Variational Gaussian filtering via Wasserstein gradient flows

In this article, we present a variational approach to Gaussian and mixture-of-Gaussians assumed filtering. Our method relies on an approximation stemming from the gradient-flow representations of a Kullback--Leibler discrepancy minimization. We outline the general method and show its competitiveness in parameter estimation and posterior representation for two models for which Gaussian approximations typically fail: a multiplicative noise and a multi-modal model.