A scalar magnetometer heading error calibration compensation method and system

Abstract

The application discloses a scalar magnetometer heading error calibration compensation method and system, and relates to the technical field of magnetic field measurement.The method comprises the following steps: analyzing the heading error of the scalar magnetometer, and establishing an error compensation model; performing a heading error calibration experiment of the scalar magnetometer, and measuring error calibration data; and using a fitting algorithm to obtain error compensation coefficients, which are used for subsequent heading error compensation.The method has the advantages that the calibration experiment process is short in time consumption, easy to operate, and capable of reducing the influence of magnetic measurement noise caused by time drift due to a long experiment process; the form of strapdown installation of the vector magnetometer and the scalar magnetometer can be integrated into an airborne magnetic measurement system, the effects of heading error compensation and motor interference compensation are achieved, and the airborne magnetic measurement precision is improved.Finally, the scalar magnetometer can realize accurate measurement in the whole heading range.

Description

Technical Field

[0001] This invention relates to the field of magnetic field measurement technology, and specifically to a scalar magnetometer heading error calibration and compensation method and system. Background Technology

[0002] Magnetometers can be classified into scalar magnetometers and vector magnetometers based on the type of physical quantity of the magnetic field they measure. Currently, the mainstream scalar magnetometers on the market are optically pumped magnetometers and atomic magnetometers. Both have outstanding advantages in terms of sensitivity and accuracy. Furthermore, because they do not require cryogenic cooling, are convenient and reliable, and can be miniaturized, they play an important role in applications such as geophysical magnetic detection, space magnetic detection, medical magnetic detection, and geomagnetic navigation.

[0003] Ideally, a scalar magnetometer can measure the total magnetic field value, which should be independent of changes in the direction of the magnetic probe relative to the magnetic field. However, in reality, when the magnitude and direction of the external magnetic field to be measured remain constant, rotating the magnetic probe changes the angle between the probe and the direction of the magnetic field, causing a change in the magnetometer's magnetic field measurement value and introducing measurement error. This error is called "heading error," which is the source of inaccuracy in magnetic field measurement. The problem of heading error is even more pronounced when the scalar magnetometer is mounted on a moving platform. For example, during geomagnetic baseline map acquisition, the opposite headings of adjacent survey lines in a "bow"-shaped route cause heading errors in the magnetic measurement data, resulting in decreased accuracy in magnetic map construction and causing magnetic map striping errors. Although heading error is a fundamental error of the scalar magnetometer, it can be calibrated through system compensation methods. Summary of the Invention

[0004] This invention addresses the problem of heading error when a scalar magnetometer is mounted on a motion platform by proposing a scalar magnetometer heading error calibration and compensation method and system.

[0005] The technical solution adopted in this invention is as follows: In a first aspect, the present invention proposes a method for calibrating and compensating the heading error of a scalar magnetometer, comprising the following steps: Step 1: Analyze the heading error of the scalar magnetometer and establish a heading error compensation model containing the magnetic field direction cosine matrix and the heading error compensation coefficient to be solved; Step 2: Strapdown and fixed installation of the first scalar magnetometer and the vector magnetometer on a horizontally placed rotatable non-magnetic platform. Place the second scalar magnetometer near the first scalar magnetometer and conduct a scalar magnetometer heading error calibration experiment. Simultaneously record the magnetic field data of the first scalar magnetometer, the second scalar magnetometer, and the vector magnetometer. Step 3: Use a fitting algorithm to solve for the heading error compensation coefficients in the heading error compensation model based on the magnetic field data, which will be used for subsequent heading error compensation.

[0006] Furthermore, the heading error compensation model is as follows: in, For heading error, Let be the heading error compensation coefficient to be solved. , , The direction cosine of the three-axis magnetic field is given by the superscript T, which is the transpose symbol.

[0007] Furthermore, the heading error compensation model is based on the heading error. and the angle between the measured magnetic field and the optical axis There are highly nonlinear functions between them exist The result is derived by performing a third-order Taylor series expansion at the given location.

[0008] Furthermore, the scalar magnetometer heading error calibration experiment in step 2 includes: Step 2.1: Strapdown and fixed installation of the first scalar magnetometer and the vector magnetometer on a horizontally placed rotatable non-magnetic platform. The long axis of the first scalar magnetometer is fixed perpendicular to the platform. Among the three magnetic measurement axes of the vector magnetometer, the X-axis and Y-axis are parallel to the platform, and the Z-axis is perpendicular. The second scalar magnetometer is then installed and placed near the first scalar magnetometer. Step 2.2: Start the second scalar magnetometer to collect scalar data of the ambient magnetic field for several minutes. If the peak-to-peak value of the fluctuation of the ambient magnetic field scalar data is less than 2nT, the environment is considered stable and subsequent experimental operations can be carried out; otherwise, adjust the experimental environment. Step 2.3: Start the first scalar magnetometer, the second scalar magnetometer, and the vector magnetometer, maintain the data acquisition state, and record the magnetic field data including timestamps; slowly rotate the non-magnetic platform in the horizontal plane first counterclockwise 360 ​​degrees, then slowly rotate clockwise 360 ​​degrees, and finally slowly rotate counterclockwise, holding it still for 10 seconds after each 45-degree rotation, until it returns to the initial position, thus completing the magnetic field data acquisition process; Step 2.4: Align the magnetic field data of the first scalar magnetometer, the second scalar magnetometer, and the vector magnetometer according to the timestamp, for use in solving the heading error compensation coefficient.

[0009] Furthermore, the process of solving for the heading error compensation coefficient includes: Step 3.1: Based on the magnetic field data obtained from the calibration experiment in Step 2, record the magnetic field data of the first scalar magnetometer as follows: The magnetic field data of the second scalar magnetometer are The three-axis magnetic field data of the vector magnetometer are N represents the number of data sampling points; Step 3.2: Based on the three-axis magnetic field data of the vector magnetometer, calculate the three-axis magnetic field direction cosine in the heading error heading model, and then obtain the magnetic field direction cosine matrix; and, subtract the magnetic field data of the first scalar magnetometer and the second scalar magnetometer to obtain the heading error; Step 3.3: Based on the heading error compensation model, establish the following expression: Where K is the heading error compensation coefficient to be solved. , For heading error, This is the cosine matrix of the magnetic field direction; Step 3.4: Fit the expression from Step 3.3 to obtain the optimal estimate of K. .

[0010] Furthermore, step 3.4 employs recursive least squares fitting.

[0011] Furthermore, the formula for calculating the direction cosine of the triaxial magnetic field in step 3.2 is as follows: in, , , The cosine of the triaxial magnetic field direction is calculated for the i-th data sampling point. , , The data represents the three-axis magnetic field data of a vector magnetometer at i data sampling points.

[0012] Furthermore, the direction cosine matrix of the magnetic field is: The superscript T is the transpose symbol.

[0013] Furthermore, the process of using the solved heading error compensation model for subsequent heading error compensation includes: The vector magnetometer is strapped in with the first scalar magnetometer to obtain the three-axis magnetic field data of the vector magnetometer in real time, calculate the current three-axis magnetic field direction cosine, and then obtain the current magnetic field direction cosine matrix. Substitute the current magnetic field direction cosine matrix and the solved heading error compensation coefficient into the heading error compensation model to calculate the current heading error estimate. The result of subtracting the current heading error estimate from the magnetic field data measured by the first scalar magnetometer is output as the compensation result.

[0014] Secondly, this invention proposes a scalar magnetometer heading error calibration and compensation system to implement the aforementioned scalar magnetometer heading error calibration and compensation method.

