  The complex-step derivative approximation is a numerical differentiation
technique that can achieve analytical accuracy, to machine precision, with a
single function evaluation. In this letter, the complex-step derivative
approximation is extended to be compatible with elements of matrix Lie groups.
As with the standard complex-step derivative, the method is still able to
achieve analytical accuracy, up to machine precision, with a single function
evaluation. Compared to a central-difference scheme, the proposed complex-step
approach is shown to have superior accuracy. The approach is applied to two
different pose estimation problems, and is able to recover the same results as
an analytical method when available.
