Miniaturized single-axis rotation modulation inertial navigation system and transposition method thereof

Abstract

The invention provides a miniaturized single-axis rotation modulation inertial navigation system and a transposition method thereof. The system comprises an MEMS inertial measurement unit, a direct-drive servo motor, an angle measurement encoder, a conductive slip ring, a navigation resolving board, a power board, an external interface, a mounting piece and an equipment shell, the transposition method comprises the following steps: controlling the transposition mechanism to perform modulation motion according to a double-position four-sequence scheme; constructing a unit vector for integration, and simulating constant error accumulation; detecting vector integral module values at half-cycle and full-cycle moments, introducing an extra sequence when the vector integral module values exceed a threshold value, and solving an optimal stop position and stop time; and executing an additional sequence to finish adaptive compensation of the angular motion interference of the carrier. The influence of carrier heading motion on rotation modulation is effectively weakened, the precision of long-endurance navigation under motion interference is improved, and compared with an existing motion isolation scheme, the continuous operation time of an indexing mechanism is shortened, the control complexity is reduced, and the system is more stable.

Description

Technical Field

[0001] The present invention belongs to the technical field of inertial navigation, and relates to a navigation and positioning device and method for a small vehicle, in particular to a miniaturized single-axis rotation modulation inertial navigation system and its rotation method. Background Art

[0002] The strapdown inertial navigation system (SINS) is a navigation technology in which inertial sensors independently calculate the motion state of a vehicle. By using gyroscopes and accelerometers to measure angular velocity and specific force information in real time, it independently calculates its own position, velocity, and attitude information, and can work independently without relying on external information sources, having strong autonomy, concealment, and all-weather operation capabilities. Compared with high-precision navigation devices such as fiber optic gyroscopes, the microelectromechanical system-based strapdown inertial navigation system (MEMS-SINS) has the advantages of low cost and small size, and has gradually become the mainstream solution for low-cost small vehicle navigation and positioning. However, the error parameters of MEMS inertial navigation are relatively large, and the constant errors of gyroscopes and accelerometers are one of the main error sources of the inertial navigation system, which restricts the accuracy of long-term navigation of MEMS inertial navigation.

[0003] When it is difficult to improve the accuracy level of inertial sensors themselves, the compensation method of sensor errors has become the key means to improve the accuracy of the navigation system. The rotation modulation technology is an effective way to achieve self-compensation of the constant errors of inertial navigation. The rotation modulation inertial navigation system (RSINS) still uses the strapdown inertial navigation algorithm. The difference is that the inertial sensors are installed on a rotating mechanism with an angle measuring device, and the rotating mechanism drives the accelerometers and gyroscopes to rotate periodically according to certain rules, so that the projection of the constant error of the device in the navigation coordinate system is integrated to zero within one cycle, which can effectively suppress the influence of constant and slow-varying errors such as constant drift of the device on the navigation and positioning accuracy.

[0004] During the operation of the rotating inertial navigation system, if the vehicle is stationary, the inertial navigation rotates relative to the navigation system according to the set rules. However, in actual situations, the vehicle is constantly moving, and the angular motion of the vehicle is coupled with the rotation modulation motion, resulting in the inertial navigation not rotating relative to the navigation system according to the set rules, thereby affecting the rotation modulation effect. An extreme case is that the angular velocity of the vehicle motion relative to the navigation system is exactly equal in magnitude and opposite in direction to the angular velocity of the rotation modulation motion. At this time, the error in the navigation system does not change, and the system completely loses the rotation modulation effect and becomes an ordinary strapdown inertial navigation solution, resulting in a decrease in navigation accuracy. Therefore, it is necessary to isolate the angular motion of the vehicle.

[0005] Existing motion isolation algorithms generally use the carrier attitude data obtained from inertial navigation solution and the set rotation modulation law to drive the IMU to perform modulation motion relative to the navigation coordinate system, so as to isolate the system from the angular motion of the carrier and reduce the influence of the carrier motion. For the problem that the angular motion of the carrier affects the rotation modulation effect, Honeywell and Sperry companies proposed a suppression method that uses the calculated IMU attitude data to drive the rotating platform, that is, during the process of stopping the indexing, keep the IMU fixed relative to the navigation system; Zhang Lundong et al. proposed a method that uses the angle value of the rotating shaft in the inertial space to control the rotation angle of the IMU. However, the method of real-time tracking the coordinate system will cause the indexing mechanism to start and stop frequently. For motors with general performance, the effect of isolating motion is not good, and the irregular operation for a long time will damage the motor life and is not conducive to system stability.

