A method for compensating gradient magnetic field interference error of hemispherical resonant gyroscope

Abstract

The present invention relates to the technical field of gyroscopes, and in particular to a method for compensating for gradient magnetic field interference errors of a hemispherical resonant gyroscope. The method further comprises the following steps: step 1, collecting three-axis magnetic field intensity components of the gyroscope in a carrier coordinate system by using a magnetometer; step 2, collecting three-axis acceleration measurement values of the gyroscope in the carrier coordinate system by using an accelerometer; step 3, constructing an extended Kalman filter using navigation information as measurement input, fusing and solving the three-axis magnetic field intensity components in step 1 and the three-axis acceleration measurement values in step 2 by using the extended Kalman filter to obtain a compensation output of the magnetometer; and connecting an inertial navigation module with magnetometer and accelerometer signals to collect three-axis magnetic field intensity components and three-axis acceleration measurement values, and then fusing and solving these data by using the extended Kalman filter. The compensation output is used to correct the attitude angle of the gyroscope, thereby reducing the influence of gradient magnetic field interference on the gyroscope output.

Description

Technical Field

[0001] The present invention relates to the technical field of gyroscopes, and in particular to a method for compensating for gradient magnetic field interference errors of a hemispherical resonant gyroscope. Background Art

[0002] A hemispherical resonator gyroscope (HRG) is a high-precision inertial navigation instrument that uses a resonant structure to measure angular velocity. In a gyroscope, magnetic materials are typically used to form the resonator. When a fluctuating magnetic field is introduced, it affects the magnetization state of these magnetic materials. Furthermore, changes in the magnetic field due to a complex external environment will lead to changes in the magnetic moment in the resonator, further causing magnetic field interference errors.

[0003] It should be noted that due to the installation characteristics of the hemispherical resonant gyroscope itself, there must be influences that affect the magnetic field around it. Therefore, the gyroscope needs to be calibrated for error and compensated for interference. In this process, a magnetometer is usually used. In addition, due to the limitations of the hard magnetic material of the gyroscope system itself, it can maintain a certain magnetic field strength even after the external magnetic field disappears. The magnetic field strength it generates is relatively stable and has an obvious gradient, which will cause interference errors in the output of the magnetometer, thereby affecting the output of the hemispherical resonant gyroscope.

[0004] Therefore, a method for compensating for the gradient magnetic field interference error of a hemispherical resonator gyroscope is urgently needed to compensate for the interference error of the gradient magnetic field. Summary of the Invention

[0005] The present invention aims to provide a method for compensating for the interference error of the gradient magnetic field of a hemispherical resonant gyroscope, which is used to compensate for the interference error of the gradient magnetic field.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for compensating for gradient magnetic field interference errors of a hemispherical resonant gyroscope comprises connecting an inertial navigation module with magnetometer and accelerometer signals, and further comprising the following steps: step 1, collecting three-axis magnetic field intensity components of the gyroscope in a carrier coordinate system via the magnetometer; step 2, collecting three-axis acceleration measurement values of the gyroscope in the carrier coordinate system via the accelerometer; step 3, constructing an extended Kalman filter using navigation information as measurement input, and fusing and solving the three-axis magnetic field intensity components in step 1 and the three-axis acceleration measurement values in step 2 via the extended Kalman filter to obtain a compensation output of the magnetometer; wherein the three-axis magnetic field intensity components in step 1 contain a carrier magnetic field interference amount; the inertial navigation module is used to collect navigation information of the gyroscope, and the fusion and solution process of the extended Kalman filter includes a state prediction process and a measurement update process, wherein the state prediction process is used to predict the predicted state of the gyroscope at the next moment, and the measurement update process is used to solve the magnetometer to obtain the compensation output of the magnetometer.

[0008] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0009] 1. The present invention connects the inertial navigation module with the magnetometer and accelerometer signals to collect three-axis magnetic field intensity components and three-axis acceleration measurement values. Then, an extended Kalman filter is used to fuse and solve these data to obtain the compensation output of the magnetometer. The above compensation output is used to correct the attitude angle of the gyroscope, thereby reducing the impact of gradient magnetic field interference on the gyroscope output;

[0010] 2. The present invention linearizes the nonlinear function at each time step, converting the nonlinear problem into a linear problem for processing. In the state prediction step, the extended Kalman filter uses the Jacobian matrix to approximate the local linear behavior of the nonlinear function. The Jacobian matrix is a matrix that describes the rate of change of the nonlinear function relative to each component of the state vector. This enables the extended Kalman filter to effectively predict the state of the system at each time step.

