Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple

Abstract

A large number of significant applications involve numerical solution of stochastic differential equations (SDE's) evolving in Lie groups such as $SO(3)$ . In the engineering literature, the proper formulation of numerical schemes has largely been ignored so that many schemes are flawed, i.e., do not guarantee the solution stays in the Lie group. There is a small mathematics literature but it is not easily accessible. With this in mind, we give a directly accessible derivation of numerical schemes for solving SDE's that do not rely on differential geometry or advanced random process theory. In doing so, we develop some new results. We illustrate the numerical schemes with simulations.