We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy minimization on the space of probability distributions equipped with the Wasserstein metric. We outline the general method and show its competitiveness in posterior representation and parameter estimation on two state-space models for which Gaussian approximations typically fail: systems with multiplicative noise and multi-modal state distributions.

翻译：我们提出了一种新颖的方法来近似高斯滤波和高斯混合滤波。该方法基于通过梯度流表示的变分近似。该梯度流源于在配备Wasserstein度量的概率分布空间上最小化Kullback-Leibler散度。我们概述了通用方法，并在两类高斯近似通常失效的状态空间模型（即具有乘性噪声的系统和多模态状态分布）上展示了其在后验表示和参数估计方面的竞争力。