## 1 Introduction  
Rotation modulation technology is an effective method to improve the accuracy of inertial navigation systems (INSs) at a low cost [1]. This technology can suppress constant or slow variation errors of inertial devices by rotating the inertial measurement unit (IMU) continuously or periodically [2]. Therefore, the power supply to the rotating part is a key technology. If the rotation scheme is set to continuous rotation or run-stop in forward and reverse directions, winding reels can be used to transmit electrical energy from the stationary unit to the rotating unit. However, wired electrical energy transfer can damage safety under loss of indexer control and restrict the free rotation of rotating parts in the rotation modulated inertial navigation system (RMINS). Therefore, applying slip-rings to solve the cable winding problem is a common method for the power supply of rotating units [3]. Nevertheless, slip-rings have the drawbacks of wear and friction, limited lifetime, and regular maintenance [4]. Based on these problems, applying wireless power transfer (WPT) technology to the RMINS is necessary to power the rotating units through a non-contact method. Electronic circuits or sensors are often installed on the rotating part in practical applications, such as shaft torque measurement [5], north finder [6], and the RMINS. The application of WPT can obviate the shortcomings of wires, wire reels, and slip-rings and greatly improve the reliability and lifetime of the system. Despite the great advantages, the WPT system also has some disadvantages. The performance of nearby electrical circuits was influenced by the electromagnetic interference noise produced by a WPT system [7]. For rotary equipment such as the RMINS, where sensors and circuits are installed on the rotating part with limited space, the magnetic flux leakage of WPT can adversely affect sensors and circuits [8]. The magnetic sensitivity index restriction of interferometric fiber optic gyroscope used in typical INSs is 0.0001-0.001\({}^{\circ}\)h\({}^{-1}\)G\({}^{-1}\)s\({}^{-1}\)[9]. Therefore, it is necessary to design a magnetic shielding structure to reduce the magnetic field leakage of the WPT system. Moreover, the limited space of the rotating part restricts the size of the receiving circuit and the winding topology for a WPT system. Therefore, the mature products of the WPT system are unsuitable for direct application in the RMINS [10]. Nowadays, electromagnetic induction wireless power transfer (EMIWPT) is often used for short-range WPT. However, a gap between the primary and secondary coil reduces the efficiency of EMIWPT. Compared with the EMIWPT, the magnetic coupling resonant wireless power transfer (MCRWPT) achieved higher power transmission efficiency (PTE) at a longer distance between the two coils [11]. Therefore, to improve the PTE of the system, the MCRWPT used in the rotary equipment is suitable because the gap exists between the primary coil and secondary coil. In recent years, several further efforts have been dedicated to applying the MCRWPT system. The related researchers have studied the MCRWPT system from two main aspects to reduce magnetic leakage and improve PTE. On the one hand, the winding topology of WPT was studied, such as optimizing coil structure and designing magnetic shield structure [12]. A novel double-layer parallel coil model was proposed for the rotary equipment to improve the PTE and output power, and the performance of the WPT system was better than that of a conventional single-layer coil [13]. However, the application of WPT caused magnetic field leakage, which adversely affected surrounding materials and humans [14]. Thus, different methods such as passive shielding, active shielding, and eliminating the magnetic field with a reactive resonant current loop were introduced to suppress magnetic field leakage [15]. To further reduce magnetic leakage, optimizing the geometry of the winding was given, which reduced the magnitude of the near magnetic field by 29.12% [16].