[0015] Compared with related technologies, the scalar magnetometer heading error calibration and compensation method provided by the present invention has the following beneficial effects: This invention proposes a scalar magnetometer heading error calibration and compensation method. By strapdown mounting a vector magnetometer and a scalar magnetometer in a fixed coordinate system, a mathematical model of heading error based on the cosine of the magnetic field direction is constructed. A short and easy-to-operate calibration experiment is conducted, estimating 19 compensation coefficients for subsequent real-time calibration of the scalar magnetometer's heading error. This method is quick and easy to operate, reducing the impact of time-varying magnetic measurement noise introduced by prolonged experimental processes. Furthermore, the strapdown mounting of the vector and scalar magnetometers can be integrated into an aeromagnetic measurement system, achieving simultaneous compensation for heading error and maneuvering interference, thus improving the accuracy of aeromagnetic measurements. Ultimately, the scalar magnetometer achieves accurate all-heading measurements within its measurable angle range. Attached Figure Description

[0016] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0017] Figure 1 Flowchart of the scalar magnetometer heading error calibration and compensation method; Figure 2 This is a schematic diagram of the strapdown installation of a vector magnetometer and a scalar magnetometer. Detailed Implementation

[0018] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0019] The present invention will now be described in further detail with reference to the accompanying drawings.

[0020] The purpose of this invention is to compensate for the heading error of a scalar magnetometer. This method features a short and easy-to-operate calibration process, reducing the impact of time-dependent magnetic measurement noise introduced by prolonged experimental procedures. Furthermore, the strapdown connection between the vector magnetometer and the scalar magnetometer allows integration into an aeromagnetic measurement system, achieving simultaneous compensation for heading error and maneuvering interference, thus improving the accuracy of aeromagnetic measurements. Ultimately, the scalar magnetometer achieves accurate all-heading measurements within its measurable angular range.

[0021] This invention proposes a method for calibrating and compensating for heading errors in a scalar magnetometer, the flowchart of which is shown below. Figure 1 As shown below, the steps will be described in detail: Step 1: Analyze the heading error of the scalar magnetometer and establish an error compensation model; Step 2: Conduct a scalar magnetometer heading error calibration experiment and measure the error calibration data; Step 3: Use a fitting algorithm to obtain the error compensation coefficients for subsequent heading error compensation.

[0022] The process of establishing the error compensation model in step 1 is as follows: By analyzing the heading error of the scalar magnetometer, i.e. the error caused by the change in the angle between the measured magnetic field and the optical axis, the following mathematical model of error is established: In the above formula, This refers to the magnetic field magnitude data measured by a scalar magnetometer. For the magnetic field being measured, The magnitude of the measured magnetic field. For heading error, The fictitious magnetic field generated by the optical shift caused by light in the probe is the main source of heading error. The magnitude of the fictitious magnetic field is... It relates to the power of the light and the frequency shift, both of which are constant in actual measurements. Let be the angle between the measured magnetic field and the optical axis. Therefore, the heading error is... It can be represented as: In the above formula, It is a constant. For heading error and the angle between the measured magnetic field and the optical axis The function of . Since the heading error (approximately 1-10 nT) is much smaller than the measured magnetic field (approximately 50000 nT), and the heading error and included angle There is a highly non-linear dependency, therefore... exist Performing a third-order Taylor series expansion, we obtain: The heading error can be obtained by sorting. : In the above formula, , , , For undetermined constants, , , These are the first, second, and third derivatives of the function, respectively. The angle between the optical axis and the measured magnetic field can be calculated from the magnetic measurement data of the vector magnetometer connected to the scalar magnetometer via strapdown. The direction of the optical axis of the scalar magnetometer after strapdown is constant in the coordinate system of the vector magnetometer, while the direction of the measured magnetic field can be calculated from the triaxial magnetic measurement data of the vector magnetometer. A schematic diagram of the strapdown installation of the vector magnetometer and scalar magnetometer is shown below. Figure 2 As shown, where The coordinate system of the vector magnetometer can be considered to be the same as the coordinate system of the strapdown system. Coincidence. Assume the measured magnetic field is... With constant direction and magnitude, let the unit vector of the optical axis in the coordinate system of the vector magnetometer be... ,in Let be a constant. Suppose that the triaxial data measured by the vector magnetometer at this time are... , representing the measured magnetic field The vector coordinates in the vector magnetometer coordinate system are: Therefore, the angle between the optical axis and the magnetic field is measured. for: In the above formula, Let cosine be the direction cosine of the magnetic field; substituting the above equation into the heading error formula and simplifying, we get: In the above formula Decomposed into These terms are then combined into the quadratic terms, and finally, the matrix formula for the heading error can be obtained. In the above formula, These are coefficients to be determined.

