An energy-based deep splitting method for the nonlinear filtering problem
Preprint, 2022

The main goal of this paper is to approximately solve the nonlinear filtering problem through deep learning. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network. This results in a computationally fast filter that takes observations as input and that does not require re-training when new observations are received. The method is tested on three examples, one linear Gaussian and two nonlinear. The method shows promising performance when benchmarked against the Kalman filter and the bootstrap particle filter.

splitting scheme

deep learning

energy-based method

stochastic partial differential equation

Filtering problem

Zakai equation

Författare

Kasper Bågmark

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Adam Andersson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Stig Larsson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.48550/arXiv.2203.17153

Mer information

Skapat

2022-04-01