[0006] Therefore, aiming at the problem that the angular motion exists in the actual navigation of the carrier and interferes with the rotation modulation effect, it is necessary to propose an optimized scheme on the basis of the existing single-axis rotation modulation indexing scheme, which can realize the isolation of the carrier's heading motion while performing error self-compensation during periodic indexing. By integrating calculations to simulate the accumulation of constant errors, adaptively add indexing order according to the degree of angular motion interference, and automatically calculate the optimal rotation stop position and residence time, so as to reduce the continuous operation time and start-stop frequency of the motor, reduce the dependence of the rotation modulation technology on high-precision indexing mechanisms, and improve the life and robustness of navigation equipment. Summary of the Invention

[0007] In order to overcome the deficiencies in the prior art, considering the need for carrier angular motion isolation in the rotation modulation technology, an optimized scheme is proposed from the perspective of reducing the motor motion frequency and reducing the probability of failure. While performing error self-compensation during periodic indexing, it realizes the isolation of the carrier's heading motion. By integrating calculations to simulate the accumulation of constant errors, adaptively add indexing order according to the degree of angular motion interference, and automatically calculate the optimal rotation stop position and residence time, so as to reduce the continuous operation time and start-stop frequency of the motor, reduce the dependence of the rotation modulation technology on high-precision indexing mechanisms, and improve the life and robustness of navigation equipment. To achieve the above object, the present invention provides the following technical solutions:

[0008] A miniaturized single-axis rotation modulation inertial navigation system, the system includes a MEMS inertial measurement unit, a direct drive servo motor, an angle measuring encoder, a motor drive board, a conductive slip ring, a navigation solution board, a power supply board, an external interface, a mounting part and a device housing. The MEMS inertial measurement unit outputs acceleration and angular velocity, which are used to calculate the carrier attitude, speed and position, and is directly mounted on the rotating platform of the direct drive servo motor through a connecting part;

[0009] The direct-drive servo motor is installed on the support of the equipment housing, drives the MEMS inertial measurement unit to perform specific periodic rotations, modulates part of the inertial navigation error into a periodic signal with zero integral, realizes error self-compensation, and the direct-drive method of the motor avoids the return error introduced by the reducer, which helps to improve the equipment accuracy;

[0010] The angle encoder is used to measure the motor rotation angle information and rotation speed information and is installed at the bottom of the motor;

[0011] The conductive slip ring provides electrical connection for the MEMS inertial navigation during rotation, is installed on the support of the equipment housing, passes through the hollow ring of the direct-drive servo motor, and has a compact design, reducing space occupation;

[0012] The navigation solution board is used to collect MEMS inertial navigation data and encoder angle measurement data, control the rotation of the servo motor and perform strapdown solution at the same time, and finally output navigation data. The navigation solution board is fixed on the housing support through the mounting part;

[0013] The power supply board is used for voltage conversion and electrical protection, provides multiple different voltages for power supply, and is fixed on the housing support through the mounting part;

[0014] The external interface is used for power input and data input / output, and is fixed on the housing support through the mounting part;

[0015] The mounting part and the equipment housing are used to install, fix and protect each internal device.

[0016] Furthermore, the indexing method includes the following steps:

[0017] S1: After completing the calibration and initial alignment of the equipment, set the initial parameters of the rotation modulation, including the indexing angular velocity ω, the stop time T, and the remaining error integration threshold R. After the initialization is completed, the navigation starts, and the direct-drive motor drives the IMU to perform periodic rotations according to the double-position four-order indexing scheme, and the inertial navigation output data and encoder output data are collected in real time;

[0018] S2: Perform strapdown solution on the IMU output data to obtain the real-time heading information of the IMU relative to the navigation coordinate system, construct a unit vector that rotates with the IMU according to the heading information, and continuously perform time integration on it from the starting moment to simulate the accumulation of constant errors in the horizontal direction;

[0019] S3: Each time when the indexing mechanism is about to rotate to the 0° position, check the magnitude of the vector integral. If it does not exceed the preset threshold, continue the normal indexing according to the double-position four-sequence method. If it exceeds the threshold, add an additional indexing sequence. Project the vector integral onto the body coordinate system, calculate the optimal stop position and stop time of the additional indexing sequence. After the execution of the additional sequence is completed, continue the normal indexing. The purpose is to make the inertial navigation stay evenly at each angle within one period, ensuring the error compensation effect of rotation modulation.

