Abstract
This paper is concerned with optimality and stability analysis of a family of ensemble Kalman filter (EnKF) algorithms. EnKF is commonly used as an alternative to the Kalman filter for high-dimensional problems, where storing the variance matrix is computationally expensive. The algorithm consists of an ensemble of interacting particles driven by a feedback control law. The control law is designed such that, in the linear Gaussian setting and asymptotic limit of infinitely many particles, the mean and variance of the particles follow the exact mean and variance of the Kalman filter. The problem of finding a control law that is exact does not have a unique solution, reminiscent of the problem of finding a transport map between two distributions. A unique control law can be identified by introducing control cost functions, that are motivated by the optimal transportation problem or Schrödinger bridge problem. The objective of this paper is to study the relationship between optimality and long-term stability of a family of exact control laws. Remarkably, the control law that is optimal in the optimal transportation sense leads to an EnKF algorithm that is not stable.
Original language | English (US) |
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Pages (from-to) | 335-340 |
Number of pages | 6 |
Journal | IFAC-PapersOnLine |
Volume | 55 |
Issue number | 30 |
DOIs | |
State | Published - 2022 |
Event | 25th IFAC Symposium on Mathematical Theory of Networks and Systems, MTNS 2022 - Bayreuthl, Germany Duration: Sep 12 2022 → Sep 16 2022 |
Keywords
- filtering
- mean-field control
- optimal transportation
ASJC Scopus subject areas
- Control and Systems Engineering