1. Introduction
As inertial navigation system (INS) has advantages of high autonomy, low cost, and small size, and it is widely used in a variety of ships, aerospace, vehicles, aircraft. However, the measurement errors of the inertial devices themselves introduced into the navigation solution cause the errors to accumulate over time [
1,
2,
3,
4]. Especially in the practical application of missile environment, long-term storage will lead to constant error drift, and the special application conditions determine that the IMU, which is mounted on the missile, cannot timely and accurately calibrate in advance [
5]. RM technique is used to modulate the constant and slowly changing drift into sine/cosine form by periodically rotating one or more axes of the inertial navigation system [
6]. Therefore, the introduction of RM can significantly improve navigation accuracy while meeting the high autonomous requirements of the missile environment [
7]. With the development of research in recent years, the application of rotation modulation in high precision inertial navigation systems such as FOG has been relatively well established. However, research on navigation systems based on MEMS sensors is still in its infancy [
8]. As MEMS has the characteristics of low cost and small volume, further research on the application of rotational modulation technology in MEMS navigation systems is of great significance for reducing the cost of high precision systems and improving the navigation accuracy of conventional missile-borne environments [
9].
Rotary strapdown inertial navigation system based on its axis of rotation number can be divided into the single-shaft rotary strapdown inertial navigation system, the biaxial rotating strapdown inertial navigation system, and triaxial rotary strapdown inertial navigation system [
8,
10,
11]. For these systems, a variety of inversion schemes can be designed. In the literature, gyroscopic measurements are used to control the rotation of the IMU, the angular motion of the modulation axis is isolated, and the measurement accuracy of single-axis rotation modulation is improved. At the same time, the strapdown algorithm is used to obtain the navigation information of various rotational modulation schemes [
12,
13]. Dual-axis rotation modulation can effectively suppress the constant error of three axes [
14]. Many rotation schemes are designed for the system by periodically rotating alternately about the two axes, with positive and negative rotation about each axis, and with the motions of each axis being symmetric in space and time, in each rotation period [
15]. Different rotation schemes are designed to minimize systematic errors. Various rotation modulation schemes designed for fiber optic gyroscope (FOG) have strong reference significance for MEMS inertial navigation [
16,
17]. However, compared with the fiber optic gyroscope, the MEMS sensor has a larger constant error and larger noise, and the error component is more complex [
18]. The traditional rotary modulation method of fiber optic gyroscope directly applied to MEMS inertial system cannot adapt to a more complex application environment. This problem is an urgent problem and challenge to improve the accuracy of MEMS-based rotary modulation systems.
To solve this problem, the research based on MEMS rotary modulation system includes two aspects: rotation scheme and error analysis [
19,
20]. Different forms of rotation schemes are compared, according to which a single-axis continuous reciprocating rotation scheme shows better performance [
21]. In order to further compensate for the error, the error characteristics of the single-axis rotation modulation system are analyzed, and the error modeling is carried out [
22]. The error models of single-axis unidirectional continuous rotation, single-axis reciprocating rotation, and single-axis multiposition reciprocating rotation are analyzed and compared. The single-axis MEMS rotation modulation error is analyzed and compensated [
23]. However, special requirements in highly dynamic environments are not considered [
24]. In a highly dynamic environment, a novel rotation scheme is designed to compensate for the modulation angular rate instability in the high spin state [
25]. After isolating the angular velocity of the projectile body, the accuracy of the inertial navigation system under a high rotation state is improved by uniaxial rotation modulation [
26]. In terms of data processing, the existing particle filter, Rao–Blackwellised particle filter and extended Kalman filter (EKF) are not suitable for fast error compensation under highly dynamic conditions due to their long estimation time and complex calculation [
27,
28,
29]. In highly dynamic environments, much research has been conducted on rotation modulation schemes and error compensation. However, the error of the modulation axis direction cannot be modulated by the traditional single-axis rotation modulation [
30,
31], and more importantly, the constant error of MEMS gyro is large, which results in the continuous accumulation of the error of the modulation axis, limiting the improvement of the navigation precision of the system [
32,
33]. This is the bottleneck that should be overcome to improve the accuracy of the system.
Since ammunition in highly dynamic environments is of small volume, low cost, high precision demand [
34], this paper proposes a new compound rotating modulation scheme based on MEMS inertial sensor. The new solution preserves the small size of the traditional missile-borne single-axis rotating modulated MEMS inertial sensor and the simple control of the rotation scheme and reasonable modulation period, which is suitable for a high updating rate of data in a highly dynamic environment. Compared with the single-axis rotation modulation system, the new system inhibits the error accumulation and divergence in the axis of rotation modulation, and the attitude error of roll angle is reduced. Pitch angle attitude error is reduced. The yaw angle attitude error is reduced.
The rest of the paper is organized as follows: in
Section 2, the principle and navigation algorithm of traditional single-axis rotation modulation are introduced. In
Section 3, the RM scheme of the two-rotation mechanism is firstly proposed, then the rotation modulation theory of the two-rotation mechanism is discussed in detail, and the principle of the navigation solution of the new scheme is introduced. In
Section 4, the effectiveness of the proposed monitoring method is verified through simulation and experiment. Finally, the conclusion is drawn in
Section 5.