Magnetometer error parameter immunity calibration method for high accuracy magnetic field traceability

Abstract

The application discloses a magnetometer error parameter anti-interference calibration method for high-accuracy magnetic field tracing, which comprises the following steps: collecting three-axis magnetic field component data of a vector magnetometer to be calibrated; dividing local data sets and fitting local ellipsoids; constructing a global cumulative effective data set and fitting a global reference ellipsoid; calculating a comprehensive deviation index of the local ellipsoids; performing interference identification and data rejection; obtaining an effective data fitting reference ellipsoid; calculating a residual sequence; performing abnormality identification and data rejection; obtaining accurate data; fitting an initial ellipsoid by using a least square method; calculating the residual of each measurement point and the residual weight; performing fine fitting by using a weighted least square method to obtain a final ellipsoid; constructing a magnetometer error model fitted by using the final ellipsoid; and outputting error correction coefficients. The method can realize real-time identification and rejection of interference data, ensure that sensor error parameters can be stably and accurately extracted under non-stationary magnetic field conditions, and thus the accuracy and robustness of the calibration result are improved.

Description

Technical Field

[0001] This invention relates to the field of magnetometer error calibration technology, and in particular to an anti-interference calibration method for magnetometer error parameters for high-accuracy magnetic field tracing. Background Technology

[0002] Vector magnetometers require error calibration before use to eliminate inherent bias, sensitivity errors, and non-orthogonality errors in the sensor itself. Ellipsoid fitting is one of the most commonly used calibration methods. Existing ellipsoid fitting calibration methods are all based on a crucial assumption: the environmental magnetic field remains stable and contains only the Earth's magnetic field. However, in actual metrology sites or field calibration environments, abrupt electromagnetic interference often occurs. When these dynamic interferences occur, the data acquired by the sensor contains anomalous components not related to the Earth's magnetic field. If this contaminated data is used in ellipsoid fitting, it will cause distortion of the fitted ellipsoid, resulting in the calculated error correction coefficients deviating significantly from the true values, ultimately affecting the accuracy of the calibration results.

[0003] To address this issue, some solutions improve fitting stability through robust algorithms, but still fail to resolve the problem of "interference data entering the fitting process." Additionally, some solutions employ methods to remove data that deviates significantly from the sine function, but this method lacks robustness under complex, non-periodic, and multi-source dynamic interference, making it difficult to effectively identify and remove interference data with varying shapes. Finally, existing methods mostly rely on post-processing for interference removal, failing to achieve real-time identification and dynamic response to interference, thus limiting their application in field calibration. Therefore, this invention proposes an anti-interference calibration method for magnetometer error parameters for high-accuracy magnetic field tracing. By constructing a robust calibration strategy of "real-time monitoring + two-step processing," and actively identifying interference and processing data in layers, it achieves real-time identification and removal of interference data, ensuring stable and accurate extraction of sensor error parameters even under non-stationary magnetic field conditions, thereby improving the accuracy and robustness of calibration results. Summary of the Invention

[0004] The purpose of this invention is to provide an anti-interference calibration method for the error parameters of a magnetometer for high-accuracy magnetic field tracing.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution: This invention includes the following steps: In the environment to be calibrated, the triaxial magnetic field component data of the vector magnetometer under calibration are continuously acquired, a sliding window is set and a local dataset is constructed, and a local ellipsoid is fitted based on the local dataset; Construct a global cumulative effective dataset and fit a global reference ellipsoid. Calculate the ellipsoid parameter deviation and comprehensive deviation index between the local ellipsoid and the global reference ellipsoid. Identify and remove interfering data based on the comprehensive deviation index to obtain effective data. A reference ellipsoid is initially fitted from the valid data. The algebraic distance from each measurement point to the reference ellipsoid is calculated to obtain the residual sequence. Outlier data is identified and removed based on the residual sequence to obtain accurate data. The initial ellipsoid is obtained by second-fitting the precise data using least squares. The residuals of each measurement point are calculated and weighted. The precise data is then finely fitted using weighted least squares. This process is repeated until the ellipsoid parameters converge and the final ellipsoid is output. In the environment to be calibrated, the three-axis magnetic field component data of the standard vector magnetometer are continuously acquired. Based on the final ellipsoid, the magnetometer error model is constructed and the error correction coefficient is output. The global cumulative valid dataset only includes historical data points that have been determined to be free of interference; The ellipsoid parameters include the coordinates of the ellipsoid center, the length of the ellipsoid semi-axis, and the ellipsoid attitude angle.

