Error calibration method and system based on three-axis fluxgate sensor

Abstract

The invention belongs to the technical field of geophysical exploration, and particularly relates to an error calibration method and system based on a three-axis fluxgate sensor. The method comprises the following steps: constructing a three-axis fluxgate sensor error model to obtain a measurement error of a to-be-calibrated three-axis fluxgate sensor; constructing an error correction model; iteratively solving the error correction model to obtain a weight vector containing error parameters of the three-axis fluxgate sensor to be calibrated; the method comprises the following steps of: inversely substituting a weight vector which is obtained by iterative solution and contains an error parameter of a to-be-calibrated three-axis fluxgate sensor into a measurement error of the to-be-calibrated three-axis fluxgate sensor to obtain a measurement error of the three-axis fluxgate sensor, and correcting three-axis magnetic field measurement data by using the measurement error of the three-axis fluxgate sensor to obtain a three-axis magnetic field calibration result. And obtaining a corrected three-axis magnetic field value. According to the method, a complex three-dimensional linear calibration problem is converted into a parameter estimation problem which is convenient to optimize and solve, and high-efficiency and high-precision rapid correction and compensation of the inherent error of the three-axis fluxgate sensor are realized.

Description

Technical Field

[0001] This application belongs to the field of geophysical exploration technology, and in particular relates to an error calibration method and system based on a triaxial fluxgate sensor. Background Technology

[0002] With the increasing demand for higher precision in magnetic field measurements in fields such as geomagnetic navigation, attitude estimation, geophysical exploration, unexploded ordnance detection, and anti-submarine warfare, triaxial fluxgate sensors, as a high-sensitivity magnetic field measurement device based on the fluxgate effect, have been widely used in these fields. Their basic working principle utilizes the nonlinear magnetization response of ferromagnetic materials under the combined action of an external magnetic field and a high-frequency excitation current to sense magnetic field information. The sources of measurement error are complex, and common errors include, but are not limited to: non-orthogonality error, sensitivity error, zero-bias error, temperature drift, and interference from soft and hard iron.

[0003] Due to limitations in manufacturing processes and processing levels, errors such as triaxial non-orthogonality, sensitivity error, zero-bias error, and inconsistencies in other electrical characteristics are inevitable during the manufacturing of triaxial fluxgate sensors. Without effective calibration, even in a stable external magnetic field environment, sensor readings may deviate significantly from the actual field strength, thus affecting the reliability of subsequent applications.

[0004] Traditional calibration methods for triaxial fluxgate sensors include techniques such as least squares and ellipsoidal fitting. Least squares estimates error parameters by fitting observed data to a mathematical model. This method is suitable for linear systems and can handle errors under certain non-ideal conditions. However, this method depends on the choice of initial estimates; if the initial parameters are not chosen appropriately, the algorithm may converge to a local optimum rather than the global optimum. Static calibration methods based on ellipsoidal fitting fit the sensor output data to an ideal ellipsoid using least squares, solving for zero bias, sensitivity, and non-orthogonal error parameters. However, in reality, due to factors such as manufacturing defects and temperature variations, the actual output shape may deviate from the ideal ellipsoid, leading to inaccurate fitting results. Furthermore, this algorithm is not effective for correcting triaxial non-orthogonal errors. Summary of the Invention

[0005] This application provides a method and system for error calibration of a three-axis fluxgate sensor, which aims to solve the problem of inherent errors in the three-axis fluxgate sensor caused by limitations in manufacturing processes and processing levels.

[0006] To achieve the above objectives, this application provides the following technical solution: According to the first aspect of this application, a method for error calibration based on a triaxial fluxgate sensor includes: In a stable and uniform magnetic field environment, triaxial magnetic field measurement data under different postures are collected using a triaxial fluxgate sensor to be calibrated, and then the true value of the triaxial magnetic field of the environment where the fluxgate to be calibrated is located is collected using a magnetic sensor. A three-axis fluxgate sensor error model is constructed. The three-axis fluxgate sensor error model represents the three-axis magnetic field measurement data as the sum of the product of the true value of the three-axis magnetic field in an ideal orthogonal coordinate system, the non-orthogonal error coefficient matrix, and the sensitivity error coefficient matrix, and the zero bias error coefficient matrix. The difference between the triaxial magnetic field measurement data and the true value of the triaxial magnetic field is obtained to obtain the measurement error of the triaxial fluxgate sensor to be calibrated. Using the vector L2 norm and the measurement error of the triaxial fluxgate sensor to be calibrated, an error correction model is constructed with triaxial magnetic field measurement data as input and the error parameters of the triaxial fluxgate sensor to be calibrated as output. Using the true value of the triaxial magnetic field as the ideal value, the gradient descent optimization algorithm with momentum term is used to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated in the error correction model, and a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated is obtained. The weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, obtained by iterative solution, is substituted into the measurement error of the triaxial fluxgate sensor to be calibrated to obtain the measurement error of the triaxial fluxgate sensor. The measurement error of the triaxial fluxgate sensor is then used to correct the triaxial magnetic field measurement data to obtain the corrected triaxial magnetic field value.

[0007] Furthermore, the non-orthogonal error coefficient matrix is ​​as follows: , This represents the non-orthogonal error coefficient matrix. Assume O-XYZ is the ideal orthogonal coordinate system of the magnetic sensor, and O-X'Y'Z' is the actual coordinate system of the magnetic sensor. The OZ axis is aligned with the O'Z' axis, and the OY' axis is placed in the YOZ plane, with the angle between the OY and OY axes represented by [missing information]. express, It is the angle between the OX' axis and the XOZ plane. It is the angle between the OX' axis and the XOY axis; The sensitivity error coefficient matrix is ​​as follows: , Represents the sensitivity error coefficient matrix. , and These are the sensitivity coefficients of the three-axis components of the magnetic field; The zero-bias error coefficient matrix is: , This represents the zero-bias error coefficient matrix. , and These are the zero bias values ​​of the three axes of the magnetic field.

[0008] Furthermore, the difference between the triaxial magnetic field measurement data and the true value of the triaxial magnetic field is calculated to obtain the measurement error of the triaxial fluxgate sensor to be calibrated, and the result is expressed as follows: In the formula , , This is triaxial magnetic field measurement data. The measurement error of the triaxial fluxgate sensor to be calibrated.

[0009] Furthermore, the error correction model is expressed as: , The target output value of the error correction model. Triaxial magnetic field measurement data Axial components, Triaxial magnetic field measurement data Axial components, Triaxial magnetic field measurement data Axis components, weight vector , This is the feature vector of the magnetic field data.

[0010] Furthermore, using the true value of the triaxial magnetic field as the ideal value, a gradient descent optimization algorithm with a momentum term is employed to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated using the error correction model. This yields a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, including: The collected triaxial magnetic field measurement data were randomly shuffled and divided into several small batches of data for iterative optimization. For each mini-batch of data, the forward propagation algorithm is used to predict the output, residual term, and loss function term of the error correction model; Perform the backpropagation algorithm, add a regularization term to the loss function term, and obtain the loss function; The gradient is obtained by differentiating the loss function; The momentum gradient descent method is adopted to update the momentum using the gradient, and the weight vector is updated based on the momentum. Iterate until the convergence or early stopping criterion is met to obtain a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated.

[0011] Furthermore, the momentum gradient descent method is employed to update the momentum using the gradient, and the weight vector is updated based on the momentum, including: calculating the momentum. Update the weight vector ,in Momentum factor The learning rate uses an exponential decay strategy, expressed as: , The initial learning rate, The decay rate of the learning rate. For the number of iterations, To minimize the learning rate, For gradient, It is the momentum before the update. It is the weight vector before the update.

[0012] Furthermore, the gradient is represented as: ,in for Regularization term, The regularization coefficient is . This represents the number of data points in the current small batch. For the first The target value of each data point in the current small batch of data. For the first The magnetic field data feature vector of each data point in the current small batch of data. For the weight vector, This is a transpose.

[0013] A triaxial fluxgate sensor error calibration system according to a second aspect embodiment of this application includes: The magnetic field data acquisition module is used to acquire triaxial magnetic field measurement data under different postures collected by the triaxial fluxgate sensor to be calibrated, and to acquire the true value of the triaxial magnetic field of the environment in which the fluxgate to be calibrated is located by the magnetic sensor. The three-axis fluxgate sensor error model calculates the difference between the three-axis magnetic field measurement data and the true value of the three-axis magnetic field to obtain the measurement error of the three-axis fluxgate sensor to be calibrated. The three-axis fluxgate sensor error model expresses the three-axis magnetic field measurement data as the sum of the product of the true value of the three-axis magnetic field in the ideal orthogonal coordinate system, the non-orthogonal error coefficient matrix, and the sensitivity error coefficient matrix, and the zero bias error coefficient matrix. The error correction model construction module utilizes the vector L2 norm and the measurement error of the triaxial fluxgate sensor to be calibrated to construct an error correction model with triaxial magnetic field measurement data as input and the error parameters of the triaxial fluxgate sensor to be calibrated as output. The model training module uses the true value of the triaxial magnetic field as the ideal value and adopts a gradient descent optimization algorithm with momentum term to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated for the error correction model, and obtains a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated. The calibration module uses the weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, obtained by iterative solution, to substitute back into the measurement error of the triaxial fluxgate sensor to be calibrated, thereby obtaining the measurement error of the triaxial fluxgate sensor. The measurement error of the triaxial fluxgate sensor is then used to correct the triaxial magnetic field measurement data, thereby obtaining the corrected triaxial magnetic field value.

[0014] Compared with the prior art, the embodiments of this application have at least the following beneficial effects: This application constructs an error correction model that takes triaxial magnetic field measurement data as input and the error parameters of the triaxial fluxgate sensor to be calibrated as output. It then uses a momentum gradient descent optimization algorithm to iteratively optimize and predict the error parameters of the triaxial fluxgate sensor, effectively solving the key technical challenge of inherent errors in triaxial fluxgate sensors caused by limitations in manufacturing processes and processing levels. This approach considers the real-time calibration requirements in practical applications while improving upon the poor adaptability and slow convergence speed of traditional methods. It achieves high-efficiency and high-precision rapid correction and compensation of the inherent errors of triaxial fluxgate sensors.

[0015] This application transforms the complex three-dimensional linear calibration problem into a parameter estimation problem that is easy to optimize and solve, balancing calibration accuracy and computational efficiency. It is particularly suitable for scenarios with stringent requirements for magnetic field measurement accuracy, such as underground space navigation, UAV attitude control, and indoor positioning. Attached Figure Description

[0016] Figure 1 A flowchart illustrating a method for calibrating the error of a three-axis fluxgate sensor, as provided in this application embodiment; Figure 2 A block diagram of a three-axis fluxgate sensor error calibration system provided in an embodiment of this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0018] The specific implementation of this application will be described in detail below with reference to specific embodiments.

[0019] See Figure 1 As shown, a method for calibrating the error of a three-axis fluxgate sensor includes the following steps: In a stable and uniform magnetic field environment, S1 uses a triaxial fluxgate sensor to be calibrated to collect triaxial magnetic field measurement data under different postures, and then uses a magnetic sensor to collect the true value of the triaxial magnetic field of the environment where the fluxgate to be calibrated is located. The magnetic sensor here is a higher precision magnetic sensor, used as the true value of the three-axis magnetic field. The higher precision magnetic sensor is not limited to the three-axis fluxgate sensor and the optically pumped magnetometer.

[0020] Specifically, an open outdoor environment far from vehicles, power lines, and steel structures was selected as the experimental site, free from dynamic magnetic interference and with a small magnetic field gradient change (≤10nT / m) within the sensor's measurement range. The probe of the triaxial fluxgate sensor was placed in the center of the working area of ​​the non-magnetic turntable. The non-magnetic turntable was slowly rotated to make the probe point evenly in all directions of the spatial sphere to collect triaxial magnetic field data. A higher-precision magnetic sensor was selected to collect magnetic field data at the same position for 3 minutes, and the average value was taken as the ideal value for subsequent calibration.

[0021] S2 constructs a three-axis fluxgate sensor error model, which represents the three-axis magnetic field measurement data as the sum of the product of the true value of the three-axis magnetic field in an ideal orthogonal coordinate system, the non-orthogonal error coefficient matrix, and the sensitivity error coefficient matrix, and the zero bias error coefficient matrix. The error model of the three-axis fluxgate sensor is expressed as follows: To achieve the measurement of triaxial magnetic field data True values ​​of the triaxial magnetic field in an ideal orthogonal coordinate system The conversion between them, where, in, The error coefficient matrix is ​​non-orthogonal. Because the error between the actual shaft and the ideal shaft is less than , It can be approximated as , The sensitivity error coefficient matrix is ​​as follows: , The zero-bias error coefficient matrix: Assuming O-XYZ is the ideal orthogonal coordinate system of the magnetic sensor, and O-X'Y'Z' is the actual coordinate system of the magnetic sensor, the OZ axis is aligned with the O'Z' axis, and the OY' axis is placed in the YOZ plane, with the angle between the OY axis and the OY axis represented by [missing information]. express, It is the angle between the OX' axis and the XOZ plane. It is the angle between the OX' axis and the XOY axis; , and These are the sensitivity coefficients of the three-axis components of the magnetic field; This represents the zero-bias error coefficient matrix. , and These are the zero bias values ​​of the three axes of the magnetic field.

[0022] S3 calculates the difference between the triaxial magnetic field measurement data and the true value of the triaxial magnetic field to obtain the measurement error of the triaxial fluxgate sensor to be calibrated. Based on the error model of the triaxial fluxgate sensor in S2, the measurement error of the triaxial fluxgate sensor to be calibrated can be derived. It can be represented as: , Ignoring second-order minor quantities, we can obtain In the formula , , , This is triaxial magnetic field measurement data. The measurement error of the triaxial fluxgate sensor to be calibrated.

[0023] S4 utilizes the vector L2 norm and the measurement error of the three-axis fluxgate sensor to be calibrated to construct an error correction model with three-axis magnetic field measurement data as input and the error parameters of the three-axis fluxgate sensor to be calibrated as output. Using the definition of the vector 2 norm and the measurement error of the triaxial fluxgate sensor to be calibrated mentioned above. Establish an error correction model: , Ignoring second-order minor quantities again, we get: .

[0024] Expand and simplify to: This is transformed into a weight vector in a multidimensional feature space. The optimization problem involves finding the true values ​​of the triaxial magnetic field. Magnetic data is measured using more precise magnetic sensors, and the feature vector of the magnetic field data is analyzed. The square terms of the three-axis magnetic field components, the cross terms between the three-axis magnetic field components, and the three-axis magnetic field components are normalized. The target output value of the error correction model. Triaxial magnetic field measurement data Axial components, Triaxial magnetic field measurement data Axial components, Triaxial magnetic field measurement data Axial components.

[0025] S5 takes the true value of the triaxial magnetic field as the ideal value and uses a gradient descent optimization algorithm with momentum term to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated in the error correction model, and obtains a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated. S6 uses the weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, obtained by iterative solution, to substitute back into the measurement error of the triaxial fluxgate sensor to be calibrated to obtain the measurement error of the triaxial fluxgate sensor. The measurement error of the triaxial fluxgate sensor is then used to correct the triaxial magnetic field measurement data to obtain the corrected triaxial magnetic field value.

