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.

中文翻译：

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矩阵李群的复步导数逼近

复步导数逼近是一种数值微分技术，可以通过单个函数评估来实现分析精度（相对于机器精度）。在这封信中，复步导数逼近被扩展为与矩阵李群的元素兼容。与标准的复步导数一样，该方法仍然能够通过单个功能评估来达到分析精度，甚至达到机器精度。与中心差分方案相比，所提出的复杂步骤方法具有更高的精度。该方法适用于两个不同的姿势估计问题，并且在可用时能够恢复与分析方法相同的结果。