A simple approach to numerical methods for stochastic differential equations in Lie groups

A large number of important engineering applications require solving stochastic differential equations (SDEs) so that geometrical constraints are satisfied, e.g. the solution has to lie in a matrix Lie group. But the few papers that properly derive numerical schemes for SDEs evolving in Lie groups are in the mathematics literature and not accessible to engineers. The engineering literature is also small but plagued with problems. With this in mind we give a direct accessible derivation of numerical schemes for solving such equations. We do not rely on differential geometry or advanced random process theory. We give simulations in a simple case to show how geometric structure is preserved.