[0026] Specifically, the weight vector obtained during training The error parameters of the triaxial fluxgate sensor to be calibrated are analyzed and substituted into the formula. The measurement error of the three-axis fluxgate sensor can be obtained. Then, the measurement error of the three-axis fluxgate sensor to be calibrated... Measurement error of triaxial fluxgate sensor Bring into This will allow us to obtain the compensated and corrected triaxial magnetic field values. .

[0027] In one embodiment, the true value of the triaxial magnetic field is taken as the ideal value, and a gradient descent optimization algorithm with a momentum term is used to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated on the error correction model, resulting in a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, including: The collected triaxial magnetic field measurement data were randomly shuffled and divided into several small batches of data for iterative optimization. For each mini-batch of data, the forward propagation algorithm is used to predict the output, residual term, and loss function term of the error correction model; Perform the backpropagation algorithm, add a regularization term to the loss function term, and obtain the loss function; The gradient is obtained by differentiating the loss function; The momentum gradient descent method is adopted to update the momentum using the gradient, and the weight vector is updated based on the momentum. Until the convergence or early stopping criterion is met, a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated is obtained.

[0028] Specifically, the initialization involves a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated. Initial learning rate and stopping iteration threshold and The collected triaxial magnetic field measurement data were randomly shuffled and divided into several small batches of data for iterative optimization. For each mini-batch of data, perform the forward propagation algorithm and predict the output of the error correction model. residual term and loss function term ,in This represents the number of data points in the current small batch. For the first The target value of each data point in the current small batch of data. For the first The magnetic field data feature vector of each data point in the current small batch of data; Perform the backpropagation algorithm and add the following to the loss function term: Calculate the loss function: , The gradient is obtained by differentiating the loss function. ,in for Regularization term, The regularization coefficient is used. The momentum is updated using the gradient descent method and the momentum is calculated. Update the weight vector ,in Momentum factor The learning rate uses an exponential decay strategy, expressed as: , The initial learning rate, The decay rate of the learning rate. For the number of iterations, To minimize the learning rate, For gradient, It is the momentum before the update. This is the weight vector before the update. Repeated training makes the loss function term of the total data less than the threshold for stopping the update. When or after multiple consecutive iterations the improvement is less than the threshold At this point, momentum gradient descent is discontinued, and the weight vector of the error parameters of the triaxial fluxgate sensor to be calibrated is output. .

[0029] In one example, the threshold It is the threshold for stopping iterations. threshold It is the early stopping threshold .

[0030] On the other hand, see Figure 2 As shown, this application provides a triaxial fluxgate sensor error calibration system, including: a magnetic field data acquisition module, which collects triaxial magnetic field measurement data under different postures using a triaxial fluxgate sensor to be calibrated in a stable and uniform magnetic field environment, and then collects the true value of the triaxial magnetic field of the environment where the fluxgate to be calibrated is located using a magnetic sensor; The three-axis fluxgate sensor error model obtains the measurement error of the three-axis fluxgate sensor to be calibrated by subtracting the three-axis magnetic field measurement data from the true value of the three-axis magnetic field. The three-axis fluxgate sensor error model expresses the three-axis magnetic field measurement data as the sum of the product of the true value of the three-axis magnetic field in the ideal orthogonal coordinate system, the non-orthogonal error coefficient matrix, and the sensitivity error coefficient matrix, and the zero bias error coefficient matrix. The error correction model construction module utilizes the vector L2 norm and the measurement error of the triaxial fluxgate sensor to be calibrated to construct an error correction model with triaxial magnetic field measurement data as input and the error parameters of the triaxial fluxgate sensor to be calibrated as output. The model training module uses the true value of the triaxial magnetic field as the ideal value and employs a gradient descent optimization algorithm with a momentum term to iteratively solve for the error parameters of the triaxial fluxgate sensor to be calibrated in the error correction model. This yields a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated. The prediction residual is calculated in each batch update, and the gradient calculation incorporates... Regularize and update the momentum term synchronously until the convergence or early stopping criterion is met, to obtain a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated; The calibration module uses the weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, obtained by iterative solution, to substitute back into the measurement error of the triaxial fluxgate sensor to be calibrated to obtain the measurement error of the triaxial fluxgate sensor. The measurement error of the triaxial fluxgate sensor is then used to correct the triaxial magnetic field measurement data to obtain the corrected triaxial magnetic field value.

