Bayesian state estimation using generalized coordinates

This paper reviews a simple solution to the continuous-discrete Bayesian nonlinear state estimation problem that has been proposed recently. The key ideas are analytic noise processes, variational Bayes, and the formulation of the problem in terms of generalized coordinates of motion. Some of the algorithms, specifically dynamic expectation maximization and variational filtering, have been shown to outperform existing approaches like extended Kalman filtering and particle filtering. A pedagogical review of the theoretical formulation is presented, with an emphasis on concepts that are not as widely known in the filtering literature. We illustrate the appliction of these concepts using a numerical example.