25(5), p.2809-2866 (2015)
Ensemble Kalman filter for nonlinear systems:
- Kelly, Law, Stuart: Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time. Nonlinearity 27, p.2579 (2014)