[0020] The double-position four-sequence indexing scheme described in step S1 includes the following steps:

[0021] S11: The indexing mechanism starts from the initial position of 0°, stays for a time T, rotates clockwise by 180°, stays for a time T, rotates clockwise by 180°, and returns to the initial position;

[0022] S12: Change the rotation direction, start from the initial position of 0°, stay for a time T, rotate counterclockwise by 180°, stay for a time T, rotate counterclockwise by 180°, and return to the initial position. Thus, one rotation period is completed.

[0023] According to the indexing method described in claim 2, characterized in that the unit vector ε I is fixedly connected to the IMU, and the direction coincides with the y-axis of the IMU. For the convenience of description, it is assumed that at the initial moment, the IMU and the body coordinate system are aligned, the y-axis of the IMU is at the 0° position of the indexing mechanism, and the coordinates of ε I in the navigation system are:

[0024] ε I n = [sinψ, cosψ, 0]

[0025] where ψ is the heading angle of the inertial navigation, and ε I n is the coordinate of the constructed unit vector in the navigation system. Integrating ε I n obtains the vector integral E I n :

[0026]

[0027] The vector integral E I n reflects the cumulative situation of the constant error in the horizontal axis of the inertial navigation in the navigation system. Conducting indexing compensation on E I n is equivalent to compensating for the cumulative constant error in the horizontal axis of the inertial navigation.

[0028] In an ideal state, the carrier does not have heading motion. After a period of rotation and stopping, the horizontal axis constant error is integrated to 0 within a period and should be completely offset. Therefore, when step S11 or S12 ends, the vector integral E I n It should be 0. However, in reality, the carrier has heading motion, which will destroy the periodicity of the modulated motion, resulting in the vector integral value not being 0 at the end of the period, leaving a residual amount that has not been offset.

[0029] The additional sequential steps described in step S3 include:

[0030] S31: When the indexing mechanism turns to 0°, that is, returns to the initial position, check the modulus of the vector integral ‖E I n ‖Whether it exceeds the preset threshold R, if it does not exceed the threshold, continue the normal transposition movement, if it exceeds the threshold, add an additional sequence;

[0031] S32: Calculate the optimal stop position and stop time of the additional sequence, the goal is to completely compensate for the remaining uncompensated accumulated constant error at the calculation time, that is, the compensation vector integral E I n In order to achieve complete compensation of the residual error within the cycle as much as possible, in the additional sequence, the indexing mechanism should be controlled to perform indexing motion relative to the navigation system according to the attitude output by the inertial navigation solution. On this basis, the specific steps of the additional sequence are:

[0032] ① Take the nearest direction, which is assumed to be clockwise here, and turn to the calculated optimal angle α according to the set modulation motion angular velocity ω, where α is the 0° heading position in the navigation coordinate system relative to the start time of the additional sequence;

[0033] ②According to the calculation results, the optimal time T to stay at position α e ;

[0034] ③ Rotate back to the original position of 0° at the opposite angular velocity -ω, update the zero position of the indexing mechanism to the current position, and the extra sequence is completed, and continue the normal indexing.

[0035] Since the additional sequence controls the rotation of the indexing mechanism relative to the navigation system, the α and ω mentioned in the above steps are both relative to the position and angular velocity of the navigation system. During the process of staying at the α position, rotating to the α position, and rotating back to the initial position, the constant error will generate additional integrals. When calculating the optimal position and time, each process needs to be included in the calculation, and the following equation can be obtained:

[0036]

[0037] where ψ 0The inertial navigation heading angle at the calculation moment, which is a constant, gives the following system of equations:

[0038]

[0039] Let Solve the equation:

[0040] Or

[0041]

[0042] T e >0, α ∈ (0, 2π)

[0043] The calculated T e is the optimal stop time, and α is the optimal stop heading position. When multiple solutions are obtained, the set of solutions that makes the total extra order time the shortest is preferentially used for the indexing motion, that is:

[0044]

[0045] where i = {1, 2}, is a set of solutions to the equation.