[0011] 3. The present invention not only takes into account dynamic behaviors that are not fully captured by the model, such as external shocks and temperature changes, but also, by introducing process noise, the state prediction equation can better simulate random disturbances in the actual system, thereby improving the robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of the present invention, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0013] Figure 1 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0014] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the examples and accompanying drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention. It should be noted that the present invention is already in the actual development and use stage.

[0015] Example 1:

[0016] As attached Figure 1 As shown, a method for compensating for gradient magnetic field interference error of a hemispherical resonant gyroscope includes connecting an inertial navigation module with magnetometer and accelerometer signals, and further comprising the following steps:

[0017] Step 1: collect the three-axis magnetic field intensity components of the gyroscope in the carrier coordinate system through a magnetometer;

[0018] Step 2: Collect the three-axis acceleration measurement values of the gyroscope in the carrier coordinate system through the accelerometer;

[0019] Step 3: Using the navigation information as the measurement input, an extended Kalman filter is constructed. The three-axis magnetic field intensity components in step 1 and the three-axis acceleration measurements in step 2 are fused and solved by the extended Kalman filter to obtain the compensation output of the magnetometer.

[0020] The three-axis magnetic field intensity components in step 1 contain the carrier magnetic field interference;

[0021] The inertial navigation module is used to collect navigation information from the gyroscope. The fusion solution process of the extended Kalman filter includes a state prediction process and a measurement update process. The state prediction process is used to predict the predicted state of the gyroscope at the next moment, and the measurement update process is used to solve the magnetometer to obtain the compensation output of the magnetometer.

[0022] The state prediction process includes: selecting the deviation of the magnetometer caused by the magnetometer's own zero bias and the carrier magnetic field interference as the state vector to construct a state prediction equation, and then predicting the predicted state of the gyroscope at the next moment through the state prediction equation;

[0023] The measurement update process includes: constructing an observation equation using the difference between navigation information and the heading calculated by the magnetometer as the observation quantity, introducing the magnetometer's deviation components on its three axes into the observation equation, and then solving the magnetometer to obtain the compensation output of the magnetometer. The compensation output of the magnetometer is used to correct the attitude angle of the gyroscope.

[0024] It's important to note that the carrier coordinate system refers to the coordinate system of the carrier (platform, aircraft, drone, etc.) on which the HRG is mounted, also known as the body coordinate system. In an inertial navigation system, all sensor data (gyroscope, accelerometer, magnetometer) is first collected and initially integrated within this coordinate system. Therefore, the three-axis magnetic field intensity components and acceleration measurements in the carrier coordinate system refer to the measurements in the three directions within this body coordinate system.

[0025] It should be noted that due to the limitations of the hard magnetic material of the gyroscope system itself, it can maintain a certain magnetic field strength even after the external magnetic field disappears. The magnetic field strength it generates is relatively stable, and there is a significant gradient, which will cause interference errors in the output of the magnetometer; thus affecting the output of the hemispherical resonant gyroscope. Based on the above problems, the applicant proposed a method for compensating for the gradient magnetic field interference error of a hemispherical resonant gyroscope. By connecting the inertial navigation module with the magnetometer and accelerometer signals, collecting the three-axis magnetic field intensity components and three-axis acceleration measurement values, and then using the extended Kalman filter to fuse and solve these data to obtain the compensation output of the magnetometer. This compensation output is used to correct the attitude angle of the gyroscope, thereby reducing the impact of gradient magnetic field interference on the gyroscope output.

[0026] More specifically, since the hemispherical resonant gyroscope is sensitive to changes in the magnetic field, changes in the magnetic field (including interference from the gyroscope's own carrier magnetic field and external gradient magnetic field interference) will affect its measured angular velocity, thereby introducing errors. The three-axis magnetic field intensity components measured by the magnetometer include the magnetic field intensity of the X, Y, and Z axes, and the direct measurement value of the magnetometer already includes its own deviation. When the magnetometer has a magnetic field interference error, the output of the gyroscope will inevitably be affected accordingly. Therefore, on this basis, it is necessary to compensate for the interference error of the gyroscope.