[0031] The error parameters of the triaxial fluxgate sensor to be calibrated obtained by analysis can also be applied to the host computer for magnetic field data acquisition, and the triaxial magnetic field measurement data can be corrected in real time online through compensation calculation.

[0032] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0033] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0034] The above are merely preferred embodiments of this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of this application, and these should also be considered within the scope of protection of this application. These will not affect the effectiveness and practicality of the implementation of this application.

Claims

1. A method for calibrating the error of a three-axis fluxgate sensor, characterized in that, include: In a stable and uniform magnetic field environment, triaxial magnetic field measurement data under different postures are collected using a triaxial fluxgate sensor to be calibrated, and then the true value of the triaxial magnetic field of the environment where the fluxgate to be calibrated is located is collected using a magnetic sensor. A three-axis fluxgate sensor error model is constructed. The three-axis fluxgate sensor error model represents the three-axis magnetic field measurement data as the sum of the product of the true value of the three-axis magnetic field in an ideal orthogonal coordinate system, the non-orthogonal error coefficient matrix, and the sensitivity error coefficient matrix, and the zero bias error coefficient matrix. The difference between the triaxial magnetic field measurement data and the true value of the triaxial magnetic field is obtained to obtain the measurement error of the triaxial fluxgate sensor to be calibrated. Using the vector L2 norm and the measurement error of the triaxial fluxgate sensor to be calibrated, an error correction model is constructed with triaxial magnetic field measurement data as input and the error parameters of the triaxial fluxgate sensor to be calibrated as output. Using the true value of the triaxial magnetic field as the ideal value, the gradient descent optimization algorithm with momentum term is used to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated in the error correction model, and a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated is obtained. The weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, obtained by iterative solution, is substituted into the measurement error of the triaxial fluxgate sensor to be calibrated to obtain the measurement error of the triaxial fluxgate sensor. The measurement error of the triaxial fluxgate sensor is then used to correct the triaxial magnetic field measurement data to obtain the corrected triaxial magnetic field value.

2. The method for calibrating the error of a three-axis fluxgate sensor according to claim 1, characterized in that, The non-orthogonal error coefficient matrix is ​​as follows: , This represents the non-orthogonal error coefficient matrix. Assume O-XYZ is the ideal orthogonal coordinate system of the magnetic sensor, and O-X'Y'Z' is the actual coordinate system of the magnetic sensor. The OZ axis is aligned with the O'Z' axis, and the OY' axis is placed in the YOZ plane, with the angle between the OY and OY axes represented by [missing information]. express, It is the angle between the OX' axis and the XOZ plane. It is the angle between the OX' axis and the XOY axis; The sensitivity error coefficient matrix is ​​as follows: , Represents the sensitivity error coefficient matrix. , and These are the sensitivity coefficients of the three-axis components of the magnetic field; The zero-bias error coefficient matrix is: , This represents the zero-bias error coefficient matrix. , and These are the zero bias values ​​of the three axes of the magnetic field.

3. The method for calibrating the error of a triaxial fluxgate sensor according to claim 2, characterized in that, The difference between the triaxial magnetic field measurement data and the true value of the triaxial magnetic field is used to obtain the measurement error of the triaxial fluxgate sensor to be calibrated, and the result is expressed as follows: In the formula , , This is triaxial magnetic field measurement data. The measurement error of the triaxial fluxgate sensor to be calibrated.

