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.

翻译：复杂的分步骤衍生物近似值是一种数字差别化技术,可以达到分析准确度、机器精确度和单一功能评价。本信将复杂的分步骤衍生物近似值扩展至与矩阵要素相容。与标准复杂的分步骤衍生物一样,该方法仍然能够达到分析准确度,直至机器精确度,并有一个单一功能评价。与中央差异计划相比,拟议的复杂分步骤方法显示具有较高的准确性。该方法适用于两个不同的构成估计问题,并能够在有分析方法可用时恢复与分析方法相同的结果。