[0023] Based on the magnetic field data from the vector magnetometer, the direction cosine of the magnetic field is calculated. The relationship between heading error and magnetic field direction cosine was established, and 19 coefficients were solved. During actual measurements, the magnetic field direction cosine was calculated based on real-time magnetic measurement data from the vector magnetometer. Then, the magnitude of the heading error is calculated by combining 19 coefficients, and the heading error is subtracted from the magnetic measurement data of the scalar magnetometer, thus completing the calibration and compensation of the heading error of the scalar magnetometer.

[0024] Step 2 involves conducting a scalar magnetometer heading error calibration experiment and measuring the error calibration data. This specifically includes the following steps: Step 2.1: Considering the need to avoid dead zone effects during actual airborne magnetic measurements, scalar magnetometers are generally placed with their probe's long axis perpendicular to the horizontal plane. Therefore, the heading error is reflected in the measurement error caused by the probe's rotation within the horizontal plane. The scalar magnetometer and vector magnetometer are strapped together and fixedly mounted on a horizontally placed, rotatable, non-magnetic platform. Let this scalar magnetometer be scalar magnetometer 1. The long axis of the scalar magnetometer is fixed perpendicular to the platform. While strapping the vector magnetometer to the scalar magnetometer, ensure that two of the three magnetic measurement axes are parallel to the platform and one is perpendicular to the horizontal. Here, we assume the X and Y axes are parallel to the platform, and the Z axis is perpendicular to the platform. Another scalar magnetometer is installed and stationary 20cm away from the non-magnetic platform to measure the magnetic diurnal variation and serve as a magnetic field reference. Let this scalar magnetometer be scalar magnetometer 2.

[0025] Step 2.2: After the magnetometer is fixed, the scalar magnetometer 2 collects scalar data of the ambient magnetic field for 10 minutes and observes whether the magnetic field environment is stable. If the overall fluctuation peak-to-peak value of the magnetic field data is less than 2nT, the environment is considered stable and subsequent experimental operations can be carried out.

[0026] Step 2.3: While maintaining the data acquisition state, slowly rotate the non-magnetic platform fixing the vector magnetometer and scalar magnetometer 1 counterclockwise in the horizontal plane, rotating 360 degrees; then slowly rotate the non-magnetic platform fixing the vector magnetometer and scalar magnetometer 1 clockwise, rotating 360 degrees; then slowly rotate the non-magnetic platform fixing the vector magnetometer and scalar magnetometer 1 counterclockwise, rotating 45 degrees each time. After each rotation, hold the position still for 10 seconds, finally returning to the initial position. This completes the calibration process. During this process, scalar magnetometer 1, scalar magnetometer 2, and vector magnetometer continuously acquire data.

[0027] Step 2.4: Obtain the data from scalar magnetometer 1, scalar magnetometer 2, and vector magnetometer for subsequent calculation of heading error compensation coefficients.

[0028] Step 3 uses a fitting algorithm to calculate the error compensation coefficient, which is then used for subsequent heading error compensation. Specifically, this includes the following steps: Step 3.1: Based on the data obtained from the calibration experiment in Step 2, assume that the data measured by scalar magnetometer 1... Data measured by scalar magnetometer 2 Data measured by a vector magnetometer The number of data sampling points is N; Step 3.2: Based on the triaxial magnetic field data measured by the vector magnetometer, calculate the direction cosine matrix in the heading error model. The formula for calculating the direction cosine is: Construct the direction cosine matrix The dimension is 19×N: The heading error is obtained by subtracting the data measured by scalar magnetometer 1 and scalar magnetometer 2. : Step 3.3: Based on the derived heading error model, establish the following expression. Where K is the heading error compensation coefficient to be fitted. Given It might be a singular matrix, so we use recursive least squares to fit and obtain the optimal estimate of K. .