[0006] Furthermore, the method for identifying and removing interfering data includes: Calculate the geometric characteristic deviation between the local ellipsoid and the global reference ellipsoid, and determine the comprehensive deviation index based on the geometric characteristic deviation. The expression is as follows: ; in For local ellipsoids The comprehensive deviation index , , For local ellipsoids of Axis center coordinates, semi-axis length, and attitude angle. For axis index, , , For the global reference ellipsoid Axis center coordinates, semi-axis length, and attitude angle. , , The statistical standard deviation of the ellipsoid center, semi-axis length, and attitude angle within the historical window; Local ellipsoids with a comprehensive deviation index greater than the offset threshold are identified as interference ellipsoids. The data in the corresponding window of the interference ellipsoid is marked as interference data, and the interference data is removed. Conversely, if the local ellipsoid is identified as a normal ellipsoid, the data in the window corresponding to the normal ellipsoid is marked as valid data.

[0007] Furthermore, the method for identifying and removing abnormal data includes: A reference ellipsoid is obtained by initially fitting the triaxial magnetic field component data after removing interference. The algebraic distance from each valid data point to the reference ellipsoid is calculated to obtain the residual sequence. The residual mean and residual standard deviation are calculated, and the residual threshold is determined based on the residual mean and residual standard deviation. The expression is as follows: ; in The residual threshold, , Let be the residual mean and residual standard deviation of the residual sequence. The residual coefficient; Valid data with residuals greater than the residual threshold are marked as outliers. After removing outliers, the reference ellipsoid is refitted. This process is repeated until no new outliers are detected, and then accurate data is output.

[0008] Furthermore, the method for outputting the final ellipsoid includes: The initial ellipsoid is obtained by quadratic fitting of the precise data using the least squares method, and the residuals at each measurement point are calculated. The residual weights are calculated based on the residuals at each measurement point, and the expression is as follows: ; in For residuals The residual weights, the first The residual of a precise data The standardized residuals of Huber's weight function, The tuning constant; Based on the residual weights, the weighted least squares method is used to fine-fit the accurate data. The second fitting and fine fitting are repeated until the ellipsoid parameters converge and the final ellipsoid is output.

[0009] Furthermore, the method for outputting the error correction coefficient includes: The total magnetic field strength is calculated by continuously acquiring triaxial magnetic field component data of a standard vector magnetometer in the environment to be calibrated. The ellipsoidal parameters of the final ellipsoid are extracted to construct the magnetometer error correction model, which is expressed as: ; in For the standard magnetic field matrix, The magnetic field matrix, measured by the vector magnetometer under calibration, is provided by the dataset corresponding to the final ellipsoid. For the combined error matrix, The total magnetic field strength is measured by a standard magnetometer. It is a zero-biased vector originating from the center of the final ellipsoid. Mapping, , , The length of the semi-axis of the final ellipsoid. The rotation matrix is ​​derived from the attitude angles of the final ellipsoid. constitute; The sensitivity matrix and non-orthogonal error matrix are obtained by performing QR decomposition on the combined error matrix; The zero-bias correction coefficients are extracted from the zero-bias vector, the sensitivity correction coefficients are extracted from the sensitivity matrix, and the non-orthogonal error correction coefficients are extracted from the non-orthogonal error matrix, thus forming the error correction coefficients.

