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We compute the Fréchet mean \({\mathscr {E}}_t\) of the solution \(X_t\) to a continuous-time stochastic differential equation in a Lie group. It provides an estimator with minimal variance of \(X_t\) . We use it in the context of Kalman filtering and more precisely to infer rotation matrices. In this paper, we focus on the prediction step between two consecutive observations. Compared to state-of-the-art approaches, our assumptions on the model are minimal.

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Continuous-Time Filtering in Lie Groups: Estimation via the Fréchet mean of solutions to stochastic differential equations

  • 会议论文

  • 发表日期：

    2026年

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  • Marc Arnaudon,
  • Magalie Bénéfice,
  • Audrey Giremus

摘要

We compute the Fréchet mean \({\mathscr {E}}_t\) of the solution \(X_t\) to a continuous-time stochastic differential equation in a Lie group. It provides an estimator with minimal variance of \(X_t\) . We use it in the context of Kalman filtering and more precisely to infer rotation matrices. In this paper, we focus on the prediction step between two consecutive observations. Compared to state-of-the-art approaches, our assumptions on the model are minimal.