The Complex-Step Derivative Approximation on Matrix Lie Groups
This work provides a more accurate numerical differentiation method for pose estimation in robotics and computer vision, but it is incremental as it adapts an existing technique to a specific domain.
The authors extended the complex-step derivative approximation to matrix Lie groups, achieving analytical accuracy up to machine precision with a single function evaluation, and demonstrated superior accuracy compared to central-difference schemes in pose estimation problems.
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.