[0046] An electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, is characterized in that: when the processor executes the program, it implements the indexing method of the miniaturized single-axis rotation modulation inertial navigation system.

[0047] A computer-readable storage medium, on which computer instructions are stored, and when the computer instructions are executed by a processor, they implement the indexing method of the miniaturized single-axis rotation modulation inertial navigation system.

[0048] Compared with the prior art, the present invention has the following advantages and beneficial effects: The single-axis rotation modulation technology used in the present invention realizes the self-compensation of the main errors of inertial navigation, improving the long-term accuracy of the inertial navigation system; through the adaptive threshold detection and the additional order compensation mechanism, the system can respond to the carrier heading disturbance in real time, significantly improving the error suppression effect in complex motion environments and enhancing the anti-interference ability of navigation; compared with the existing carrier angular motion isolation and rotation method, it reduces the complexity of the rotation motor control, reduces the demand for high-precision motors. During the navigation process, compared with the traditional method, the actual working time ratio of the rotation mechanism is reduced by more than 50%, which can effectively extend the service life of the device, reduce power consumption, and make the device performance more stable; through the threshold detection and the additional order compensation every half cycle, the influence of the carrier angular motion on the navigation accuracy is within the controllable range, and theoretically the angular motion interference is completely compensated at the end of the additional order, and the positioning result fluctuates less and is more accurate. In the most extreme case, the accumulated horizontal constant error due to the carrier angular motion does not exceed: where ε represents the true IMU horizontal constant error vector; the device uses MEMS as the inertial measurement unit, and the rotation mechanism motor is integrated with the drive, with a compact overall structure design, small size, low cost, high precision, and good stability, giving full play to the advantages of MEMS inertial navigation, and is particularly suitable for the autonomous navigation and positioning of small unmanned carriers for long-term tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is the hardware structure diagram of the miniaturized single-axis rotation modulation inertial navigation system of the present invention;

[0050] Figure 2 is the prototype structure diagram of the miniaturized single-axis rotation modulation inertial navigation system of the present invention;

[0051] Figure 3 is the schematic flow diagram of the single-axis rotation scheme provided by the present invention.

[0052] In the figure: 1. MEMS inertial measurement unit, 2. Direct drive servo motor, 3. Angle measuring encoder, 4. Motor drive board, 5. Conductive slip ring, 6. Navigation solution board, 7. Power supply board, 8. External interface, 9. Mounting part, 10. Equipment housing. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] The following will specifically describe the technical solutions provided by the present invention in detail with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0054] Embodiment 1: Refer to Figure 2, the present invention provides a miniaturized single-axis rotation modulation inertial navigation system. The system hardware includes: a MEMS inertial measurement unit 1, a direct drive servo motor 2, an angle encoder 3, a motor drive board 4, a conductive slip ring 5, a navigation solution board 6, a power supply board 7, an external interface 8, a mounting part 9, and a device housing 10.

[0055] The MEMS inertial measurement unit outputs acceleration and angular velocity for calculating the carrier attitude, velocity, and position, and is directly mounted on the rotating platform of the direct drive servo motor through a connecting part.

[0056] The direct drive servo motor is mounted on the support of the device housing, drives the MEMS inertial measurement unit to perform specific periodic rotation, modulates part of the inertial navigation error into a periodic signal with zero integral, and realizes error self-compensation. The direct drive method of the motor avoids the backlash error introduced by the reducer and helps to improve the device accuracy.

[0057] The angle encoder is used to measure the motor rotation angle information and rotation speed information and is mounted at the bottom of the motor.

[0058] The conductive slip ring provides electrical connection for the MEMS inertial navigation under rotation, is mounted on the support of the device housing, passes through the hollow ring of the direct drive servo motor, and has a compact design to reduce space occupation.

[0059] The navigation solution board is used to collect MEMS inertial navigation data and encoder angle measurement data, control the rotation of the servo motor and perform strapdown solution at the same time, and finally output navigation data. The navigation solution board is fixed on the housing support through the mounting part.

