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19208111 Masterseminar Stochastics "Stochastische Filtertheorie"

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 perkowski@math.fu-berlin.de


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

Talks

Date Speaker Subject
18.10. - -
25.10. - First meeting, discussion of subjects
01.11. N.N. TBA
08.11. N.N. TBA
15.11. N.N. TBA
22.11. N.N. TBA
29.11. N.N. TBA
06.12. N.N. TBA
13.12. N.N. TBA
2022    
03.01. N.N. TBA
10.01. N.N. TBA
17.01. N.N. TBA
24.01. N.N. TBA
31.01. N.N. TBA
07.02. N.N. TBA
14.02. N.N. TBA

Literature:

Among others the following. Further literature will be made available during the seminar.

Kalman filter (classical, linear problem, discrete time):

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“):

Ensemble Kalman filter (approximate distributions by particles):

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)

Particle filters:

Curse of dimensionality:

Ensemble Kalman filter for nonlinear systems: