## 1 Introduction  
Inertial navigation is a completely autonomous navigation mode. In the absence of external information input during navigation, the inertial navigation system (INS) can output the complete navigation parameters [1; 2; 3; 4; 5]. RINS has a similar frame and rotation axis as the platform inertial navigation system, which can offset the constant and slowly-varying errors of the inertial measurement unit (IMU) and improve the navigation accuracy by about one order of magnitude [6; 7; 8; 9]. RINS also has advantages in initial alignment [10; 11] and self-calibration [12; 13; 14; 15; 16; 17], which have drawn much attention recently [18; 19; 20; 21]. Different kinds of single [22; 23; 24; 25], dual [26; 27; 28], and tri-axis RINS [18; 29; 30] can be designed according to actual requirements. It is important to improve the navigation accuracy of INS by improving system technology instead of choosing more accurate inertial devices. For RINS, the use of a multi-degree of freedom structure can be mainly explained in two aspects: On the one hand, RINS can isolate the angular motion of the external carrier in dynamic navigation by designing various high-precision motor control methods, which can be found in many research articles [18; 23; 29; 30; 31]. On the other hand, the optimal design of the rotation scheme can decrease the impact of IMU-related errors on navigation accuracy, and this manuscript mainly focuses on this part. According to different application situations and system structures, various rotation schemes can be designed for RINS. For single-axis RINS, the commonly used rotation schemes include single-axis continuous forward and reverse rotation as well as a four-position stop [25, 32, 33, 34, 35, 36, 37]. Both dual-axis and tri-axis systems have the ability to modulate zero bias error in all three directions. However, dual-axis systems are more common due to their simple structure and lower cost. These systems can use continuous forward and reverse schemes [28, 38], as well as various multi-position stop schemes, such as 8-position, 16-position, 32-position, and 64-position [16, 18, 27, 39]. There is limited literature available on the design of tri-axis rotation schemes [40]. Those rotation schemes can be divided into two groups: multi-position stop and continuous rotation. Each of these two rotation schemes has its own characteristics. In a multi-position stop scheme, the IMU remains stationary for a large percentage of time [41] except for the flipping actions, which are less demanding on the system's electromechanical mechanism. Therefore, at present, the commonly used rotation schemes are multi-position stop schemes [16, 32, 39, 42], but with the continuous improvement of motor control accuracy, continuous rotation schemes are becoming more and more popular due to the ability to modulate the errors of inertial devices [33, 38, 40]. Most of the rotation modulation schemes mentioned in previous research only make use of a single rotation mode. However, this restriction presents challenges for RINS in effectively suppressing various inertial device errors. Keeping stationary in the symmetric position at the same time can effectively offset the constant error of the IMU in the multi-position stop scheme. However, if the errors vary significantly with time, continuous rotation would be a better and more effective method to suppress the constant or slowly-varying error perpendicular to the rotation axis, which will be explained in more depth in the following sections. Continuous rotation would enlarge the oscillation of the navigation output, and the zero bias error in the direction of rotation cannot be compensated. Additionally, it is important to note that the installation errors and the scale factor errors of FOG can easily result in horizontal misalignment angles when flipping around the horizontal axis in the multi-position stop scheme [43].