Variational Formulation of the Particle Flow Particle Filter

This paper provides a formulation of the particle flow particle filter from the perspective of variational inference. We show that the transient density used to derive the particle flow particle filter follows a time-scaled trajectory of the Fisher-Rao gradient flow in the space of probability densities. The Fisher-Rao gradient flow is obtained as a continuous-time algorithm for variational inference, minimizing the Kullback-Leibler divergence between a variational density and the true posterior density.

@article{yi2025_2505.04007,
  title={ Variational Formulation of the Particle Flow Particle Filter },
  author={ Yinzhuang Yi and Jorge Cortés and Nikolay Atanasov },
  journal={arXiv preprint arXiv:2505.04007},
  year={ 2025 }
}