Three-axis fluxgate sensor error calibration method, system, equipment and medium

Abstract

The invention discloses a three-axis fluxgate sensor error calibration method, system and device and a medium, and relates to the field of error calibration, and the method comprises the steps: obtaining initial geomagnetic field magnetic measurement data, weak magnetic field magnetic measurement data and a geomagnetic total field module value of a three-axis fluxgate sensor; determining an orthogonality error and a sensitivity error based on geomagnetic field magnetic measurement data, a geomagnetic total field module value and a fluxgate sensor error model for the h iteration; substituting the orthogonality error and the sensitivity error into a fluxgate sensor error model, and determining a zero offset error based on weak magnetic field magnetic measurement data; judging whether the zero-offset relative deviation value is smaller than a preset threshold value or not; if yes, outputting the orthogonality error, the sensitivity error and the zero offset error during the h-th iteration as fluxgate error values; and if not, carrying out zero offset correction on the geomagnetic field magnetic measurement data by adopting the zero offset error during the h iteration, and carrying out the (h + 1) iteration. According to the invention, the calculation precision of the error of the three-axis fluxgate sensor is improved.

Description

Technical Field

[0001] This application relates to the field of error calibration, and in particular to a method, system, device and medium for error calibration of a three-axis fluxgate sensor. Background Technology

[0002] Three-axis fluxgate sensors can measure vector geomagnetic fields, exhibiting high resolution and good robustness. They have been widely used in geomagnetic navigation and orientation, land resource exploration, and earth science research. Vector magnetometry has become a research hotspot due to its ability to acquire more information about the vector geomagnetic field, and three-axis fluxgate sensors have therefore received more attention.

[0003] The geomagnetic field signal is weak and sensitive, and triaxial fluxgate sensors are highly susceptible to environmental noise and instrument interference when measuring the geomagnetic field. Therefore, a crucial task for triaxial fluxgate sensors in magnetometry is to calibrate and correct instrument errors. Ideally, when the external magnetic field is constant, the total geomagnetic field modulus output by an ideal triaxial fluxgate sensor should be constant and unchanging with attitude, and the spatial distribution of the sensor's three-component output values ​​should be an ideal sphere with the total geomagnetic field modulus as its radius. However, in reality, due to manufacturing limitations, triaxial fluxgate sensors inevitably suffer from triaxial orthogonality errors, sensitivity errors, and zero-bias errors. This causes the total geomagnetic field modulus output by the triaxial fluxgate sensor to vary with attitude, and the spatial distribution of its three-component output values ​​becomes an ellipsoid. This error is called the steering error.

[0004] The calibration of a three-axis fluxgate sensor involves obtaining the orthogonality error, sensitivity error, and zero bias error of the three-axis fluxgate sensor through direct measurement or indirect inversion, in order to eliminate the steering error and restore the spatial distribution of the output value of the three-axis fluxgate sensor from an ellipsoid to an ideal sphere.

[0005] Therefore, in order to ensure the measurement accuracy of the triaxial fluxgate sensor, it is necessary to accurately obtain the orthogonality error, sensitivity error, and zero bias error. Summary of the Invention

[0006] The purpose of this application is to provide a method, system, device and medium for error calibration of a three-axis fluxgate sensor, which can improve the error calculation accuracy of the three-axis fluxgate sensor.

[0007] To achieve the above objectives, this application provides the following solution:

[0008] In a first aspect, this application provides a method for calibrating the error of a three-axis fluxgate sensor, including:

[0009] Acquire preliminary geomagnetic field measurement data, weak magnetic field measurement data, and total geomagnetic field modulus value of a three-axis fluxgate sensor; the preliminary geomagnetic field measurement data includes measurement data of at least 6 different rotational attitudes, and the weak magnetic field measurement data includes measurement data of at least 4 different rotational attitudes.

[0010] For the h-th iteration, based on the geomagnetic field measurement data at the h-th iteration, the total geomagnetic field modulus, and the fluxgate sensor error model, the orthogonality error and sensitivity error at the h-th iteration are determined; h>0, the geomagnetic field measurement data at the 1st iteration is the preliminary geomagnetic field measurement data; the fluxgate sensor error model includes orthogonality error and sensitivity error;

[0011] Substitute the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, and determine the zero bias error at the h-th iteration based on the weak magnetic field measurement data.

[0012] If h = 1, then the zero bias relative deviation value at the h-th iteration is set to infinity; otherwise, the zero bias relative deviation value at the h-th iteration is determined based on the zero bias error at the h-th iteration and the zero bias error at the (h-1)-th iteration.

[0013] Determine whether the relative deviation value of the zero bias at the h-th iteration is less than a preset threshold; if so, output the orthogonality error, sensitivity error and zero bias error at the h-th iteration as the fluxgate error value; if not, use the zero bias error at the h-th iteration to perform zero bias correction on the preliminary geomagnetic field measurement data to obtain the geomagnetic field measurement data at the (h+1)-th iteration, and perform the (h+1)-th iteration.

[0014] Secondly, this application provides a three-axis fluxgate sensor error calibration system, comprising:

[0015] The data acquisition module is used to acquire preliminary geomagnetic field measurement data, weak magnetic field measurement data and total geomagnetic field modulus value of the triaxial fluxgate sensor; the preliminary geomagnetic field measurement data includes measurement data of at least 6 different rotational attitudes and the weak magnetic field measurement data includes measurement data of at least 4 different rotational attitudes.

[0016] The orthogonal sensitivity error determination module is used to determine the orthogonality error and sensitivity error for the h-th iteration based on the geomagnetic field measurement data, the geomagnetic total field modulus, and the fluxgate sensor error model; h>0, the geomagnetic field measurement data for the first iteration is the preliminary geomagnetic field measurement data; the fluxgate sensor error model includes orthogonality error and sensitivity error.

[0017] The zero bias error determination module is used to substitute the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, and determine the zero bias error at the h-th iteration based on the weak magnetic field measurement data.

[0018] The iteration module is used to set the zero-bias relative deviation value at the h-th iteration to infinity when h=1; otherwise, it determines the zero-bias relative deviation value at the h-th iteration based on the zero-bias error at the h-th iteration and the zero-bias error at the (h-1)-th iteration; it determines whether the zero-bias relative deviation value at the h-th iteration is less than a preset threshold; if so, it outputs the orthogonality error, sensitivity error, and zero-bias error at the h-th iteration as the fluxgate error value; if not, it uses the zero-bias error at the h-th iteration to perform zero-bias correction on the preliminary geomagnetic field measurement data to obtain the geomagnetic field measurement data at the (h+1)-th iteration, and performs the (h+1)-th iteration.

[0019] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described three-axis fluxgate sensor error calibration method.

[0020] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described three-axis fluxgate sensor error calibration method.

[0021] According to the specific embodiments provided in this application, this application has the following technical effects:

[0022] This application provides a method, system, device, and medium for calibrating the error of a three-axis fluxgate sensor. By utilizing the magnetic measurement data of the three-axis fluxgate sensor under the geomagnetic field and weak magnetic field, the error of the three-axis fluxgate sensor is iteratively calculated, which can significantly improve the error calculation accuracy of the three-axis fluxgate sensor, and thus calibrate the three-axis fluxgate sensor more accurately. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A diagram showing the relationship between the non-orthogonal and orthogonal coordinate systems of a three-axis fluxgate sensor.

[0025] Figure 2A flowchart illustrating a method for calibrating the error of a three-axis fluxgate sensor, provided in an embodiment of this application;

[0026] Figure 3 A technical flowchart illustrating a method for calibrating the error of a three-axis fluxgate sensor, provided in an embodiment of this application;

[0027] Figure 4 The graph shows the relationship between the maximum deviation of the total field modulus and the single-axis non-orthogonal angle error in a geomagnetic field with a total field modulus of 50,000 nT.

