Gradient flows in uncertainty propagation and filtering of linear Gaussian systems

The purpose of this work is mostly expository and aims to elucidate the Jordan-Kinderlehrer-Otto (JKO) scheme for uncertainty propagation, and a variant, the Laugesen-Mehta-Meyn-Raginsky (LMMR) scheme for filtering. We point out that these variational schemes can be understood as proximal operators in the space of density functions, realizing gradient flows. These schemes hold the promise of leading to efficient ways for solving the Fokker-Planck equation as well as the equations of non-linear filtering. Our aim in this paper is to develop in detail the underlying ideas in the setting of linear stochastic systems with Gaussian noise and recover known results.

• Publication year

  2017

• Venue

  IEEE Conference on Decision and Control

• Publication date

  2017-04-01

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1109/CDC.2017.8264109arXiv 1704.00102
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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