[0010] The beneficial effects of this invention are: This invention relates to an anti-interference calibration method for error parameters of magnetometers used for high-accuracy magnetic field tracing. Compared with existing technologies, this invention has the following technical advantages: This invention employs a method of local ellipsoidal fitting with a sliding window and comparison with a global model to achieve real-time monitoring and quantitative identification of dynamic magnetic field interference. It can detect dynamic magnetic field interference in a timely manner during the data acquisition stage and prevent interfered data from participating in calibration. This invention employs a two-step method of "coarse removal + fine fitting," which ensures both the efficiency of outlier removal and the accuracy and robustness of parameter estimation through robust weighted fitting, thus balancing computational efficiency and anti-interference capability. This invention enables the ellipsoid fitting calibration method to be applied to application scenarios with dynamic magnetic field interference, such as airborne magnetic measurement, vehicle-mounted mobile measurement, and ship magnetic detection. It fills the technical gap of existing methods that are difficult to calibrate stably under interference environments and expands its application scope. This invention combines the geometric features (center, radius, and attitude) of ellipsoid fitting with time series analysis, which has a stronger ability to identify complex, non-periodic, and multi-source dynamic disturbances. It overcomes the limitations of traditional methods that rely solely on the deviation of the sine function. Furthermore, by calculating the deviation between the local ellipsoid and the global model in real time, it can quantify data quality and provide users with an assessment of the on-site disturbance level and an indication of calibration reliability. Attached Figure Description

[0011] Figure 1 This is a flowchart of the steps of the magnetometer error parameter anti-interference calibration method for high-accuracy magnetic field tracing according to the present invention; Figure 2 This is a schematic diagram of local ellipsoid fitting and interference monitoring of the sliding window in an embodiment of the present invention; Figure 3 This is a flowchart of the two-step data processing method in an embodiment of the present invention. Detailed Implementation

[0012] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0013] The present invention provides a method for anti-interference calibration of magnetometer error parameters for high-accuracy magnetic field tracing, comprising the following steps: like Figure 1 As shown, this embodiment includes the following steps: In the environment to be calibrated, the triaxial magnetic field component data of the vector magnetometer under calibration are continuously acquired, a sliding window is set and a local dataset is constructed, and a local ellipsoid is fitted based on the local dataset; Construct a global cumulative effective dataset and fit a global reference ellipsoid. Calculate the ellipsoid parameter deviation and comprehensive deviation index between the local ellipsoid and the global reference ellipsoid. Identify and remove interfering data based on the comprehensive deviation index to obtain effective data. A reference ellipsoid is initially fitted from the valid data. The algebraic distance from each measurement point to the reference ellipsoid is calculated to obtain the residual sequence. Outlier data is identified and removed based on the residual sequence to obtain accurate data. The initial ellipsoid is obtained by second-fitting the precise data using least squares. The residuals and residual weights of each measurement point are calculated. The precise data is then finely fitted using weighted least squares. The iteration is repeated until the ellipsoid parameters converge and the final ellipsoid is output. In the environment to be calibrated, the three-axis magnetic field component data of the standard vector magnetometer are continuously acquired. Based on the final ellipsoid, the magnetometer error model is constructed and the error correction coefficient is output. The global cumulative valid dataset only includes historical data points that have been determined to be free of interference; The ellipsoid parameters include the coordinates of the ellipsoid center, the length of the ellipsoid semi-axis, and the ellipsoid attitude angle.