[0027] Secondly, the magnetometer is used to collect the three-axis magnetic field strength components of the gyroscope in the carrier coordinate system. This data reflects the magnetic field conditions of the environment in which the gyroscope is located, including the magnetic field generated by the external environment and the carrier itself. At the same time, the accelerometer is used to collect the three-axis acceleration measurement values of the gyroscope in the carrier coordinate system; then these collected data are used as input and combined with the navigation information of the gyroscope to construct an extended Kalman filter. In the extended Kalman filter, the state prediction process predicts the predicted state of the gyroscope at the next moment through the state transfer matrix and the process noise vector. This process takes into account the dynamic characteristics and internal noise of the system; Subsequently, the measurement update process uses actual observation data, such as navigation information and the heading difference calculated by the magnetometer, to correct the predicted state. In this process, the observation matrix maps the state vector to the observation space, and the Kalman gain matrix determines how to combine the predicted state and the observed value to obtain the optimal state estimate, thereby achieving accurate fusion solution of the three-axis magnetic field strength components and three-axis acceleration measurement values of the gyroscope.

[0028] Through the iterative process of state prediction and measurement updates described above, the extended Kalman filter continuously adjusts and optimizes its estimate of the gyroscope state, thereby obtaining a compensation output from the magnetometer. This output is directly used to correct the gyroscope's attitude angle to eliminate or reduce the effects of gradient magnetic field interference. Specifically, the compensation output adjusts the gyroscope's attitude angle using a rotation matrix and angular velocity vector. This adjustment process takes into account the integration time interval, the attitude angle obtained by integrating the gyroscope's angular velocity, and the compensation output from the magnetometer. In this way, the gyroscope's attitude angle is corrected, thereby improving the accuracy and reliability of the gyroscope's output.

[0029] The method involved in this embodiment can process data in real time, provide continuous attitude estimation, and meet the output requirements of the real-time gyroscope. In addition, this embodiment has good adaptability and can adapt to dynamically changing magnetic field environments and provide accurate navigation information. This adaptability enables the gyroscope to maintain high performance under different operating conditions, and can work effectively both in complex scenarios such as urban canyons and in open scenarios.

[0030] Example 2:

[0031] This embodiment only describes the parts that are different from the first embodiment. Specifically, in step 1, the three-axis magnetic field intensity components of the magnetometer are measured values and satisfy:

[0032] ;

[0033] in, is the three-axis magnetic field intensity component of the magnetometer;

[0034] is the deviation of the magnetometer;

[0035] is the three-axis geomagnetic field strength of the gyroscope in the carrier coordinate system;

[0036] To measure noise.

[0037] It should be noted that the three-axis magnetic field intensity components of the magnetometer are expressed as measured values, including the magnetometer's own bias, the gyroscope's three-axis geomagnetic field strength in the carrier coordinate system, and measurement noise. This process allows for more accurate identification and quantification of various error sources in magnetometer measurements, providing a basis for subsequent error compensation. Specifically, the compensation process begins with preprocessing the data collected by the magnetometer. In this step, the magnetometer's bias is identified through a mathematical model, thereby isolating the magnetic field changes caused by the external environment. Next, this data is used, combined with the gyroscope's navigation information, to construct an extended Kalman filter. The extended Kalman filter is an effective algorithm that can achieve optimal state estimation in nonlinear systems. In this process, the extended Kalman filter estimates and corrects the gyroscope's attitude angle in real time through two key steps: state prediction and measurement update.

[0038] In the state prediction step, the Extended Kalman Filter uses the previous state estimate and control inputs to predict the current system state. Subsequently, in the measurement update step, the Extended Kalman Filter uses actual observation data, such as magnetometer and accelerometer measurements, to correct the predicted state. Through this iterative process, the Extended Kalman Filter continuously adjusts its estimate of the gyroscope state, resulting in a more accurate attitude angle estimate. This estimate, combined with the compensation output of the magnetometer, is used to correct the gyroscope's attitude angle to eliminate or reduce the effects of gradient magnetic field interference. This correction accounts for bias and noise in the magnetometer measurement, as well as magnetic field interference caused by changes in the external environment, providing a more comprehensive and accurate compensation solution.

