The defects of the traditional strapdown inertial navigation algorithms become well acknowledged and the enhanced traditional algorithms were quite recently proposed trying to mitigate both theoretical and algorithmic defects. In this paper, the accuracies of the traditional algorithms, the enhanced algorithms, and the velocity algorithm based on the velocity translation vector are re-investigated in the common case of two samples, for the first time against the true reference provided by the functional iteration approach that has provable convergence and essentially reduces the noncommutativity errors to machine precision. Notably, the analyses by the help of MATLAB symbolic toolbox reveal the marginal effect of the enhanced algorithms, and the error orders of all algorithms analyzed against functional iteration are consistent with the existing literatures. Numerical results under coning motions agree with analyses that the enhanced algorithms have little significant accuracy improvement over the traditional algorithms, while the functional iteration approach possesses significant accuracy superiority even in sustained lowly dynamic conditions.

翻译：传统捷联惯性导航算法的缺陷已广为人知，近年来提出的增强型传统算法旨在缓解其理论和算法层面上的缺陷。本文以双样本通用情况为例，首次采用具有可证明收敛性且能将非交换性误差降低至机器精度的函数迭代方法提供的真值参考，重新评估了传统算法、增强型算法以及基于速度平移向量的速度算法的精度。值得注意的是，借助MATLAB符号工具箱的分析表明，增强型算法的改进效果微乎其微，且所有算法相对于函数迭代法的误差阶次与现有文献一致。在圆锥运动条件下的数值计算结果与分析相符：增强型算法相较于传统算法并无显著精度提升，而函数迭代方法即便在持续低动态条件下仍具有显著精度优势。