[0029] Step 3.4: When the actual heading error occurs, the vector magnetometer and scalar magnetometer are strapped together to obtain triaxial magnetic field data in real time, calculate the direction cosine matrix, and then apply the compensation coefficients obtained from the fitting. Substituting the values ​​into the heading error compensation model, the estimated heading error is obtained. Data was obtained from a scalar magnetometer. By subtracting the estimated heading error from the mean, the heading error of the scalar magnetometer can be compensated. This is illustrated in the following formula: in It is the result after compensation.

[0030] Based on the same inventive concept, this embodiment also provides a scalar magnetometer heading error calibration and compensation system, including: The heading error compensation model establishment module is used to analyze the heading error of the scalar magnetometer and establish a heading error compensation model containing the magnetic field direction cosine matrix and the heading error compensation coefficient to be solved. The calibration experiment data acquisition module is used to strap down and fix the first scalar magnetometer and the vector magnetometer on a horizontally placed rotatable non-magnetic platform, place the second scalar magnetometer near the first scalar magnetometer, conduct a scalar magnetometer heading error calibration experiment, and simultaneously record the magnetic field data of the first scalar magnetometer, the second scalar magnetometer and the vector magnetometer. The heading error compensation coefficient solution module is used to solve the heading error compensation coefficient in the heading error compensation model based on the magnetic field data using a fitting algorithm. The real-time heading error compensation module is used to perform the subsequent real-time heading error compensation process using the solved heading error compensation model, and outputs the compensated measurement results.

[0031] For the system embodiments, since they basically correspond to the method embodiments, relevant details can be found in the descriptions of the method embodiments; the implementation methods of the remaining modules will not be repeated here. The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0032] The system embodiments of the present invention can be applied to any device with data processing capabilities, such as a computer or other similar device. The system embodiments can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution.

[0033] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. Those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for calibrating and compensating heading error of a scalar magnetometer, characterized in that, Includes the following steps: Step 1: Analyze the heading error of the scalar magnetometer and establish a heading error compensation model containing the magnetic field direction cosine matrix and the heading error compensation coefficient to be solved; The heading error compensation model is based on the heading error. and the angle between the measured magnetic field and the optical axis There are highly nonlinear functions between them exist After performing a third-order Taylor series expansion, the heading error compensation model is derived as follows: ； in, For heading error, Let be the heading error compensation coefficient to be solved. , , The direction cosine of the three-axis magnetic field is given by the superscript T, which indicates the transpose. Step 2: Strapdown and fixed installation of the first scalar magnetometer and the vector magnetometer on a horizontally placed rotatable non-magnetic platform. Place the second scalar magnetometer near the first scalar magnetometer and conduct a scalar magnetometer heading error calibration experiment. Simultaneously record the magnetic field data of the first scalar magnetometer, the second scalar magnetometer, and the vector magnetometer. The scalar magnetometer heading error calibration experiment includes: Step 2.1: Strapdown and fixed installation of the first scalar magnetometer and the vector magnetometer on a horizontally placed rotatable non-magnetic platform. The long axis of the first scalar magnetometer is fixed perpendicular to the platform. Among the three magnetic measurement axes of the vector magnetometer, the X-axis and Y-axis are parallel to the platform, and the Z-axis is perpendicular. The second scalar magnetometer is then installed and placed near the first scalar magnetometer. Step 2.2: Start the second scalar magnetometer to collect scalar data of the ambient magnetic field for several minutes. If the peak-to-peak value of the fluctuation of the ambient magnetic field scalar data is less than 2nT, the environment is considered stable and subsequent experimental operations can be carried out; otherwise, adjust the experimental environment. Step 2.3: Start the first scalar magnetometer, the second scalar magnetometer, and the vector magnetometer, maintain the data acquisition state, and record the magnetic field data including timestamps; slowly rotate the non-magnetic platform in the horizontal plane first counterclockwise 360 ​​degrees, then slowly rotate clockwise 360 ​​degrees, and finally slowly rotate counterclockwise, holding it still for 10 seconds after each 45-degree rotation, until it returns to the initial position, thus completing the magnetic field data acquisition process; Step 2.4: Align the magnetic field data of the first scalar magnetometer, the second scalar magnetometer, and the vector magnetometer according to the timestamps for use in solving the heading error compensation coefficient; Step 3: Use a fitting algorithm to solve for the heading error compensation coefficients in the heading error compensation model based on the magnetic field data, which will be used for subsequent heading error compensation.