4. The method for calibrating the error of a three-axis fluxgate sensor according to claim 3, characterized in that, The error correction model is expressed as: , The target output value of the error correction model. Triaxial magnetic field measurement data Axial components, Triaxial magnetic field measurement data Axial components, Triaxial magnetic field measurement data Axis components, weight vector , This is the feature vector of the magnetic field data.

5. The method for calibrating the error of a triaxial fluxgate sensor according to claim 3, characterized in that, Using the true value of the triaxial magnetic field as the ideal value, a gradient descent optimization algorithm with a momentum term is used to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated, resulting in a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, including: The collected triaxial magnetic field measurement data were randomly shuffled and divided into several small batches of data for iterative optimization. For each mini-batch of data, the forward propagation algorithm is used to predict the output, residual term, and loss function term of the error correction model; Perform the backpropagation algorithm, add a regularization term to the loss function term, and obtain the loss function; The gradient is obtained by differentiating the loss function; The momentum gradient descent method is adopted to update the momentum using the gradient, and the weight vector is updated based on the momentum. Iterate until the convergence or early stopping criterion is met to obtain a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated.

6. The method for calibrating the error of a triaxial fluxgate sensor according to claim 5, characterized in that, The momentum gradient descent method is employed, using the gradient to update momentum, and then updating the weight vector based on momentum. This includes: calculating momentum. Update the weight vector ,in Momentum factor The learning rate uses an exponential decay strategy, expressed as: , The initial learning rate, The decay rate of the learning rate. For the number of iterations, To minimize the learning rate, For gradient, It is the momentum before the update. It is the weight vector before the update.

7. The method for calibrating the error of a three-axis fluxgate sensor according to claim 5, characterized in that, The gradient is represented as: ,in for Regularization term, The regularization coefficient is . This represents the number of data points in the current small batch. For the first The target value of each data point in the current small batch of data. For the first The magnetic field data feature vector of each data point in the current small batch of data. For the weight vector, This is a transpose.

8. A three-axis fluxgate sensor error calibration system, characterized in that, include: The magnetic field data acquisition module is used to acquire triaxial magnetic field measurement data under different postures collected by the triaxial fluxgate sensor to be calibrated, and to acquire the true value of the triaxial magnetic field of the environment in which the fluxgate to be calibrated is located by the magnetic sensor. The three-axis fluxgate sensor error model calculates the difference between the three-axis magnetic field measurement data and the true value of the three-axis magnetic field to obtain the measurement error of the three-axis fluxgate sensor to be calibrated. The three-axis fluxgate sensor error model expresses the three-axis magnetic field measurement data as the sum of the product of the true value of the three-axis magnetic field in the ideal orthogonal coordinate system, the non-orthogonal error coefficient matrix, and the sensitivity error coefficient matrix, and the zero bias error coefficient matrix. The error correction model construction module utilizes the vector L2 norm and the measurement error of the triaxial fluxgate sensor to be calibrated to construct an error correction model with triaxial magnetic field measurement data as input and the error parameters of the triaxial fluxgate sensor to be calibrated as output. The model training module uses the true value of the triaxial magnetic field as the ideal value and adopts a gradient descent optimization algorithm with momentum term to iteratively solve the error parameters of the triaxial fluxgate sensor to be calibrated for the error correction model, and obtains a weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated. The calibration module uses the weight vector containing the error parameters of the triaxial fluxgate sensor to be calibrated, obtained by iterative solution, to substitute back into the measurement error of the triaxial fluxgate sensor to be calibrated, thereby obtaining the measurement error of the triaxial fluxgate sensor. The measurement error of the triaxial fluxgate sensor is then used to correct the triaxial magnetic field measurement data, thereby obtaining the corrected triaxial magnetic field value.

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