An Optimal Transport Formulation of Bayes' Law for Nonlinear Filtering Algorithms. (arXiv:2203.11869v2 [math.OC] UPDATED)

This paper presents a variational representation of the Bayes' law using
optimal transportation theory. The variational representation is in terms of
the optimal transportation between the joint distribution of the (state,
observation) and their independent coupling. By imposing certain structure on
the transport map, the solution to the variational problem is used to construct
a Brenier-type map that transports the prior distribution to the posterior
distribution for any value of the observation signal. The new formulation is
used to derive …

algorithms arxiv bayes filtering law math transport