[0060] The power supply board is used for voltage conversion and electrical protection, provides multiple different voltages for power supply, and is fixed on the housing support through the mounting part.

[0061] The external interface is used for power supply input and data input / output, and is fixed on the housing support through the mounting part.

[0062] The mounting part and the device housing are used to install, fix, and protect each internal component.

[0063] The software for controlling the indexing method is built into the navigation solution board and specifically includes the following steps:

[0064] S1: After completing the calibration and initial alignment of the device, set the initial parameters of the rotation modulation, including the indexing angular velocity ω, the stop time T, and the remaining error integral threshold R. After initialization is completed, navigation starts, and the direct drive motor drives the IMU to perform periodic rotation according to the double-position four-sequence indexing scheme, and real-time collects the inertial navigation output data and the encoder output data.

[0065] S2: Perform strapdown algorithm on the output data of the IMU to obtain the real-time heading information of the IMU relative to the navigation coordinate system. Construct a unit vector that rotates with the IMU according to the heading information, and continuously perform time integration on it starting from the initial moment to simulate the accumulation of constant errors in the horizontal direction.

[0066] S3: Every time the indexing mechanism is about to rotate to the 0° position, check the magnitude of the vector integral. If it does not exceed the preset threshold, continue normal indexing according to the double-position four-sequence method. If it exceeds the threshold, add an additional indexing sequence. Project the vector integral onto the vehicle coordinate system, calculate the optimal stop position and stop time of the additional indexing sequence. After the additional sequence is completed, continue normal indexing. The purpose is to make the inertial navigation stay evenly at each angle within one cycle to ensure the error compensation effect of rotation modulation.

[0067] The double-position four-sequence indexing scheme described in step S1 includes the following steps:

[0068] S11: The indexing mechanism starts from the initial position of 0°, stays for a time T, rotates 180° clockwise, stays for a time T, rotates 180° clockwise, and returns to the initial position.

[0069] S12: Change the rotation direction, start from the initial position of 0°, stay for a time T, rotate 180° counterclockwise, stay for a time T, rotate 180° counterclockwise, and return to the initial position. Thus, one rotation cycle is completed.

[0070] According to the indexing method described in claim 2, characterized in that the unit vector ε described in step S2 I is fixedly connected to the IMU, and the direction coincides with the y-axis of the IMU. For the convenience of explanation, it is assumed that at the initial moment, the IMU and the vehicle coordinate system are aligned, and the y-axis of the IMU is at the 0° position of the indexing mechanism, and ε I in the navigation system has the following coordinates:

[0071] ε I n = [sinψ, cosψ, 0]

[0072] where ψ is the heading angle of the inertial navigation, and ε I n is the coordinate of the constructed unit vector in the navigation system. Integrate ε I n to obtain the vector integral E I n :

[0073]

[0074] The vector integral E I nIt reflects the accumulation of the horizontal axis constant error of the inertial navigation system in the navigation system. I n Performing indexing compensation is equivalent to compensating for the accumulated constant error of the inertial navigation horizontal axis.

[0075] In an ideal state, the carrier does not have heading motion. After a period of rotation and stopping, the horizontal axis constant error is integrated to 0 within a period and should be completely offset. Therefore, when step S11 or S12 ends, the vector integral E I n It should be 0. However, in reality, the carrier has heading motion, which will destroy the periodicity of the modulated motion, resulting in the vector integral value not being 0 at the end of the period, leaving a residual amount that has not been offset.

[0076] The additional sequential steps described in step S3 include:

[0077] S31: When the indexing mechanism turns to 0°, that is, returns to the initial position, check the modulus of the vector integral ‖E I n ‖Whether it exceeds the preset threshold R, if it does not exceed the threshold, continue the normal transposition movement, if it exceeds the threshold, add an additional sequence;

[0078] S32: Calculate the optimal stop position and stop time of the additional sequence, the goal is to completely compensate for the remaining uncompensated accumulated constant error at the calculation time, that is, the compensation vector integral E I n In order to achieve complete compensation of the residual error within the cycle as much as possible, in the additional sequence, the indexing mechanism should be controlled to perform indexing motion relative to the navigation system according to the attitude output by the inertial navigation solution. On this basis, the specific steps of the additional sequence are:

[0079] ① Take the nearest direction, which is assumed to be clockwise here, and turn to the calculated optimal angle α according to the set modulation motion angular velocity ω, where α is the 0° heading position in the navigation coordinate system relative to the start time of the additional sequence;

[0080] ②According to the calculation results, the optimal time T to stay at position α e ;

[0081] ③ Rotate back to the original position of 0° at the opposite angular velocity -ω, update the zero position of the indexing mechanism to the current position, and the extra sequence is completed, and continue the normal indexing.

