Fundamentals of Stochastic Filtering
Filtering is a subject about the sequential estimation of a stochastic dynamical system based on noisy observations. In this course, we will introduce the basic concepts of stochastic filtering, from both theoretical and numerical perspectives.
In the theoretical part, this course will focus on the filtering equations, which are stochastic partial differential equations governing the evolution of the solution of filtering problems. Existence, uniqueness and other important properties of the equations will be discussed.
In the numerical part, classical and modern filtering algorithms will be introduced, including Kalman filter, PDE-based filtering algorithms and particle filters. If time permits, we will also briefly discuss data-driven filtering algorithms based on deep learning.
In the theoretical part, this course will focus on the filtering equations, which are stochastic partial differential equations governing the evolution of the solution of filtering problems. Existence, uniqueness and other important properties of the equations will be discussed.
In the numerical part, classical and modern filtering algorithms will be introduced, including Kalman filter, PDE-based filtering algorithms and particle filters. If time permits, we will also briefly discuss data-driven filtering algorithms based on deep learning.
Lecturer
Zeju Sun
Date
14th September, 2025 ~ 10th January, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Friday | 09:50 - 12:15 | A3-2-301 | ZOOM 11 | 435 529 7909 | BIMSA |
Prerequisite
Calculus, Advanced probability, Partial differential equations
Syllabus
1. Introduction of stochastic filtering and preliminaries
Filtering Theory
2. Filtering equations----the change-of-probability-measure approach
3. Filtering equations----the innovation process approach
4. Filtering equations----existence and uniqueness
5. The robust representation formula
6. Finite-dimensional filters
7. The density of the conditional distribution
Numerical Algorithms
8. Time-discretization and discrete-time filter
9. Kalman-based filtering algorithm I: EKF, UKF and CKF
10. Kalman-based filtering algorithm II: Ensemble Kalman filter
11. PDE-based filtering algorithm I: Spectral methods
12. PDE-based filtering algorithm II: Yau-Yau algorithm
13. Particle filter I: Resampling particle filters
14. Particle filter II: Feedback particle filters
15. Selected topics
Filtering Theory
2. Filtering equations----the change-of-probability-measure approach
3. Filtering equations----the innovation process approach
4. Filtering equations----existence and uniqueness
5. The robust representation formula
6. Finite-dimensional filters
7. The density of the conditional distribution
Numerical Algorithms
8. Time-discretization and discrete-time filter
9. Kalman-based filtering algorithm I: EKF, UKF and CKF
10. Kalman-based filtering algorithm II: Ensemble Kalman filter
11. PDE-based filtering algorithm I: Spectral methods
12. PDE-based filtering algorithm II: Yau-Yau algorithm
13. Particle filter I: Resampling particle filters
14. Particle filter II: Feedback particle filters
15. Selected topics
Reference
[1] Bain, A., & Crisan, D. (2009). Fundamentals of stochastic filtering. Springer.
[2] Yau, S. S. T., Chen, X., Jiao, X., Kang, J., Sun, Z., & Tao, Y. (2024). Principles of Nonlinear Filtering Theory. Springer Nature.
[2] Yau, S. S. T., Chen, X., Jiao, X., Kang, J., Sun, Z., & Tao, Y. (2024). Principles of Nonlinear Filtering Theory. Springer Nature.
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English