[0039] Example 3:

[0040] This embodiment only describes the parts that are different from the first embodiment. Specifically, the state prediction process satisfies: ;

[0041] in, is the state vector;

[0042] are the components of the magnetometer deviation on the X, Y, and Z axes respectively;

[0043] Represents the transpose of a vector.

[0044] The state prediction equation is: ;

[0045] in, At time step Moment, based on time step The predicted state vector;

[0046] is the state transfer matrix;

[0047] For the time step Moment, based on time step An estimate of the state vector of ;

[0048] is the process noise vector.

[0049] It should be noted that in this embodiment, the core of state prediction lies in constructing a precise state prediction equation that can describe the gyroscope's behavior under various interferences and predict its future state. The starting point of the state prediction process is the gyroscope's current state vector, which contains all the necessary information to describe the gyroscope's dynamic behavior, such as angular velocity and attitude angle. This information is acquired in real time by the gyroscope and accelerometer and input into the state prediction equation as part of the state vector. The state prediction equation is typically a nonlinear function that predicts the state at the next moment based on the system's dynamic model, the current state vector, and possible control inputs. In this embodiment, this equation is further refined to include the components of the magnetometer's deviations on the X, Y, and Z axes. These deviations are caused by the magnetometer's own zero bias and the carrier magnetic field interference. This refinement enables the state prediction equation to more accurately simulate the gyroscope's behavior in real-world environments, thereby improving prediction accuracy.

[0050] To address the nonlinearities in the state prediction equation, this embodiment employs an extended Kalman filter (EKF) technique. This linearizes the nonlinear function at each time step, transforming the nonlinear problem into a linear one. During the state prediction step, the EKF uses the Jacobian matrix to approximate the local linear behavior of the nonlinear function. The Jacobian matrix describes the rate of change of the nonlinear function relative to the components of the state vector, enabling the EKF to effectively predict the system state at each time step.

[0051] Another key factor in the state prediction equation is the state transfer matrix, which describes the evolution of the system state over time. The state transfer matrix takes into account the physical characteristics and working environment of the gyroscope, such as the attitude angle obtained by integrating the angular velocity, and possible process noise. Process noise is a random variable that describes the uncertainty of the system model. It not only takes into account dynamic behaviors that are not fully captured by the model, such as external shocks and temperature changes, but by introducing process noise, the state prediction equation can also better simulate random disturbances in the actual system, thereby improving the robustness of the system.

[0052] In the state prediction process, the extended Kalman filter also involves the prediction of the state covariance matrix, which describes the distribution of state estimation uncertainty. The prediction of the state covariance matrix is achieved by multiplying the current state covariance matrix and the Jacobian matrix, and summing the process noise covariance matrix. This process takes into account the uncertainty in the prediction process and provides the necessary information for the subsequent measurement update step.

[0053] Example 4:

[0054] This embodiment only describes the parts that are different from the first embodiment. Specifically, the observation equation satisfies:

[0055] ;

[0056] in, is the observed quantity, namely the three-axis magnetic field intensity components and the three-axis acceleration measurement values;

[0057] is the observation matrix;

[0058] is the state vector;

[0059] is the observation noise.

[0060] The observation matrix satisfies, ;

[0061] are the row vectors of the observation matrix respectively;

[0062] in,

[0063] ;

[0064] in, ;

[0065] represents partial derivative;

[0066] are the three-axis magnetic field intensity components respectively;

[0067] are intermediate variables, specifically, After the three-axis magnetometer observation value is transformed by the attitude angle (especially the pitch angle and roll angle), it is constructed into an intermediate expression for building the observation model. Among them, L represents the difference component of the magnetometer y and z components after rotating around the roll angle, that is, the transverse magnetic field information after the body roll angle projection; N represents the composite component of the magnetometer three-axis components in the body x-axis direction after rotating around the roll and pitch angles, that is, the heading component after attitude compensation; M is used to construct the scale factor so that the final output angle or direction difference falls into a reasonable linear observation domain;

[0068] Indicates the roll angle;

[0069] Indicates the pitch angle.

[0070] The measurement update process satisfies:

[0071] ;

[0072] in, The status after measurement update;

[0073] is the Kalman filter gain matrix.

