Gaussian Variational State Estimation for Nonlinear State-Space Models

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

Automated summary

This paper addresses the state estimation problem in nonlinear state-space models by developing an assumed Gaussian solution based on variational inference. By formulating the problem as an optimization problem and solving it using first- and second-order derivatives, the approach is applicable to both Gaussian and non-Gaussian probabilistic models in nonlinear systems. The method outperforms alternative assumed Gaussian approaches in challenging scenarios like target tracking using von Mises-Fisher distribution.