It is analyzed that for a nested rotation inertial navigation system (NRINS) constructed from three ring fiber optic gyros nested within each other the main residual errors after rotation modulation are gyro angle random walk (ARW) and non-modulated gyro drift. It is pointed out that different orientations of the gyro sensitive axis lead to different equivalent ARWs, and the non-modulated gyro drift caused by the nested installation of three ring gyros is also different. The mechanism of generation of non-modulated drift in the embedded system and the general relationship with the axis sequence configuration are expounded. The equivalent ARW and non-modulated gyro drift in the inner frame rotation modulation mode and their influence on the alignment and navigation of the system are analyzed and deduced. Finally, taking the two typical applications of short-time and long-time navigation as examples, the influence of different gyro axis sequence configuration schemes on the navigation accuracy of the NRINS is verified through static navigation experiments, and the best axis sequence configuration scheme under the two applications is determined. By optimizing the gyro axis sequence configuration, the accuracy of navigation can be improved by about two times, which is of great significance. This work has important reference value for further improving the accuracy of NRINS and maximizing the accuracy advantage of gyros in different applications.