Gaussian Variational State Estimation for Nonlinear State-Space Models

In this paper, the problem of state estimation, in context both filtering and smoothing, for nonlinear state-space models is considered. Due to nature models, estimation generally intractable as it involves integrals general functions filtered smoothed distributions lack closed-form solutions. As such, common approximate problem. we develop an assumed Gaussian solution based on variational inference, which offers key advantage a flexible, but principled, mechanism approximating required distributions. Our main contribution lies new formulation optimisation problem, can then be solved using standard routines that employ exact first- second-order derivatives. The resulting approach minimal number assumptions applies directly systems with non-Gaussian probabilistic models. performance our demonstrated several examples; challenging scalar system, model simple robotic target tracking von Mises-Fisher distribution outperforms alternative approaches estimation.