[0082] Since it is the control indexing mechanism that rotates relative to the navigation system in the additional sequence, both α and ω described in the above steps are the position and angular velocity relative to the navigation system. During the stay at the α position and the processes of rotating to and back from the α position, the constant error will generate additional integrals. When calculating the optimal position and time, all processes need to be included in the calculation, and the following equations can be obtained:

[0083]

[0084] where ψ 0 is the inertial navigation course angle at the calculation moment and is a constant. The following system of equations can be obtained:

[0085]

[0086] Let Solve the equation:

[0087] Or

[0088]

[0089] T e >0, α ∈ (0, 2π)

[0090] The calculated T e is the optimal stop time, and α is the optimal stop heading position. When multiple solutions are obtained, the set of solutions that makes the total time of the additional sequence the shortest is preferentially used for the indexing motion, that is:

[0091]

[0092] where i = {1, 2}, is a set of solutions of the equation.

[0093] The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also regarded as the protection scope of the present invention.

Claims

1. A miniaturized single-axis rotation modulation inertial navigation system, characterized in that: The system includes a MEMS inertial measurement unit, a direct drive servo motor, an angle encoder, a motor drive board, a conductive slip ring, a navigation solver board, a power supply board, an external interface, a mounting part and a device housing; Among them, the MEMS inertial measurement unit outputs acceleration and angular velocity, which are used to calculate the carrier's attitude, speed, and position, and is directly installed on the rotating platform of the direct-drive servo motor through a connector; The direct-drive servo motor is installed on the support of the equipment housing, driving the MEMS inertial measurement unit to perform a specific periodic rotation, modulating part of the inertial guidance error into a periodic signal with zero integral. The angle encoder is used to measure the motor's rotation angle and speed information and is installed at the bottom of the motor; The conductive slip ring provides electrical connection for the MEMS inertial navigation system under rotation. It is installed on the support of the equipment housing and passes through the hollow ring of the direct drive servo motor. The navigation solver board is used to collect MEMS inertial navigation data and encoder angle measurement data, and at the same time control the rotation of the servo motor, perform strapdown solution, and finally output navigation data. The navigation solver board is fixed on the housing support through the mounting parts; The power board is used for voltage conversion and electrical protection, provides multiple power supplies with different voltages, and is fixed on the housing support through mounting parts; The external interface is used for power input and data input and output, and is fixed on the housing support through a mounting piece; The mounting parts and the equipment housing are used to install, fix and protect various internal components.

2. A method for indexing a miniaturized single-axis rotation modulation inertial navigation system, characterized in that: Using the miniaturized single-axis rotation modulation inertial navigation system according to claim 1, the indexing method comprises the following steps: S1: After completing the calibration and initial alignment of the equipment, set the initial parameters of the rotation modulation, including the indexing angular velocity ω, the stop time T, and the residual error integral threshold R. After the initialization is completed, navigation begins, and the direct drive motor drives the IMU to rotate periodically according to the dual-position four-order indexing scheme, and collects the inertial navigation output data and encoder output data in real time; S2: Perform strapdown calculation on the IMU output data to obtain the real-time heading information of the IMU relative to the navigation coordinate system. According to the heading information, a unit vector rotating with the IMU is constructed. Starting from the starting time, the time integration is continuously performed to simulate the accumulation of constant error in the horizontal direction. S3: Every time the indexing mechanism is about to turn to the 0° position, check the modulus of the vector integral. If it does not exceed the preset threshold, continue the normal indexing according to the double-position four-order method. If it exceeds the threshold, add an additional indexing order, project the vector integral on the carrier coordinate system, calculate the optimal stop position and stop time of the additional indexing order, and continue the normal indexing after the additional order is completed. The purpose is to make the inertial navigation stay evenly at each angle within one cycle to ensure the error compensation effect of the rotation modulation.