[0028] Figure 5 The graph shows the relationship between the maximum deviation of the total field modulus and the uniaxial sensitivity error in a geomagnetic field with a total field modulus of 50,000 nT.

[0029] Figure 6 The graph shows the relationship between the maximum deviation of the total field modulus and the uniaxial zero bias error in a geomagnetic field with a total field modulus of 50,000 nT.

[0030] Figure 7 The graph shows the relationship between the maximum deviation of the total field modulus and the uniaxial non-orthogonal angle error in a weak magnetic field with a total field modulus of 500 nT.

[0031] Figure 8 The graph shows the relationship between the maximum deviation of the total field modulus and the uniaxial sensitivity error in a weak magnetic field with a total field modulus of 500 nT.

[0032] Figure 9 The graph shows the relationship between the maximum deviation of the total field modulus and the uniaxial zero bias error in a weak magnetic field with a total field modulus of 500 nT.

[0033] Figure 10 This is a spatial distribution diagram of the three components of the sampling points of a triaxial fluxgate magnetic sensor under noise-free conditions in the geomagnetic field (50000 nT).

[0034] Figure 11 The graph shows the variation of the total field intensity (thin gray line represents noise-free data points, and dotted dashed line represents noisy data points) of all sampling points under the geomagnetic field (50000nT) and the total field intensity (thick black line) of the noise-free sampling points after compensation and correction.

[0035] Figure 12 The spatial distribution of the three components of the sampling points of the triaxial fluxgate magnetic sensor under a weak magnetic field (500 nT) with no noise is shown.

[0036] Figure 13 The graph shows the variation of the total field intensity (thin gray line represents noise-free data points, and dotted dashed line represents noisy data points) of all sampling points under a weak magnetic field (500 nT) and the total field intensity (thick black line) of the noise-free sampling points after compensation and correction.

[0037] Figure 14 The spatial distribution of the three components of the sampling points of the triaxial fluxgate magnetic sensor under noise in the geomagnetic field (50000 nT);

[0038] Figure 15 The graph shows the difference in total field intensity between sampling points under noisy and noiseless geomagnetic fields (50000 nT);

[0039] Figure 16 The spatial distribution of the three components of the sampling points of the triaxial fluxgate magnetic sensor under a weak magnetic field (500 nT) with noise is shown.

[0040] Figure 17 The graph shows the difference in total field intensity between sampling points under noisy and noiseless weak magnetic fields (500 nT);

[0041] Figure 18 The spatial distribution diagram of the three components of the sampling points of the triaxial fluxgate magnetic sensor under the compensated geomagnetic field when there is noise.

[0042] Figure 19 The total field intensity curves of noisy sampling point data under the geomagnetic field before compensation (thin gray line) and after compensation (thick dashed line);

[0043] Figure 20 The graph shows the difference in total field intensity of the sampling points under the geomagnetic field before and after noise addition (thin gray line) and the difference in total field intensity of the sampling points under the geomagnetic field after compensation relative to the constant modulus of 50000 nT (thick dashed line). Detailed Implementation

[0044] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0045] There are two main methods for calibrating the errors of triaxial fluxgate sensors. One method involves comparing the sensor with a high-performance triaxial fluxgate sensor in the same orientation within a known stable geomagnetic field, directly measuring and calculating the sensor error. This method requires a high-performance fluxgate sensor, precise knowledge of the magnetic field at the sensor's location, and accurate control of the sensor's orientation, making it demanding and cumbersome. The other method is an indirect inversion method, primarily including ellipsoidal fitting, which involves fitting an ellipsoid formed by the three components of the fluxgate rotation measurement and estimating the error term based on the mathematical relationship between the ellipsoid's geometric parameters and error parameters; and optimization methods such as the least squares method, which directly solves the quadratic surface equations for the error parameters to minimize the difference in the total field modulus of the calibrated fluxgate.

[0046] Current methods typically invert orthogonality error, sensitivity error, and zero-bias error simultaneously, requiring the solution of a 9-parameter nonlinear inversion problem. With numerous unknown parameters and some correlation between them, it's difficult to guarantee solution accuracy, and robustness is easily affected by environmental noise and other factors. More importantly, the contributions of different error terms to the final steering error vary significantly, resulting in vastly different inversion accuracies. Under geomagnetic field conditions, the inversion accuracy of zero-bias error is far lower than that of orthogonality and sensitivity errors. For example, under geomagnetic field conditions (approximately 50,000 nT), a mere 0.5° angular deviation between a single axis and the standard orthogonal axis can introduce nearly 400 nT of error into the single-axis measurement and approximately 200 nT into the total field modulus. The sensitivity error of the Bartington Mag648 product (±0.5%) can cause a measurement modulus error of up to 250 nT. In contrast, the maximum single-axis zero-bias error of a typical fluxgate sensor is only a few to tens of nanoseconds, contributing only tens of nanoseconds to the total field modulus measurement error—a minimal contribution. Therefore, when simultaneously inverting the errors of the nine parameters under the geomagnetic field environment, the impact of magnetic noise of the same level on the inversion accuracy of the zero bias error is much greater than that of the orthogonality and sensitivity errors, and the inversion accuracy of the zero bias error is the lowest. Conversely, the inversion deviation of the zero bias error will also lead to the inversion deviation of the orthogonality and sensitivity errors, resulting in an overall decrease in the solution accuracy of all error terms.

[0047] To accurately determine the error parameters of the fluxgate sensor, especially the zero-bias error, this application constructs an error model and conducts simulation analysis. The results show that the total field magnitude deviation caused by the zero-bias error is largely independent of the external magnetic field strength, while the total field magnitude deviation caused by the orthogonality error and sensitivity error is correlated with the external magnetic field strength. The weaker the external magnetic field strength, the smaller the total field magnitude deviation caused by the same orthogonality error and sensitivity error. In a geomagnetic field environment (e.g., 50000 nT), the total field magnitude deviation caused by the orthogonality error and sensitivity error is much greater than that caused by the zero-bias error. The total field magnitude deviation is more sensitive to changes in the former two, and the inversion accuracy of the former two is higher than that of the latter. In a weak magnetic field environment (e.g., 500 nT), the total field magnitude deviation caused by the orthogonality error and sensitivity error is smaller than that caused by the zero-bias error. The total field magnitude deviation is more sensitive to the zero-bias error. Compared to the geomagnetic field environment, the inversion accuracy of the zero-bias error is significantly improved, while the inversion accuracy of the orthogonality and sensitivity errors is relatively reduced.

[0048] Based on the principle obtained from simulation analysis that the total field modulus deviation of fluxgate is more sensitive to orthogonality and sensitivity under geomagnetic field and more sensitive to zero bias under weak magnetic field, this application proposes a three-axis fluxgate sensor error calibration method. By using the measurement data of the three-axis fluxgate sensor under geomagnetic field and weak magnetic field, the fluxgate sensor error is iteratively calculated, which can significantly improve the inversion accuracy of fluxgate sensor error, especially zero bias error, and calibrate the three-axis fluxgate sensor more accurately.

[0049] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] The primary task in calibrating a three-axis fluxgate sensor is to construct an error model, analyze the three error formation mechanisms and their impact on the fluxgate sensor's rotational error, and then establish an error calculation method. Based on the error model and the actual output value of the three-axis fluxgate sensor, the error of the fluxgate sensor is estimated.

[0051] Ideally, the three axes of a fluxgate sensor are orthogonal. However, due to manufacturing limitations, perfect orthogonality is not practically possible. Therefore, the three magnetic field components measured by the fluxgate sensor deviate from the ideally orthogonal three components of the spatial magnetic field; this is known as non-orthogonality error.

[0052] The three-axis fluxgate sensor measures the projection values ​​of the spatial magnetic field vector along each axis. Let OXYZ be a three-axis orthogonal coordinate system, and the projection values ​​of the spatial magnetic field vector onto its three axes OX, OY, and OZ are respectively B... x B y B z Let OX1Y1Z1 be a non-orthogonal coordinate system formed by the three axes of a three-axis fluxgate sensor. The origins of two coordinate systems coincide. The projection values ​​of the spatial magnetic field vector onto the three axes OX1, OY1, and OZ1 of the non-orthogonal coordinate system are F... x 、F y 、F z To simplify the error model, assume OZ and OZ1 are coaxial, OY1 lies in the OYZ plane with an angle γ between OY1 and the OY axis, OX1 has an angle β between it and the OXY plane, and the projection of OX1 onto the OXY plane has an angle α with the OX axis. Figure 1 As shown.

[0053] The orthogonal three-component vector of the spatial magnetic field is represented as B = [B x B y B z ] T The output vector of the three-axis fluxgate sensor is represented as F = [F x F y F z ]T The superscript T indicates matrix transpose. According to Figure 1 The coordinate transformation relationships in the equation are:

[0054] F = PB (1)

[0055] Where P is the transformation matrix, also known as the orthogonality error matrix:

[0056]

[0057] As can be seen from formula (1), when the included angles γ, β and α are all 0, F = B. At this time, the three axes of the three-axis fluxgate sensor are orthogonal and there is no orthogonality error. When the three included angles are not all 0, F ≠ B. At this time, the three axes of the three-axis fluxgate sensor are not completely orthogonal and there is an orthogonality error.

[0058] Theoretically, when the same magnetic field is applied to the three axes of a three-axis fluxgate sensor, its output value should be consistent. However, in reality, the gain (also known as sensitivity) between the three axes will be inconsistent due to differences in the amplification and conditioning circuits. This results in different output values ​​generated by the three axes under the same magnetic field excitation; this error is called sensitivity error. It is generally believed that the output value of a three-axis fluxgate sensor containing sensitivity error is proportional to the true magnetic field value. Let the sensitivities of the three axes of the three-axis fluxgate sensor be S... x S y S z Then the sensitivity error matrix S can be written as:

[0059]

[0060] The triaxial fluxgate sensor's core exhibits residual magnetism, and its internal amplification, conditioning, and data acquisition circuits also exhibit zero-point offset. These two factors combined effectively superimpose a fixed magnetic field onto the three axes of the sensor, causing a shift in the triaxial output values ​​during magnetic field measurement. This is known as zero-bias error. Let the zero-bias of the three axes of the triaxial fluxgate sensor be O... x O y O z Then the zero bias error matrix O can be written as:

[0061]

[0062] Considering the orthogonality error, sensitivity error, and zero bias error of the triaxial fluxgate sensor, the output vector of the triaxial fluxgate sensor can be expressed as:

[0063] F = SPB + O (5)

[0064] Formula (5) is the error model expression for the triaxial fluxgate sensor. Based on this formula, the deviation of the fluxgate measurement modulus caused by three types of errors under geomagnetic and weak magnetic field environments can be simulated and calculated. By uniformly rotating the triaxial fluxgate sensor in a stable magnetic field to collect points, the maximum deviation of the total field modulus at all points during the rotation process can be used to measure the impact of the triaxial fluxgate sensor error. The maximum deviation ΔB of the total field modulus at all N measurement points during the rotation process can be calculated using the following formula:

[0065] ΔB = max k＝1,2,…N (||F|-|B||) (6)

[0066] Where |·| represents taking the absolute value.

[0067] From the expression formula (5) of the fluxgate sensor error model, the three-component vector B of the spatial magnetic field orthogonally can be represented by the output vector F of the three-axis fluxgate sensor as follows:

[0068] B = P -1 S -1 (FO) (7)

[0069] It can be seen that we only need to find α, β, γ, and S x S y S z O x O y O z With nine error parameters, the true value of the geomagnetic field in space can be calculated from the output value of the triaxial fluxgate sensor.

[0070] Under a stable magnetic field environment, the orthogonal three-component vector B of the spatial magnetic field can be considered to remain unchanged, that is, the total geomagnetic field modulus |B| is constant. Squaring and expanding equation (7) yields a three-component vector F of the fluxgate sensor output value. x 、F y 、F z The equation of the quadratic surface is in the following form:

[0071]

[0072] Among them, a i (i = 1, 2, ... 9) are the geometric parameters of the quadratic surface.

[0073] In fact, under a constant magnetic field environment, the spatial rotational magnetic measurement trajectory of a three-axis fluxgate sensor lies on a standard ellipsoid. Therefore, the aforementioned quadratic surface equation is actually the standard ellipsoid equation. By collecting a series of measured values ​​F generated by fluxgate attitude changes, and based on the constant total magnetic field modulus |B|, the various error parameters can be inverted using ellipsoidal fitting or the least squares method, thus achieving the calibration of the three-axis fluxgate sensor. This is currently the mainstream method for error calibration of three-axis fluxgate sensors. However, this method requires simultaneous inversion of nine error parameters of the three-axis fluxgate sensor. With many unknown parameters, its robustness and accuracy are easily affected by factors such as environmental noise.

[0074] Based on the principle obtained from simulation analysis that the total field modulus deviation of fluxgate is more sensitive to orthogonality and sensitivity under geomagnetic field and more sensitive to zero bias under weak magnetic field, this application proposes a three-axis fluxgate sensor error calibration method. By using the measurement data of the three-axis fluxgate sensor under geomagnetic field and weak magnetic field, the fluxgate sensor error is iteratively calculated, which can significantly improve the inversion accuracy of fluxgate sensor error, especially zero bias error, and calibrate the three-axis fluxgate sensor more accurately.

[0075] In one exemplary embodiment, such as Figure 2 and Figure 3 As shown, a method for calibrating the error of a three-axis fluxgate sensor is provided. This method is executed by a computer device, which can be executed by a computer device such as a terminal or a server alone, or by a terminal and a server together. It includes the following steps 101 to 107.

[0076] Step 101: Obtain preliminary geomagnetic field measurement data, weak magnetic field measurement data, and total geomagnetic field modulus value from the triaxial fluxgate sensor. The preliminary geomagnetic field measurement data includes measurement data from at least 6 different rotational attitudes, and the weak magnetic field measurement data includes measurement data from at least 4 different rotational attitudes.

[0077] Specifically, the three-axis fluxgate sensor is placed in a stable geomagnetic field environment and a weak magnetic field environment, respectively. The sensor is controlled to rotate at a constant speed (e.g., rotating uniformly around each of the three sensing axes in sequence, or rotating freely at a constant speed in any direction) with the sensing unit as the center point. Three-component magnetic measurement data (at least 6 sets) are collected under the geomagnetic field environment and three-component magnetic measurement data (at least 4 sets) under the weak magnetic field environment. Simultaneously, a total field magnetometer is used to measure the geomagnetic total field modulus at the location of the fluxgate probe under the geomagnetic field environment, obtaining preliminary geomagnetic field measurement data, weak magnetic field measurement data, and the geomagnetic total field modulus.

[0078] In a simulation analysis example of a three-axis fluxgate magnetic field, a three-axis fluxgate sensor is rotated uniformly in a constant geomagnetic field with a total field modulus of 50000 nT. The horizontal azimuth angle is uniformly taken in the range of 0 to 359°, and the polarization angle with the vertical direction is uniformly taken in the range of 0 to 179°. The sampling interval is set to 1°. The variation range of the three errors of the three-axis fluxgate sensor is referenced from the Bartington brand Mag648 fluxgate sensor, and the error range is appropriately expanded to make the analysis more universal. The variation range of the non-orthogonal axis error is set to -2° to 2°, the sensitivity error range is set to -0.02 to 0.02, and the zero bias error range is set to -100 nT to 100 nT. Assuming that the three-axis fluxgate sensor has no sensitivity error and zero bias error, and that one axis has a non-orthogonal angle error with the ideal axis, the relationship curve between the maximum deviation of the total field modulus and the non-orthogonal angle error can be calculated according to formula (6), such as Figure 4 As shown. Assuming the three-axis fluxgate sensor has no orthogonality error and zero bias error, but one axis has a sensitivity error, the relationship curve between the maximum deviation of the total field modulus and the sensitivity error can be calculated, as shown in the figure. Figure 5 As shown. Assuming the three-axis fluxgate sensor has no orthogonality error and sensitivity error, but one axis has a zero bias error, the curve showing the relationship between the maximum deviation of the total field modulus and the zero bias error can be calculated, as shown below. Figure 6 As shown, a single-axis angular deviation of only 0.5° or a single-axis sensitivity error of 0.005 can introduce a deviation of approximately 200 nT in the total field modulus. In contrast, the maximum single-axis zero-bias error of a typical triaxial fluxgate sensor ranges from several nanoseconds to tens of nanoseconds, resulting in a total field modulus deviation approximately equal to the zero-bias error itself. In other words, under the geomagnetic field, the deviation in the total field modulus caused by orthogonality error and sensitivity error is far greater than the deviation caused by zero-bias error. The total field modulus deviation is more sensitive to changes in the former two, and the inversion accuracy of the former two under the geomagnetic field is far higher than that of the latter.

[0079] Repeating the above rotational sampling measurement and calculation under a constant weak magnetic field with a total field modulus of 500 nT, the maximum deviation of the total field modulus under the weak magnetic field can also be obtained as well as the uniaxial non-orthogonal angle error. Figure 7 ), sensitivity error ( Figure 8 ), zero bias error ( Figure 9The relationship curve of the change of the total field modulus is shown. At this time, a single-axis angle deviation of up to 2° or a single-axis sensitivity error of 0.02 can only bring a deviation of less than 10 nT to the total field modulus, while the deviation of the total field modulus brought by the single-axis zero bias error is still about the size of the zero bias error itself, which can easily reach tens of nanoseconds. Through further simulation calculations, when the total field modulus of the ambient magnetic field decreases further, the deviation of the total field modulus caused by the orthogonality error and sensitivity error also decreases further, while the deviation of the total field modulus brought by the single-axis zero bias error is still about the size of the zero bias error itself. That is to say, in contrast to the geomagnetic field, the deviation of the total field modulus caused by the orthogonality error and sensitivity error is smaller than the deviation of the total field modulus caused by the zero bias error under the weak magnetic field; the deviation of the total field modulus is more sensitive to the change of the zero bias error, and the inversion accuracy of the zero bias error is higher than the former two.

[0080] Step 102: For the h-th iteration, based on the geomagnetic field measurement data at the h-th iteration, the total geomagnetic field modulus, and the fluxgate sensor error model, determine the orthogonality error and sensitivity error at the h-th iteration. If h > 0, the geomagnetic field measurement data at the first iteration is the preliminary geomagnetic field measurement data. The fluxgate sensor error model includes orthogonality error and sensitivity error.

[0081] In a specific application example, step 102 includes steps 21 and 22.

[0082] Step 21: Calculate the geometric parameters of the translationless ellipsoid based on the geomagnetic field measurement data at the h-th iteration.

[0083] Specifically, based on the geomagnetic field measurement data at the h-th iteration, a geomagnetic matrix V = [V1 V2] is constructed. Based on this geomagnetic matrix, the formula is used... Determine the geometric parameters of the translationless ellipsoid.

[0084] The derivation process for obtaining the geometric parameters of the translationless ellipsoid is as follows:

[0085] If we ignore the zero bias, or assume that the zero bias error is 0, the fluxgate sensor error model can be simplified to:

[0086] F = SPB (9)

[0087] Accordingly, formula (7) simplifies to:

[0088] B = P -1 S -1 F (10)

[0089] Similarly, squaring the above equation and expanding it, we obtain the equation of the quadratic surface in the following form:

[0090]

[0091] Where A = [a1, a2, a3, a4, a5, a6, -1] T Let be the geometric parameter matrix of the quadratic surface. Formula (11) is merely a special case of formula (8) where the zero bias is 0, and therefore it is also the equation of the ellipsoid, and does not contain any relation to F. x 、F y 、F z The first-order term is therefore a translationless ellipsoid equation. Compared with formula (8), the ellipsoid equation at this time has only 6 unknown parameters, reducing the complexity of ellipsoid fitting and parameter inversion, and enhancing stability.

[0092] Based on the principle that the total field modulus of the magnetic field is constant when the magnetic field is stable, various algorithms such as least squares method, particle swarm method or genetic algorithm can be used to invert the geometric parameters and fluxgate error of the above quadratic surface equation. This application proposes a method for inverting the orthogonality error and sensitivity error by fitting a translationless ellipsoid.

[0093] By collecting a series of measurements generated by fluxgate attitude changes, the translationless ellipsoid equation shown in formula (11) can be fitted. According to the algebraic fitting method that defines the fitting error distance using algebraic distance, the i-th group of three-component magnetic measurement data F in the geomagnetic field measurement data... 1,i =[F 1,xi ,F 1,yi ,F 1,zi The algebraic distance between the surface Γ(A,v)=0 and the quadratic surface Γ(A,v)=0 can be expressed as Γ(A,v)=0. i If we consider the condition that the sum of the squared algebraic distances between the set of n (n≥6) sets of three-component magnetic measurement data and the quadratic surface Γ(A,v)=0 is minimized, then the geometric parameters of the translationless ellipsoid can be solved using the least squares method, i.e.:

[0094]

[0095] Where V is the geomagnetic matrix. F 1,xi For the i-th x-axis magnetic measurement data in the geomagnetic field measurement data, F 1,yi F represents the i-th y-axis magnetic measurement data in the geomagnetic field measurement data. 1,zi Let represent the i-th z-axis magnetic measurement data in the geomagnetic field measurement data, and n represent the number of the three components of the geomagnetic field measurement data.

[0096] The minimum value is obtained when the partial derivative of the above equation with respect to A is 0. Taking the partial derivative of the above equation with respect to A, we get:

[0097] V T VA=O 7×1 (13)

[0098] Among them, O 7×1 It is a 7x1 zero matrix. The geomagnetic matrices V and A are divided into the following blocks:

[0099]

[0100] Where V1 is the first submatrix in the geomagnetic matrix. V2 is the second submatrix in the geomagnetic matrix, an n x 1 matrix with all elements equal to 1. A1 is the geometric parameter matrix of the translationless ellipsoid, A1 = [a1 a2 a3 a4 a5 a6]. T a1, a2, a3, a4, a5, and a6 are geometric parameters of the translationless ellipsoid, and A2 = [-1]. T .

[0101] Then formula (13) can be written as:

[0102]

[0103] The derivation and simplification yield the following:

[0104]

[0105] Obviously, It is a reversible square matrix, and both sides of the above equation are multiplied by the left. Organizing can yield

[0106]

[0107] By collecting a series of measurements generated by the attitude changes of the fluxgate, matrices V1 and V2 can be constructed, and the geometric parameter matrix A1 of the translationless ellipsoid can be obtained according to formula (17).

[0108] By deriving the correspondence between the geometric parameters of the translationless ellipsoid and the fluxgate error parameters when the zero bias error is 0, the fluxgate error parameters when the zero bias error is 0 can be calculated.

[0109] Step 22: Calculate the orthogonality error and sensitivity error at the h-th iteration based on the total geomagnetic field modulus, the geometric parameters of the translationless ellipsoid, and the fluxgate sensor error model.

[0110] Specifically, a first intermediate matrix is ​​constructed based on the relationship between the parameters in the fluxgate sensor error model and the geometric parameters of the translationless ellipsoid. A second intermediate matrix is ​​constructed based on the first intermediate matrix and the geomagnetic field modulus. Orthogonal sensitivity parameters are calculated based on the second intermediate matrix. Orthogonality error and sensitivity error are calculated based on the orthogonality sensitivity parameters to obtain the orthogonality error and sensitivity error at the h-th iteration.

[0111] The derivation process for calculating the orthogonality error and sensitivity error is as follows:

[0112] The equation of the translationless ellipsoid of formula (11) can be written in the following matrix form:

[0113] F T EF-1=0 (18)

[0114] Where E is the first intermediate matrix.

[0115] Taking the square of the triaxial fluxgate error model equation when the zero bias error is 0, as shown in formula (10), we get:

[0116] |B| 2 =B T B = F T (P -1 S -1 ) T P -1 S -1 F (19)

[0117] After sorting, we can obtain:

[0118]

[0119] Formula (18) and formula (20) are equivalent. Combining the two formulas, we get:

[0120]

[0121] Reversing both ends and rearranging, we get:

[0122]

[0123] Combining equations (21) and (22), we get:

[0124]

[0125] Among them, sp1, sp2, sp3, sp4, sp5, and sp6 are all orthogonal sensitivity parameters.

[0126] but:

[0127]

[0128] make:

[0129]

[0130] Where C is the second intermediate matrix, and C1, C2, C3, C4, C5, and C6 are all elements in the second intermediate matrix.

[0131] Substituting formulas (25) and (24) into formula (22) and rearranging, we get:

[0132]

[0133] Therefore, we can conclude that:

[0134]

[0135] After obtaining the geometric parameters of the translationless ellipsoid, the geomagnetic field modulus at the location of the three-axis fluxgate is measured by a high-precision total field magnetometer. Then, the orthogonality error and sensitivity error of the three-axis fluxgate sensor when the zero bias error is 0 can be calculated according to formulas (18), (25), (26) and (27).

[0136] In step 102 of this application, the equation of the translationless ellipsoid where the three-component measurement data points are located is fitted based on the geomagnetic field measurement data. Specifically, matrices V1 and V2 are constructed according to formula (14), and the geometric parameter matrix of the translationless ellipsoid is obtained according to formula (17). Then, ignoring the zero bias error, the orthogonality error and sensitivity error are calculated by substituting the geomagnetic field modulus value into the constructed error model containing only orthogonality error and sensitivity error, and the relationship between its parameters and the geometric parameters of the translationless ellipsoid. Specifically, the first intermediate matrix E is constructed according to formula (18), the second intermediate matrix C is constructed according to formula (25), and then the orthogonality error and sensitivity error are obtained according to formulas (26) and (27).

[0137] Step 103: Substitute the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, and determine the zero bias error at the h-th iteration based on the weak magnetic field measurement data.

[0138] Specifically, the orthogonality error and sensitivity error at the h-th iteration are substituted into the fluxgate sensor error model to construct a third intermediate matrix D. The zero-bias correlation matrix is ​​determined based on the third intermediate matrix and the weak magnetic field measurement data. The zero-bias error is calculated based on the zero-bias correlation matrix and the third intermediate matrix to obtain the zero-bias error at the h-th iteration.

[0139] The derivation process for calculating the zero bias error is as follows:

[0140] After obtaining the orthogonality error and sensitivity error under the geomagnetic field, they are substituted into the fluxgate sensor error model. Under a weak magnetic field, based on the principle that the total field modulus of the magnetic field is constant when the external magnetic field is stable, the zero bias error is obtained by the least squares method. If all three errors, including zero bias, exist, squaring both sides of formula (7) can be written as:

[0141] |B| 2 =BT B = (FO) T (P -1 S -1 ) T P -1 S -1 (FO) (28)

[0142] When the orthogonality error and sensitivity error are known, (P) -1 S -1 ) T P -1 S -1 It is known, and can be written in the form of an invertible square matrix as follows:

[0143]

[0144] Where D is the third intermediate matrix, d 11 d 12 d 13 d 22 d 23 d 33 All of them are elements in the third intermediate matrix.

[0145] Substituting formula (29) into formula (28), and after a series of derivations, we can obtain:

[0146] [F x F y F z 1]G=F T DF (30)

[0147] Where G is the zero partial correlation matrix, D(i=1,2,3,:) is the i-th row of the third intermediate matrix D.

[0148] Under a constant weak magnetic field, a series of m (m≥4) sets of weak magnetic field measurement data generated by fluxgate attitude changes are collected. For any set of magnetic measurement data, formula (30) is theoretically valid, and only the zero-bias correlation matrix G is an unknown quantity related to the zero-bias error. For the j-th set of magnetic measurement data F 2,j =[F 2,xj ,F 2,yj ,F 2,zj ],have Among them, F 2,xj For the j-th x-axis magnetic measurement data in the weak magnetic field magnetic measurement data, F 2,yj For the j-th y-axis magnetic measurement data in the weak magnetic field magnetic measurement data, F 2,zj denoted as the j-th z-axis magnetic measurement data in the weak magnetic field magnetic measurement data, and m represents the number of the three components of the weak magnetic field magnetic measurement data.

[0149] The equation formed by combining m sets of magnetic measurement data as shown in formula (30) can be written in the following matrix form:

[0150] UG = J (31)

[0151] Where U is the weak magnetic field measurement data matrix. J is the fourth intermediate matrix. F 2,j Let F be the j-th measurement value in the weak magnetic field measurement data. 2,j =[F 2,xj ,F 2,yj ,F 2,zj ].

[0152] U is usually not a square matrix and cannot be directly inverted. In formula (31), both sides of the equation are multiplied on the left by the transpose of U to construct an invertible square matrix. Then, both sides of the equation are multiplied on the left by the inverse of this square matrix to obtain:

[0153] (U T U) -1 U T UG = (U T U) -1 U T J; G = (U T U) -1 U T J (32)

[0154] The right-hand side of the above equation consists of known quantities. After obtaining the zero partial correlation matrix G, we take G1 = [G(1,:) G(2,:) G(3,:)] T Let G(1,:) be the first row of data in G, G(2,:) be the second row of data in G, and G(3,:) be the third row of data in G. Then we have:

[0155]

[0156] If D is an invertible square matrix, the zero-bias error matrix can be calculated by multiplying both ends of D by its inverse.

[0157]

[0158] In step 103 of this application, for weak magnetic field measurement data, the orthogonality error and sensitivity error obtained in step 102 are substituted into the fluxgate sensor error model. Based on the principle that the total field modulus of the magnetic field is constant when the external magnetic field is stable, the zero bias error is obtained by the least squares method. Specifically, based on the orthogonality error and sensitivity error obtained in step 102, the third intermediate matrix D is constructed according to formula (29); based on the weak magnetic field measurement data, matrices U and J are constructed according to formula (31), and the zero bias error is calculated by formulas (32) to (34).

[0159] Step 104: If h = 1, then set the zero-bias relative deviation value at the h-th iteration to infinity; otherwise, determine the zero-bias relative deviation value at the h-th iteration based on the zero-bias error at the h-th iteration and the zero-bias error at the (h-1)-th iteration.

[0160] In a specific application example, when h>1, the zero bias relative deviation value at the h-th iteration is calculated using the following formula:

[0161]

[0162] Where, δ O O is the zero-bias relative deviation value at the h-th iteration. h O represents the zero bias error at the h-th iteration. h-1 This represents the zero bias error during the (h-1)th iteration.