2. The scalar magnetometer heading error calibration and compensation method according to claim 1, characterized in that, The process of solving the heading error compensation coefficient includes: Step 3.1: Based on the magnetic field data obtained from the calibration experiment in Step 2, record the magnetic field data of the first scalar magnetometer as follows: The magnetic field data of the second scalar magnetometer are The three-axis magnetic field data of the vector magnetometer are N represents the number of data sampling points; Step 3.2: Based on the three-axis magnetic field data of the vector magnetometer, calculate the three-axis magnetic field direction cosine in the heading error compensation model, and then obtain the magnetic field direction cosine matrix; and, subtract the magnetic field data of the first scalar magnetometer and the second scalar magnetometer to obtain the heading error; Step 3.3: Based on the heading error compensation model, establish the following expression: ； Where K is the heading error compensation coefficient to be solved. , For heading error, This is the cosine matrix of the magnetic field direction; Step 3.4: Fit the expression from Step 3.3 to obtain the optimal estimate of K. .

3. The scalar magnetometer heading error calibration and compensation method according to claim 2, characterized in that, Step 3.4 uses the recursive least squares method for fitting.

4. The scalar magnetometer heading error calibration and compensation method according to claim 2, characterized in that, The formula for calculating the direction cosine of the triaxial magnetic field in step 3.2 is as follows: ； in, , , The cosine of the triaxial magnetic field direction is calculated for the i-th data sampling point. , , The data represents the three-axis magnetic field data of a vector magnetometer at i data sampling points.

5. The scalar magnetometer heading error calibration and compensation method according to claim 2, characterized in that, The direction cosine matrix of the magnetic field is: ； The superscript T is the transpose symbol.

6. The scalar magnetometer heading error calibration and compensation method according to claim 1, characterized in that, The process of using the solved heading error compensation model for subsequent heading error compensation includes: The vector magnetometer is strapped in with the first scalar magnetometer to obtain the three-axis magnetic field data of the vector magnetometer in real time, calculate the current three-axis magnetic field direction cosine, and then obtain the current magnetic field direction cosine matrix. Substitute the current magnetic field direction cosine matrix and the solved heading error compensation coefficient into the heading error compensation model to calculate the current heading error estimate. The result of subtracting the current heading error estimate from the magnetic field data measured by the first scalar magnetometer is output as the compensation result.

7. A scalar magnetometer heading error calibration and compensation system, used to implement the scalar magnetometer heading error calibration and compensation method according to claim 1, characterized in that, The system includes: The heading error compensation model establishment module is used to analyze the heading error of the scalar magnetometer and establish a heading error compensation model containing the magnetic field direction cosine matrix and the heading error compensation coefficient to be solved. The calibration experiment data acquisition module is used to strap down and fix the first scalar magnetometer and the vector magnetometer on a horizontally placed rotatable non-magnetic platform, place the second scalar magnetometer near the first scalar magnetometer, conduct a scalar magnetometer heading error calibration experiment, and simultaneously record the magnetic field data of the first scalar magnetometer, the second scalar magnetometer and the vector magnetometer. The heading error compensation coefficient solution module is used to solve the heading error compensation coefficient in the heading error compensation model based on the magnetic field data using a fitting algorithm. The real-time heading error compensation module is used to perform the subsequent real-time heading error compensation process using the solved heading error compensation model, and outputs the compensated measurement results.

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