[0014] In this embodiment, the method for identifying and removing interfering data includes: Calculate the geometric characteristic deviation between the local ellipsoid and the global reference ellipsoid, and determine the comprehensive deviation index based on the geometric characteristic deviation. The expression is as follows: ; in For local ellipsoids The comprehensive deviation index , , For local ellipsoids of Axis center coordinates, semi-axis length, and attitude angle. For axis index, , , For the global reference ellipsoid Axis center coordinates, semi-axis length, and attitude angle. , , The statistical standard deviation of the ellipsoid center, semi-axis length, and attitude angle within the historical window; Local ellipsoids with a comprehensive deviation index greater than the offset threshold are identified as interference ellipsoids. The data in the corresponding window of the interference ellipsoid is marked as interference data, and the interference data is removed. Conversely, if the local ellipsoid is determined to be a normal ellipsoid, the data in the window corresponding to the normal ellipsoid is marked as valid data; In actual assessment, Figure 2 This is a schematic diagram of local ellipsoid fitting and interference monitoring in a sliding window. The vector magnetometer to be calibrated is placed in the environment to be calibrated, and continuous acquisition of triaxial magnetic field component data begins. The global cumulative effective dataset is initialized to empty, and the global reference ellipsoid parameters are initialized to empty. During this process, a standard magnetometer is placed next to the vector magnetometer to measure the total magnetic field data for use as the magnetic field reference value in ellipsoid fitting (to calculate the total magnetic field strength). Set the sliding window length and window sliding step size. For every N new data points collected (according to the sliding step size), construct a local dataset within the current window, perform ellipsoid fitting on the local dataset to obtain the local ellipsoid of the current window, and output the ellipsoid parameters. The ellipsoid parameters include the ellipsoid center coordinates (corresponding to the zero bias parameter of the vector magnetometer), the ellipsoid semi-axis length (corresponding to the sensitivity parameter of the vector magnetometer), and the ellipsoid attitude angle (corresponding to the non-orthogonality error of the vector magnetometer). If there are insufficient data points in the window or the fitting fails (e.g., due to ill-conditioned matrix or non-convergence of iteration), skip the window and continue to the next window. Maintain a global cumulative valid dataset, which contains only historical data points that have been determined to be "undisturbed". Periodically refit the ellipsoid based on the global cumulative valid dataset to obtain global reference ellipsoid parameters (9 dimensions in total, including the ellipsoid center coordinates, ellipsoid semi-axis length and ellipsoid attitude angle in three dimensions). Calculate the ellipsoid parameter deviation between the local ellipsoid and the global reference ellipsoid parameters, and select a comprehensive deviation index. When the comprehensive deviation index is greater than the offset threshold, it is determined that the data in the current window is affected by the dynamic magnetic field. All data points in the window are marked as interference data. For the data segment that is determined to be interference, all data points in the window are removed from the dataset to be fitted and do not participate in the subsequent global model update and final ellipsoid fitting. Data points not identified as interference are added to the global cumulative valid dataset. When the amount of new data in the global cumulative valid dataset reaches a set threshold, the ellipsoid fitting is performed again, and the global reference ellipsoid parameters are updated so that they gradually converge to the true sensor error parameters.

[0015] In this embodiment, the method for identifying and removing abnormal data includes: A reference ellipsoid is obtained by initially fitting the triaxial magnetic field component data after removing interference. The algebraic distance from each valid data point to the reference ellipsoid is calculated to obtain the residual sequence. The residual mean and residual standard deviation are calculated, and the residual threshold is determined based on the residual mean and residual standard deviation. The expression is as follows: ; in The residual threshold, , Let be the residual mean and residual standard deviation of the residual sequence. The residual coefficient; Valid data with residuals greater than the residual threshold are marked as outliers. After removing outliers, the reference ellipsoid is refitted. The process is iterated until no new outliers are detected, and then accurate data is output. In actual evaluation, for the valid data retained by real-time monitoring in step S1, a preliminary ellipsoid fitting is first performed to obtain the reference ellipsoid parameters. The algebraic distance from each measurement point to the fitted ellipsoid is calculated, and a residual sequence is constructed. Based on the statistical distribution of the residuals (mean and standard deviation), an adaptive threshold is set to quickly identify and remove outliers that deviate significantly, and output accurate data. This step aims to quickly purify the dataset and provide a relatively "clean" data foundation for subsequent fine fitting.

[0016] In this embodiment, the method for outputting the final ellipsoid includes: The initial ellipsoid is obtained by quadratic fitting of the precise data using the least squares method, and the residuals at each measurement point are calculated. The residual weights are calculated based on the residuals at each measurement point, and the expression is as follows: ; in For residuals The residual weights, the first The residual of a precise data The standardized residuals of Huber's weight function, The tuning constant; Based on the residual weights, the weighted least squares method is used to fine fit the accurate data. The second fitting and fine fitting are repeated until the ellipsoid parameters converge and the final ellipsoid is output. In actual assessment, Figure 3 The flowchart shows the two-step data processing method. Iterative weighted least squares method is used for fine fitting, and different weights are assigned to each data point according to the size of the residual: normal points are given high weights and outlier points are given low weights. By iteratively weighted fitting, the influence of outliers on parameter estimation is gradually reduced until the ellipsoidal parameters converge. This step not only ensures the fitting accuracy but also further enhances the robustness of the algorithm.

[0017] In this embodiment, the method for outputting the error correction coefficient includes: The total magnetic field strength is calculated by continuously acquiring triaxial magnetic field component data of a standard vector magnetometer in the environment to be calibrated. The ellipsoidal parameters of the final ellipsoid are extracted to construct the magnetometer error correction model, which is expressed as: ; in For the standard magnetic field matrix, The magnetic field matrix, measured by the vector magnetometer under calibration, is provided by the dataset corresponding to the final ellipsoid. For the combined error matrix, The total magnetic field strength is measured by a standard magnetometer. It is a zero-biased vector originating from the center of the final ellipsoid. Mapping, , , The length of the semi-axis of the final ellipsoid. The rotation matrix is ​​derived from the attitude angles of the final ellipsoid. constitute; The sensitivity matrix and non-orthogonal error matrix are obtained by performing QR decomposition on the combined error matrix; Zero-bias correction coefficients are extracted from the zero-bias vector, sensitivity correction coefficients are extracted from the sensitivity matrix, and non-orthogonal error correction coefficients are extracted from the non-orthogonal error matrix to form the error correction coefficients. In actual evaluation, based on the final ellipsoid parameters, the correspondence between the ellipsoid shape matrix and the combined error matrix is ​​established, the zero bias vector is extracted, the combined correction matrix is ​​solved, the error correction coefficients are output, and the vector magnetometer measurement data is corrected according to the magnetometer error correction model.

[0018] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for anti-interference calibration of error parameters of a magnetometer used for high-accuracy magnetic field tracing, characterized in that, Includes the following steps: S1. Continuously acquire the three-axis magnetic field component data of the vector magnetometer to be calibrated in the environment to be calibrated, set a sliding window and construct a local dataset, and fit a local ellipsoid based on the local dataset; S2. Construct a global cumulative effective dataset and fit a global reference ellipsoid. Calculate the ellipsoid parameter deviation and comprehensive deviation index between the local ellipsoid and the global reference ellipsoid. Identify and remove interfering data based on the comprehensive deviation index to obtain effective data. S3. Obtain a reference ellipsoid by initially fitting the effective data, calculate the algebraic distance from each measurement point to the reference ellipsoid to obtain the residual sequence, identify and remove outlier data based on the residual sequence, and obtain accurate data. S4. Use least squares to perform a second fitting of the precise data to obtain the initial ellipsoid, calculate the residuals of each measurement point and sum the residual weights, use weighted least squares to perform a fine fitting of the precise data, repeat the iteration until the ellipsoid parameters converge and output the final ellipsoid. S5. Continuously acquire the three-axis magnetic field component data of the standard vector magnetometer in the environment to be calibrated, construct the magnetometer error model based on the final ellipsoid and output the error correction coefficient; The global cumulative valid dataset only includes historical data points that have been determined to be undisturbed; The ellipsoid parameters include the coordinates of the ellipsoid center, the length of the ellipsoid semi-axis, and the ellipsoid attitude angle.