[0163] Step 105: Determine whether the relative deviation value of the zero bias at the h-th iteration is less than a preset threshold. The threshold is generally set based on experience and is taken in the range of 0.05 to 0.20.

[0164] Step 106: If yes, then the orthogonality error, sensitivity error, and zero bias error at the h-th iteration are output as fluxgate error values.

[0165] Step 107: If not, then use the zero bias error O from the h-th iteration. h The preliminary geomagnetic field measurement data is subjected to zero-bias correction to obtain the geomagnetic field measurement data at the (h+1)th iteration (i.e., the difference between the preliminary geomagnetic field measurement data and the zero-bias error at the h-th iteration is used as the geomagnetic field measurement data at the (h+1)th iteration), and the h+1th iteration is performed. Obviously, the orthogonality error and sensitivity error calculated again based on the assumption of no zero bias are closer to the actual values ​​at this time. Substituting the orthogonality error and sensitivity error calculated at this time into the zero bias calculation under a weak magnetic field, the result is also closer to the actual value. This process is repeated iteratively until the relative deviation of the zero bias between two consecutive iterations is less than a preset threshold.

[0166] Three-axis fluxgate sensors generally have zero bias. The orthogonality error and sensitivity error obtained without considering the zero bias, as well as the zero bias parameters obtained based on them, are close to the true values, but there are deviations. They can be gradually approached to the true values ​​through iteration.

[0167] In this application, iterative calculation is performed through steps 104 to 107. The main process is as follows: First, determine whether the relative deviation value of the zero bias between two consecutive iterations is less than a preset threshold. If so, output the fluxgate error value obtained in the current iteration as the final result. If not, use the calculated zero bias error to perform zero bias correction on the preliminary geomagnetic field measurement data. Based on the corrected geomagnetic field measurement data, calculate the orthogonality error, sensitivity error, and zero bias error according to steps 102 and 103. This iterative process continues until the relative deviation value of the zero bias between two consecutive iterations reaches the preset threshold.

[0168] The effectiveness, inversion accuracy, and robustness of the technical solution of this application are verified through an embodiment below.

[0169] Assuming the theoretical error parameters of the three-axis fluxgate sensor are shown in the second row of Table 1, the sensitivity errors of the three axes are set to greater than 1, less than 1, and equal to 1 (no deviation), respectively; the orthogonality errors of the three axes are set to greater than 0°, less than 0°, and equal to 0° (no deviation), respectively; the maximum absolute value of the angle deviation is set to an extreme value of 10°; and the zero bias errors of the three axes are set to greater than 0, less than 0, and equal to 0 (no deviation), respectively; the maximum absolute value of the zero bias error is set to an extreme value of 100nT, in order to fully test the applicability of the technical solution of this application to error inversion in different ranges.

[0170] Table 1. Theoretical error of the magnetic sensor and iterative inversion results of this application when noise-free.

[0171]

[0172] A triaxial fluxgate sensor was placed under a constant geomagnetic field with a total magnetic field modulus of 50000 nT and a constant weak magnetic field with a total magnetic field modulus of 500 nT, respectively. Spherical uniform sampling measurements were performed by rotating the sensor's sensing unit as the center point. The rotation range was from azimuth angle 0 to 360° and elevation angle 0° to 180°, with rotation angle intervals of 20°. This yielded the spatial distribution of the three components of the sampling points of the triaxial fluxgate sensor under noise-free geomagnetic field conditions, as follows: Figure 10 As shown; it can be seen that due to the error of the three-axis fluxgate sensor, the spatial distribution of the sampling points is not a sphere, but a uniform distribution on an ellipsoid; the total field intensity variation curve of all sampling points is shown in the figure. Figure 11 As shown by the thin gray line, it can be seen that due to the error of the three-axis fluxgate sensor, the total field intensity curve is not a straight line that is always the total field modulus value, but has large fluctuations. Its maximum deviation from the constant geomagnetic field modulus value of 50000nT can reach 5000nT, which intuitively demonstrates the necessity of fluxgate error calibration and rotation difference correction.

[0173] Similarly, the spatial distribution of the three components of the sampling points of the magnetic sensor to be calibrated under a weak magnetic field with no noise can be obtained, such as Figure 12 As shown, the sampling points are also uniformly distributed on an ellipsoidal surface. The total field intensity variation curve of all sampling points under a weak magnetic field is shown in the figure. Figure 13 As shown by the thin gray line, the total field intensity curve also exhibits significant fluctuations, with a maximum deviation of nearly 140 nT from the constant weak magnetic field total field modulus of 500 nT.

[0174] according to Figure 3 The technical process of this application, as shown, first does not set a threshold for the zero-bias relative deviation, and iteratively calculates the error of the triaxial fluxgate sensor. The results of the first 5 iterations are shown in Table 1. Considering the floating-point error factor of the computer, the result of the second iteration is already the theoretical value, and the zero-bias relative deviation from the first iteration is within 10. -5 The magnitude is close to 0; and the results of the 3rd to 5th iterations remain stable at the theoretical value, with the relative deviation from zero in each iteration being 10 times that of the previous iteration. -3 ~10 -4 This demonstrates the effectiveness and accuracy of the technical method presented in this application, and also shows that the iterative algorithm for calculating the error of the three-axis fluxgate sensor presented in this application is convergent.

[0175] After obtaining the error parameters of the three-axis fluxgate sensor through inversion, the magnetic measurement data can be compensated according to formula (7) to correct the steering error. The total field intensity curve of the noiseless sampling point under the geomagnetic field after compensation and correction is shown in Figure 1. Figure 11 As shown by the thick black line, the total field intensity curve is essentially a straight line with a constant total field modulus of 50,000 nT; the total field intensity curve of the noise-free sampling points under the compensated and corrected weak magnetic field is as follows. Figure 13 As shown by the thick black line, the total field intensity curve is basically a straight line with a constant total field modulus of 500 nT, indicating that the magnetic field deviation error has been completely corrected, reflecting the accuracy of the error parameter inversion.

[0176] Real-world magnetic measurements always involve environmental magnetic noise, necessitating verification of the robustness of the proposed method. Gaussian white noise with a standard deviation of 500 nT is added to the three-component sampling data under the geomagnetic field, resulting in a noisy three-component magnetic measurement dataset from a triaxial fluxgate sensor under the geomagnetic field. The spatial distribution of the three components of the sampling points is shown below. Figure 14 As shown; the total field intensity curve of the sampling points after adding noise is as follows. Figure 11 The dotted line shows the total field intensity difference curves at the sampling points under noisy and noiseless geomagnetic fields, as shown in the figure. Figure 15 As shown, due to the presence of noise, the distribution of some sampling points under the geomagnetic field deviates from the ellipsoid. Compared with the total field intensity variation curve when there is no noise, the fluctuations in the total field intensity curve when there is noise add noise points. The maximum difference in total field intensity caused by noise is nearly 1500 nT, which increases the difficulty of accurate inversion of magnetic sensor parameters.

[0177] Similarly, Gaussian white noise with a standard deviation of 50 nT is added to the three-component sampling point data under a weak magnetic field to obtain a noisy three-component magnetic measurement dataset of the magnetic sensor to be calibrated under a weak magnetic field. The spatial distribution of the three components of the sampling points is as follows: Figure 16 As shown; the total field intensity curve of the sampling points after adding noise is as follows. Figure 13 The dotted line indicates the total field intensity difference curve between the noisy and noiseless sampling points; the curves are shown below. Figure 17 As shown, due to the presence of noise, the distribution of some sampling points under weak magnetic fields deviates significantly from the ellipsoid. The total field intensity curve with noise has significantly more noise points compared to the one without noise, and the maximum difference in total field intensity caused by noise is nearly 150 nT.