3. The indexing method of the miniaturized single-axis rotation modulation inertial navigation system according to claim 2, characterized in that: The two-position four-order indexing scheme in step S1 includes the following steps: S11: The indexing mechanism starts from the initial position 0°, stays for time T, rotates 180° clockwise, stays for time T, rotates 180° clockwise, and returns to the initial position; S12: Change the rotation direction, starting from the initial position 0°, stay for time T, rotate 180° counterclockwise, stay for time T, rotate 180° counterclockwise, return to the initial position, and a rotation cycle is completed.

4. The indexing method of the miniaturized single-axis rotation modulation inertial navigation system according to claim 3, characterized in that: The unit vector ε in step S2 I It is fixedly connected to the IMU, and its direction coincides with the y-axis of the IMU. Assume that the IMU and the carrier coordinate system are aligned at the initial moment, and the y-axis of the IMU is located at the 0° position of the index mechanism. I The coordinates in the navigation system are: e I n =[sinψ,cosψ,0] Among them, ψ is the heading angle of the inertial navigation, ε I n is the coordinate of the constructed unit vector in the navigation system, for ε I n Integrate to get the vector integral E I n : Vector integral E I n It reflects the accumulation of the horizontal axis constant error of the inertial navigation system in the navigation system. I n Performing indexing compensation is equivalent to compensating for the accumulated constant error of the inertial navigation horizontal axis. In an ideal state, the carrier does not have heading motion. After a period of rotation and stopping, the horizontal axis constant error is integrated to 0 within a period and should be completely offset. When step S11 or S12 ends, the vector integral E I n It should be 0. However, in reality, the carrier has heading motion, which will destroy the periodicity of the modulated motion, resulting in the vector integral value not being 0 at the end of the period, leaving a residual amount that has not been offset.

5. The indexing method of the miniaturized single-axis rotation modulation inertial navigation system according to claim 2, characterized in that: The additional sequential steps in step S3 include: S31: When the indexing mechanism turns to 0°, that is, returns to the initial position, check the modulus of the vector integral ‖E I n ‖Whether it exceeds the preset threshold R, if it does not exceed the threshold, continue the normal transposition movement, if it exceeds the threshold, add an additional sequence; S32: Calculate the additional order optimal stop position α and stop time T e The goal is to completely compensate for the accumulated constant error remaining uncompensated at the time of calculation, that is, to compensate for the vector integral E I n In order to achieve complete compensation of the residual error within the cycle as much as possible, in the additional sequence, the indexing mechanism should be controlled to perform indexing motion relative to the navigation system according to the attitude output by the inertial navigation solution. On this basis, the specific steps of the additional sequence are: ① Take the nearest direction, which is assumed to be clockwise here, and turn to the calculated optimal angle α according to the set modulation motion angular velocity ω, where α is the 0° heading position in the navigation coordinate system relative to the start time of the additional sequence; ②According to the calculation results, the optimal time T to stay at position α e ; ③ Rotate back to the original position of 0° at the opposite angular velocity -ω, and update the zero position of the indexing mechanism to the current position. At this point, the extra sequence is completed and the normal indexing continues. Since the additional sequence controls the rotation of the indexing mechanism relative to the navigation system, α and ω are both the position and angular velocity relative to the navigation system. During the process of staying at the α position, rotating to the α position, and rotating back to the initial position, the constant error will generate additional integrals. When calculating the optimal position and time, each process needs to be included in the calculation, and the following equation is obtained: Where ψ0 is the inertial navigation heading angle at the calculation time, which is a constant, and the equation group can be obtained: make Solve the equation: or T e >0,α∈(0,2π) The calculated T e is the optimal stopping time, α is the optimal stopping heading position. When multiple solutions are obtained, the set of solutions that makes the total extra sequence time the shortest is preferred for transposition motion, that is: where i = {1,2}, is a set of solutions to the equation.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the indexing method of the miniaturized single-axis rotation modulation inertial navigation system as described in any one of claims 1 to 5 is implemented.

7. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed by the processor, the indexing method of the miniaturized single-axis rotation modulation inertial navigation system according to any one of claims 1 to 5 is implemented.

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