2. The anti-interference calibration method for magnetometer error parameters for high-accuracy magnetic field tracing according to claim 1, characterized in that, The method for identifying and removing interfering data includes: Calculate the geometric characteristic deviation between the local ellipsoid and the global reference ellipsoid, and determine the comprehensive deviation index based on the geometric characteristic deviation. The expression is as follows: ； in For local ellipsoids The comprehensive deviation index , , For local ellipsoids of Axis center coordinates, semi-axis length, and attitude angle. For axis index, , , For the global reference ellipsoid Axis center coordinates, semi-axis length, and attitude angle. , , The statistical standard deviation of the ellipsoid center, semi-axis length, and attitude angle within the historical window; Local ellipsoids with a comprehensive deviation index greater than the offset threshold are identified as interference ellipsoids. The data in the window corresponding to the interference ellipsoid is marked as interference data, and the interference data is removed. Conversely, if the local ellipsoid is identified as a normal ellipsoid, the data in the window corresponding to the normal ellipsoid is marked as valid data.

3. The anti-interference calibration method for magnetometer error parameters for high-accuracy magnetic field tracing according to claim 1, characterized in that, The method for identifying and removing abnormal data includes: A reference ellipsoid is obtained by initially fitting the triaxial magnetic field component data after removing interference. The algebraic distance from each valid data point to the reference ellipsoid is calculated to obtain the residual sequence. The residual mean and residual standard deviation are calculated, and the residual threshold is determined based on the residual mean and residual standard deviation. The expression is as follows: ； in The residual threshold, , Let be the residual mean and residual standard deviation of the residual sequence. The residual coefficient; Valid data with residuals greater than the residual threshold are marked as outliers. After removing outliers, the reference ellipsoid is refitted. This process is repeated until no new outliers are detected, and then accurate data is output.

4. The anti-interference calibration method for magnetometer error parameters for high-accuracy magnetic field tracing according to claim 1, characterized in that, The method for outputting the final ellipsoid includes: The initial ellipsoid is obtained by quadratic fitting of the precise data using the least squares method, and the residuals at each measurement point are calculated. The residual weights are calculated based on the residuals at each measurement point, and the expression is as follows: ; in For residuals The residual weights, the first The residual of a precise data The standardized residuals of Huber's weight function, The tuning constant; Based on the residual weights, the weighted least squares method is used to fine-fit the accurate data. The second fitting and fine fitting are repeated until the ellipsoid parameters converge and the final ellipsoid is output.

5. The anti-interference calibration method for magnetometer error parameters for high-accuracy magnetic field tracing according to claim 1, characterized in that, The method for output error correction coefficients includes: The total magnetic field strength is calculated by continuously acquiring triaxial magnetic field component data of a standard vector magnetometer in the environment to be calibrated. The ellipsoidal parameters of the final ellipsoid are extracted to construct the magnetometer error correction model, which is expressed as: ; in For the standard magnetic field matrix, The magnetic field matrix, measured by the vector magnetometer under calibration, is provided by the dataset corresponding to the final ellipsoid. For the combined error matrix, The total magnetic field strength is measured by a standard magnetometer. It is a zero-biased vector originating from the center of the final ellipsoid. Mapping, , , The length of the semi-axis of the final ellipsoid. The rotation matrix is ​​derived from the attitude angles of the final ellipsoid. constitute; The sensitivity matrix and non-orthogonal error matrix are obtained by performing QR decomposition on the combined error matrix; The zero-bias correction coefficients are extracted from the zero-bias vector, the sensitivity correction coefficients are extracted from the sensitivity matrix, and the non-orthogonal error correction coefficients are extracted from the non-orthogonal error matrix, thus forming the error correction coefficients.

Images