[0178] according to Figure 3 The technical process shown initially does not set a threshold for the zero-bias relative deviation, and iteratively calculates the magnetic sensor error. The results of the first five iterations are shown in Table 2. It can be seen that a stable result can still be obtained in the second iteration. Compared to the theoretical value, the maximum relative deviation of the triaxial sensitivity is 0.32%, the maximum relative deviation of the orthogonality is 4.6%, and the maximum relative deviation of the zero bias is 4.13%. Considering that noise introduces a maximum deviation of nearly 1500 nT in the total field intensity at the sampling point under the geomagnetic field, this result is quite accurate. The zero-bias relative deviation between the second and first iterations is within 10... -5 The magnitude is similar, and the relative deviation of zero bias in the 3rd to 5th iterations is 10 times that of the previous iteration. -3 ~10 -4 This further demonstrates that the iterative algorithm in this application is convergent.

[0179] For the three-component magnetic measurement datasets containing noise from a triaxial fluxgate sensor under the same geomagnetic field and weak magnetic field, the fluxgate error was inverted using the traditional ellipsoidal fitting method. The inversion results were compared with the inversion results obtained in this application, as shown in Table 2. In Table 2, "geomagnetic field ellipsoid" represents the inversion result of the traditional ellipsoidal fitting method for the dataset containing noise from the same geomagnetic field, and "weak magnetic field ellipsoid" represents the inversion result of the traditional ellipsoidal fitting method for the dataset containing noise from the same weak magnetic field. It can be seen that the zero-bias error deviation obtained by the "geomagnetic field ellipsoid" inversion can reach 60 nT, which is much larger than the zero-bias error deviation obtained in this application. The maximum relative deviation of the triaxial sensitivity obtained by the "weak magnetic field ellipsoid" inversion is 3.7%, and the maximum relative deviation of the orthogonality is 21.4%, both of which are an order of magnitude larger than the relative deviations of the sensitivity and orthogonality obtained in this application. Furthermore, the zero-bias error obtained in this application is slightly smaller than that obtained by the "weak magnetic field ellipsoid" inversion, and the sensitivity and orthogonality deviations are slightly smaller than or equivalent to those obtained by the "geomagnetic field ellipsoid" inversion. These results indicate that the method in this application has strong robustness and higher inversion accuracy than the traditional ellipsoid fitting method.

[0180] Table 2 shows the inversion results of this application under noisy conditions and the inversion results of the traditional ellipsoid fitting method.

[0181]

[0182]

[0183] According to formula (7), the magnetic sensor error parameters obtained by inversion in this application are used to compensate for the noisy sampling point data under the geomagnetic field. The spatial distribution of the three components of the geomagnetic field sampling points after compensation is as follows: Figure 18 As shown, its total field intensity variation curve is as follows: Figure 19 As shown by the thick dashed line, it can be seen that, considering the unavoidable magnetic measurement noise error, the spatial distribution of the three components of the sampling point after compensation is basically restored to a sphere. The total field intensity curve of the sampling point fluctuates around a constant total field intensity of 50,000 nT, with a fluctuation amplitude of no more than 1,500 nT, which is significantly smaller than the 5,000 nT before compensation, fully demonstrating the accuracy and robustness of this application.

[0184] Finally, the difference in total field intensity of the sampling points under the geomagnetic field before and after noise addition, and the difference in total field intensity of the sampling points under the geomagnetic field after compensation relative to the constant modulus of 50000 nT, were compared. Figure 20 As shown, the two results are basically consistent, indicating that the fluctuation of the total field intensity after compensation is caused by objective environmental noise, and the deviation of the total field intensity caused by the magnetic sensor error has been corrected. This once again demonstrates the accuracy and robustness of this application.

[0185] In one exemplary embodiment, a three-axis fluxgate sensor error calibration system is provided, including: a data acquisition module, an orthogonal sensitivity error determination module, a zero bias error determination module, and an iteration module.

[0186] The data acquisition module is used to acquire preliminary geomagnetic field measurement data, weak magnetic field measurement data, and total geomagnetic field modulus value from the triaxial fluxgate sensor. The preliminary geomagnetic field measurement data includes measurement data from at least six different rotational attitudes, and the weak magnetic field measurement data includes measurement data from at least four different rotational attitudes.

[0187] The orthogonal sensitivity error determination module is used to determine the orthogonality error and sensitivity error for the h-th iteration based on the geomagnetic field measurement data, the total geomagnetic field modulus, and the fluxgate sensor error model. If h > 0, the geomagnetic field measurement data from the first iteration is the preliminary geomagnetic field measurement data. The fluxgate sensor error model includes orthogonality error and sensitivity error.

[0188] The zero bias error determination module is used to substitute the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, and determine the zero bias error at the h-th iteration based on the weak magnetic field measurement data.

[0189] The iteration module is used to set the zero-bias relative deviation value at the h-th iteration to infinity when h=1; otherwise, it determines the zero-bias relative deviation value at the h-th iteration based on the zero-bias error at the h-th iteration and the zero-bias error at the (h-1)-th iteration; and determines whether the zero-bias relative deviation value at the h-th iteration is less than a preset threshold. If so, the orthogonality error, sensitivity error, and zero-bias error at the h-th iteration are output as the fluxgate error value. If not, the zero-bias error at the h-th iteration is used to perform zero-bias correction on the preliminary geomagnetic field measurement data to obtain the geomagnetic field measurement data at the (h+1)-th iteration, and the (h+1)-th iteration is performed.

[0190] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0191] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0192] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0193] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for calibrating the error of a three-axis fluxgate sensor, characterized in that, The method includes: Acquire preliminary geomagnetic field measurement data, weak magnetic field measurement data, and total geomagnetic field modulus value of a three-axis fluxgate sensor; the preliminary geomagnetic field measurement data includes measurement data of at least 6 different rotational attitudes, and the weak magnetic field measurement data includes measurement data of at least 4 different rotational attitudes. For the h-th iteration, based on the geomagnetic field measurement data at the h-th iteration, the total geomagnetic field modulus, and the fluxgate sensor error model, the orthogonality error and sensitivity error at the h-th iteration are determined; h>0, the geomagnetic field measurement data at the 1st iteration is the preliminary geomagnetic field measurement data; the fluxgate sensor error model includes orthogonality error and sensitivity error; Substitute the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, and determine the zero bias error at the h-th iteration based on the weak magnetic field measurement data. If h = 1, then the zero bias relative deviation value at the h-th iteration is set to infinity; otherwise, the zero bias relative deviation value at the h-th iteration is determined based on the zero bias error at the h-th iteration and the zero bias error at the (h-1)-th iteration. Determine whether the relative deviation value of the zero bias at the h-th iteration is less than a preset threshold; if so, output the orthogonality error, sensitivity error and zero bias error at the h-th iteration as the fluxgate error value; if not, use the zero bias error at the h-th iteration to perform zero bias correction on the preliminary geomagnetic field measurement data to obtain the geomagnetic field measurement data at the (h+1)-th iteration, and perform the (h+1)-th iteration.

2. The error calibration method for a three-axis fluxgate sensor according to claim 1, characterized in that, Acquire preliminary geomagnetic field data, weak magnetic field data, and total geomagnetic field modulus value from a triaxial fluxgate sensor, specifically including: The three-axis fluxgate sensor was placed in a stable geomagnetic field environment and a weak magnetic field environment, respectively, and the three-axis fluxgate sensor was controlled to rotate at a constant speed with the sensing unit of the three-axis fluxgate sensor as the center point. Three-component magnetic measurement data under geomagnetic field environment and three-component magnetic measurement data under weak magnetic field environment were collected. At the same time, the total field magnetometer was used to measure the geomagnetic total field modulus value at the location of the fluxgate probe under geomagnetic field to obtain preliminary geomagnetic field measurement data, weak magnetic field measurement data and geomagnetic total field modulus value.