[0074] It is important to note that the actual measurements of the magnetometer and accelerometer are used as observations, and an observation matrix H is constructed that accounts for magnetometer bias, thereby achieving accurate estimation of the state (particularly magnetometer bias and attitude). Specifically, the observations are the actual sensor observations, and the observation equation describes the relationship between the state vector and the observation data. During the measurement update process, the observation matrix is a matrix that maps the state vector to the observation space and describes how the state vector affects the observation data. The observation matrix includes magnetometer bias, which is caused by both the magnetometer's own zero bias and the carrier magnetic field interference. This detailed definition allows the observation matrix H to more accurately simulate the errors in the actual observation process, thereby improving the accuracy of the state estimate.

[0075] The Kalman gain matrix is a coefficient used in the extended Kalman filter to determine how to combine the predicted state and the observed value to obtain the optimal state estimate. The calculation of the Kalman gain matrix takes into account observation noise and state prediction uncertainty, achieving the optimal state estimate by minimizing the error covariance. The calculation of the Kalman gain matrix involves the observation noise covariance matrix R and the prediction error covariance matrix, which describe the uncertainty in the observation and prediction processes. During the measurement update step, the extended Kalman filter uses the Kalman gain matrix to adjust the predicted state to bring it closer to the actual state. In this way, the extended Kalman filter can continuously adjust its estimate of the gyroscope state, thereby obtaining a more accurate attitude angle estimate. This estimate, combined with the compensation output of the magnetometer, is used to correct the gyroscope attitude angle to eliminate or reduce the influence of gradient magnetic field interference.

[0076] Example 5:

[0077] This embodiment only describes the parts that differ from the first embodiment. Specifically, the correction process of the gyroscope attitude angle by the compensation output of the magnetometer satisfies:

[0078] ;

[0079] ;

[0080] in, is the rotation matrix;

[0081] is the angular velocity vector;

[0082] is the integration time interval;

[0083] is the attitude angle after correction;

[0084] is the attitude angle obtained by integrating the gyroscope angular velocity;

[0085] is the compensation output of the magnetometer.

[0086] It should be noted that in the state prediction step, the extended Kalman filter uses the state estimate and control input from the previous moment to predict the system state at the current moment. In the measurement update step, the extended Kalman filter uses actual observation data, such as measurements from the magnetometer and accelerometer, to correct the predicted state. Through this iterative process, the extended Kalman filter can continuously adjust its estimate of the gyroscope state, thereby obtaining a more accurate attitude angle estimate. This estimate, combined with the compensation output of the magnetometer, is used to correct the gyroscope's attitude angle to eliminate or reduce the effects of gradient magnetic field interference. Specifically, the compensation output of the magnetometer adjusts the gyroscope's attitude angle using a rotation matrix and an angular velocity vector. This adjustment process takes into account the integration time interval, the attitude angle obtained by integrating the gyroscope's angular velocity, and the compensation output of the magnetometer. In this way, the gyroscope's attitude angle is corrected, thereby improving the accuracy and reliability of the gyroscope's output.

[0087] Example 6:

[0088] This embodiment only describes the parts that differ from the first embodiment. Specifically, the difference between the observation value, the navigation information, and the heading calculated by the magnetometer satisfies:

[0089] ;

[0090] in, ;

[0091] For navigation information;

[0092] The heading calculated by the magnetometer.

[0093] It should be noted that by constructing a comprehensive observation model, the measurement values of the magnetometer and accelerometer are combined with the navigation information of the gyroscope to calculate the heading difference. This heading difference is the difference between the heading calculated by the magnetometer and the heading in the navigation information. It reflects the impact of magnetic field interference on gyroscope measurements. By accurately measuring this difference, the system can identify the specific impact of magnetic field interference on gyroscope output and compensate accordingly.

[0094] In this process, the Extended Kalman Filter (EKF) is used to address the state estimation problem in nonlinear systems. The EKF linearizes the nonlinear function at each time step, transforming the nonlinear problem into a linear problem. In the state prediction step, the EKF uses the state estimate and control input from the previous moment to predict the system state at the current moment. In this step, the accuracy of the system dynamic model is crucial, as it determines the accuracy of the prediction. Subsequently, in the measurement update step, the EKF uses actual observation data, such as measurements from magnetometers and accelerometers, to correct the predicted state. In this step, the observation matrix and the Kalman gain matrix play a central role, determining how the observation data can be effectively integrated into the state estimate.

