Optimality vs Stability Trade-off in Ensemble Kalman Filters

Amirhossein Taghvaei, Prashant G. Mehta, Tryphon T. Georgiou

Research output: Contribution to journalConference articlepeer-review


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 languageEnglish (US)
Pages (from-to)335-340
Number of pages6
Issue number30
StatePublished - 2022
Event25th IFAC Symposium on Mathematical Theory of Networks and Systems, MTNS 2022 - Bayreuthl, Germany
Duration: Sep 12 2022Sep 16 2022


  • filtering
  • mean-field control
  • optimal transportation

ASJC Scopus subject areas

  • Control and Systems Engineering


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