3. The error calibration method for a three-axis fluxgate sensor according to claim 1, characterized in that, Based on the geomagnetic field measurement data at the h-th iteration, the total geomagnetic field modulus, and the fluxgate sensor error model, the orthogonality error and sensitivity error at the h-th iteration are determined, specifically including: Based on the geomagnetic field measurement data at the h-th iteration, the geometric parameters of the translationless ellipsoid are obtained. Based on the total geomagnetic field modulus, the geometric parameters of the translationless ellipsoid, and the fluxgate sensor error model, calculate the orthogonality error and sensitivity error at the h-th iteration.

4. The error calibration method for a three-axis fluxgate sensor according to claim 3, characterized in that, Based on the geomagnetic field measurement data at the h-th iteration, the geometric parameters of the translationless ellipsoid are obtained, including: Based on the geomagnetic field measurement data at the h-th iteration, a geomagnetic matrix is ​​constructed: V = [V1 V2]; where V is the geomagnetic matrix, and V1 is the first submatrix in the geomagnetic matrix. F 1,xi For the i-th x-axis magnetic measurement data in the geomagnetic field measurement data, F 1,yi F represents the i-th y-axis magnetic measurement data in the geomagnetic field measurement data. 1,zi V1 represents the i-th z-axis magnetic measurement data in the geomagnetic field measurement data, n represents the number of three-component magnetic measurement data in the geomagnetic field measurement data, n≥6, and V2 represents the second submatrix in the geomagnetic matrix, which is an n-row, 1-column matrix with all elements being 1. Based on the aforementioned geomagnetic matrix, the formula is used. Determine the geometric parameters of the translationless ellipsoid; where A1 is the geometric parameter matrix of the translationless ellipsoid, A1 = [a1 a2 a3 a4 a5 a6] T a1, a2, a3, a4, a5, and a6 are all geometric parameters of a translationless ellipsoid.

5. The error calibration method for a three-axis fluxgate sensor according to claim 3, characterized in that, Based on the total geomagnetic field modulus, the geometric parameters of the translationless ellipsoid, and the fluxgate sensor error model, the orthogonality error and sensitivity error at the h-th iteration are calculated, specifically including: Based on the relationship between the parameters in the fluxgate sensor error model and the geometric parameters of the translationless ellipsoid, a first intermediate matrix is ​​constructed: Where E is the first intermediate matrix, and a1, a2, a3, a4, a5, and a6 are all geometric parameters of the translationless ellipsoid. Based on the first intermediate matrix and the total geomagnetic field modulus, construct the second intermediate matrix: Where C is the second intermediate matrix, |B| is the total geomagnetic field modulus, and C1, C2, C3, C4, C5, and C6 are all elements in the second intermediate matrix; Based on the second intermediate matrix, the formula is used. Calculate the orthogonal sensitivity parameters; where sp1, sp2, sp3, sp4, sp5, and sp6 are all orthogonal sensitivity parameters. Based on the orthogonal sensitivity parameters, the formula is used. Calculate the orthogonality error and sensitivity error to obtain the orthogonality error and sensitivity error at the h-th iteration; where, S is the sensitivity error matrix. x For the sensitivity along the x-axis, S y For the sensitivity of the y-axis, S z For the z-axis sensitivity, Let α be the orthogonality error matrix, β be the angle between the projection of OX1 onto the OXY plane and the OX axis, β be the angle between OX1 and the OXY plane, γ be the angle between OY1 and the OY axis, OXYZ be a three-axis orthogonal coordinate system, and OX1Y1Z1 be a non-orthogonal coordinate system formed by the three axes of the three-axis fluxgate sensor. OZ and OZ1 are coaxial, and OY1 is located in the OYZ plane.

6. The error calibration method for a three-axis fluxgate sensor according to claim 1, characterized in that, Substituting the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, and based on the weak magnetic field measurement data, the zero bias error at the h-th iteration is determined, specifically including: Substituting the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, a third intermediate matrix is ​​constructed: Where D is the third intermediate matrix, d 11 d 12 d 13 d 22 d 23 d 33 All are elements in the third intermediate matrix, where P is the orthogonality error matrix and S is the sensitivity error matrix; Based on the third intermediate matrix and the weak magnetic field measurement data, the formula G = (U T U) -1 U T J determines the zero-partial correlation matrix; where G is the zero-partial correlation matrix and U is the weak magnetic field measurement data matrix. F 2,xj For the j-th x-axis magnetic measurement data in the weak magnetic field magnetic measurement data, F 2,yj For the j-th y-axis magnetic measurement data in the weak magnetic field magnetic measurement data, F 2,zj Let J be the j-th z-axis magnetic measurement data in the weak magnetic field magnetic measurement data, m be the number of the three components of the weak magnetic field magnetic measurement data, m≥4, and J be the fourth intermediate matrix. F 2,j Let F be the j-th measurement value in the weak magnetic field measurement data. 2,j =[F 2,xj ,F 2,yj ,F 2,zj ]; Based on the zero partial correlation matrix and the third intermediate matrix, the formula is used. Calculate the zero-bias error matrix to obtain the zero-bias error at the h-th iteration; where, The zero-bias error matrix, O x Zero bias on the x-axis, O y Zero bias on the y-axis, O z With zero bias along the z-axis, G1 = [G(1,:) G(2,:) G(3,:] T G(1,:) is the first row of data in G, G(2,:) is the second row of data in G, and G(3,:) is the third row of data in G.

7. The error calibration method for a three-axis fluxgate sensor according to claim 1, characterized in that, When h>1, the zero-bias relative deviation value at the h-th iteration is calculated using the following formula: Where, δ O O is the zero-bias relative deviation value at the h-th iteration. h O represents the zero bias error at the h-th iteration. h-1 This represents the zero bias error during the (h-1)th iteration.

8. A three-axis fluxgate sensor error calibration system, applied to the three-axis fluxgate sensor error calibration method according to any one of claims 1-7, characterized in that, The system includes: The data acquisition module is used to acquire preliminary geomagnetic field measurement data, weak magnetic field measurement data and total geomagnetic field modulus value of the triaxial fluxgate sensor; the preliminary geomagnetic field measurement data includes measurement data of at least 6 different rotational attitudes and the weak magnetic field measurement data includes measurement data of at least 4 different rotational attitudes. The orthogonal sensitivity error determination module is used to determine the orthogonality error and sensitivity error for the h-th iteration based on the geomagnetic field measurement data, the geomagnetic total field modulus, and the fluxgate sensor error model; h>0, the geomagnetic field measurement data for the first iteration is the preliminary geomagnetic field measurement data; the fluxgate sensor error model includes orthogonality error and sensitivity error. The zero bias error determination module is used to substitute the orthogonality error and sensitivity error at the h-th iteration into the fluxgate sensor error model, and determine the zero bias error at the h-th iteration based on the weak magnetic field measurement data. The iteration module is used to set the zero-bias relative deviation value at the h-th iteration to infinity when h=1; otherwise, it determines the zero-bias relative deviation value at the h-th iteration based on the zero-bias error at the h-th iteration and the zero-bias error at the (h-1)-th iteration; it determines whether the zero-bias relative deviation value at the h-th iteration is less than a preset threshold; if so, it outputs the orthogonality error, sensitivity error, and zero-bias error at the h-th iteration as the fluxgate error value; if not, it uses the zero-bias error at the h-th iteration to perform zero-bias correction on the preliminary geomagnetic field measurement data to obtain the geomagnetic field measurement data at the (h+1)-th iteration, and performs the (h+1)-th iteration.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the error calibration method for a three-axis fluxgate sensor according to any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the error calibration method for the three-axis fluxgate sensor as described in any one of claims 1-7.

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