Investigation of Enhanced Inertial Navigation Algorithms by Functional Iteration

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.