[0095] The technical solution of this embodiment further optimizes the design of the Kalman filter, particularly when processing the differences between observations and navigation information and headings calculated by the magnetometer. By precisely modeling and processing these differences, the system can more accurately estimate the impact of magnetic field interference on the gyroscope output and compensate accordingly. This approach not only improves the gyroscope's measurement accuracy, but also enhances the reliability and stability of the entire navigation system.

[0096] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for compensating for gradient magnetic field interference errors in a hemispherical resonant gyroscope, comprising connecting an inertial navigation module to magnetometer and accelerometer signals, characterized in that: The following steps are also included: Step 1: collect the three-axis magnetic field intensity components of the gyroscope in the carrier coordinate system through a magnetometer; Step 2: Collect the three-axis acceleration measurement values of the gyroscope in the carrier coordinate system through the accelerometer; Step 3: Using the navigation information as the measurement input, an extended Kalman filter is constructed. The three-axis magnetic field intensity components in step 1 and the three-axis acceleration measurements in step 2 are fused and solved by the extended Kalman filter to obtain the compensation output of the magnetometer. The three-axis magnetic field intensity components in step 1 contain the carrier magnetic field interference; The inertial navigation module is used to collect navigation information from the gyroscope. The fusion solution process of the extended Kalman filter includes a state prediction process and a measurement update process. The state prediction process is used to predict the predicted state of the gyroscope at the next moment, and the measurement update process is used to solve the magnetometer to obtain the compensation output of the magnetometer. The state prediction process includes: selecting the deviation of the magnetometer caused by the magnetometer's own zero bias and the carrier magnetic field interference as the state vector to construct a state prediction equation, and then predicting the predicted state of the gyroscope at the next moment through the state prediction equation; The measurement update process includes: constructing an observation equation based on the navigation information and the heading difference calculated by the magnetometer. After introducing the magnetometer deviation components on its three axes into the observation equation, the magnetometer is solved to obtain the compensation output of the magnetometer. The compensation output of the magnetometer is used to correct the attitude angle of the gyroscope. The observation matrix satisfies, ; are the row vectors of the observation matrix respectively; in, ； in, ; represents partial derivative; are the components of the magnetometer deviation on the X, Y, and Z axes respectively; are the three-axis magnetic field intensity components respectively; are intermediate variables respectively; Indicates the roll angle; Indicates the pitch angle; The compensation output of the magnetometer satisfies the following correction process for the gyroscope attitude angle: ； ； in, is the rotation matrix; is the angular velocity vector; is the integration time interval; is the attitude angle after correction; is the attitude angle obtained by integrating the gyroscope angular velocity; is the compensation output of the magnetometer.

2. The method for compensating for gradient magnetic field interference error of a hemispherical resonator gyroscope according to claim 1, characterized in that: In step 1, the three-axis magnetic field intensity components of the magnetometer are measured values and satisfy: ； in, is the three-axis magnetic field intensity component of the magnetometer; is the deviation of the magnetometer; is the three-axis geomagnetic field strength of the gyroscope in the carrier coordinate system; To measure noise.

3. The method for compensating for gradient magnetic field interference error of a hemispherical resonator gyroscope according to claim 1, characterized in that: The state prediction process satisfies, ; in, is the state vector; are the components of the magnetometer deviation on the X, Y, and Z axes respectively; Represents the transpose of a vector.

4. The method for compensating for gradient magnetic field interference error of a hemispherical resonator gyroscope according to claim 1, characterized in that: The state prediction equation is: ; in, At time step Moment, based on time step The predicted state vector; is the state transfer matrix; For the time step Moment, based on time step An estimate of the state vector of ; is the process noise vector.

5. The method for compensating for gradient magnetic field interference error of a hemispherical resonator gyroscope according to claim 1, characterized in that: The observation equation satisfies: ； in, is the observed quantity, namely the three-axis magnetic field intensity components and the three-axis acceleration measurement values; is the observation matrix; is the state vector; is the observation noise.

6. The method for compensating for gradient magnetic field interference error of a hemispherical resonator gyroscope according to claim 5, characterized in that: The measurement update process satisfies: ； in, The status after measurement update; is the Kalman filter gain matrix.

7. A method for compensating for gradient magnetic field interference errors of a hemispherical resonator gyroscope according to claim 5 or 6, characterized in that: The difference between the observed value, navigation information and the heading calculated by the magnetometer satisfies: ； in, ; For navigation information; The heading calculated by the magnetometer.

Images