Three-axis fluxgate sensor orthogonality error calibration method, device, equipment, medium and product

Abstract

The invention discloses a three-axis fluxgate sensor orthogonality error calibration method and device, equipment, a medium and a product, and relates to the field of error calibration, and the method comprises the steps: obtaining a magnetic measurement data set of a to-be-calibrated three-axis fluxgate sensor; according to the magnetic measurement data set, geometric parameters of the ellipsoid where the magnetic measurement sampling points are located are fitted, and normalized ellipsoid geometric parameters are obtained; and obtaining a three-axis fluxgate orthogonality parameter according to the parameter normalization ellipsoid geometric parameter and a pre-constructed three-axis fluxgate orthogonality parameter expression represented by the parameter normalization ellipsoid geometric parameter. According to the method, under the condition that contribution of the sensitivity error and the zero offset error to the measurement error of the fluxgate sensor is considered, the orthogonality parameter can be independently obtained, the sensitivity and the zero offset error are not needed, the three-axis orthogonality detection capability and precision of the three-axis fluxgate sensor are improved, and the reliability of a detection result is improved.

Description

Technical Field

[0001] The present application relates to the field of error calibration, and in particular to a method, device, equipment, medium and product for calibrating the orthogonality error of a three-axis fluxgate sensor. Background Art

[0002] Three-axis fluxgate sensors can measure the vector geomagnetic field with high resolution and good robustness, and are widely used in geomagnetic navigation and orientation, land and resources surveys, and earth science research. In recent years, vector magnetic measurement has become a research hotspot due to its ability to obtain vector geomagnetic fields that carry more information, and three-axis fluxgate sensors have therefore received increasing attention.

[0003] The geomagnetic field signal is weak and sensitive, making three-axis fluxgate sensors highly susceptible to environmental noise and instrument interference when measuring the geomagnetic field. Therefore, a key task in measuring magnetic field with three-axis fluxgate sensors is to calibrate and correct instrument errors. When the external magnetic field is constant, the total geomagnetic field modulus output by an ideal three-axis fluxgate sensor should be constant and invariant with attitude. The spatial distribution of the three-component output values ​​should be a perfect sphere with the total geomagnetic field modulus as its radius. However, due to manufacturing process limitations, three-axis fluxgate sensors inevitably suffer from three-axis orthogonality error, sensitivity error, and bias error. This causes the total geomagnetic field modulus output by the three-axis fluxgate sensor to vary with attitude, transforming the spatial distribution of the three-component output values ​​into an ellipsoid. This error is called the steering error. Calibration of a three-axis fluxgate sensor involves obtaining the three-axis fluxgate orthogonality error, sensitivity error, and bias error through direct measurement or indirect inversion. This is then used to eliminate the steering error, restoring the spatial distribution of the three-axis fluxgate sensor output values ​​from an ellipsoid to an ideal sphere.

[0004] Ideally, the three axes of a fluxgate sensor are orthogonal. However, due to manufacturing process limitations, these three axes cannot be completely orthogonal. Consequently, the three-component magnetic field values ​​measured by the sensor deviate from the ideal three-component values ​​of the spatial magnetic field, a phenomenon known as orthogonality error. Compared to sensitivity error and bias error, the three-axis orthogonality error of a fluxgate sensor is fixed at the factory and does not change with environmental changes. After calibrating the three-axis orthogonality error, it can be used as a known quantity when performing steering error compensation on a magnetic platform mounted fluxgate sensor, improving the stability and accuracy of the fluxgate sensor's steering error compensation. Therefore, accurate calibration of the three-axis orthogonality is crucial for fluxgate sensor measurement applications.

[0005] Directly using a fully orthogonal, high-performance three-axis fluxgate sensor for comparison, or calibrating the orthogonality with a high-precision, non-magnetic turntable, is a vector calibration method that requires precise control of the ambient magnetic field and the sensor's attitude. This is tedious and challenging to implement. Currently, the orthogonality error of three-axis fluxgate sensors is primarily determined through indirect inversion scalar calibration. Commonly used scalar calibration methods fall into two categories. One is the ellipsoid fitting method, which fits the ellipsoid formed by the fluxgate sensor's rotational measurements and estimates the error term based on the mathematical relationship between the ellipsoid's geometric parameters and the error parameters. The other is nonlinear optimization methods that minimize the standard deviation of the corrected fluxgate total field modulus. These methods include least squares methods, real-coded genetic algorithms, particle swarm genetic algorithms, maximum likelihood methods, Gauss-Newton iteration algorithms, and improved invasive weed algorithms.

[0006] The current orthogonality scalar calibration method has three limitations:

[0007] (1) In many cases, it is only necessary to obtain the orthogonality error of the three axes of the fluxgate sensor, without having to determine the sensitivity and bias errors. However, current orthogonality calibration methods generally require the simultaneous determination of the sensitivity or bias of the three axes, and are unable to invert the orthogonality error independently while considering the contribution of the sensitivity and bias errors to the fluxgate steering error. The coupled inversion of sensitivity and bias errors increases the number of inversion parameters, which intensifies the computational complexity and non-uniqueness of the orthogonality inversion problem.

[0008] (2) The ellipsoid fitting method and most nonlinear optimization methods require the total geomagnetic field strength to be known. This is usually done with a high-precision total-field magnetometer to measure the total geomagnetic field at the location of the fluxgate sensor to be calibrated. However, the ambient magnetic field is not uniform and constant, and measurement deviations between magnetometers are inevitable due to manufacturing processes. This makes it difficult to obtain the precise total geomagnetic field value at the location of the three-axis fluxgate sensor to be calibrated, which inevitably introduces errors in the orthogonality calibration.

[0009] (3) At present, some nonlinear optimization methods lack the empirical constraint that "the fluxgate measurement values ​​are distributed on an ellipsoidal surface", and are more likely to fall into local optimality than the ellipsoid fitting method. Summary of the Invention

[0010] The purpose of this application is to provide a three-axis fluxgate sensor orthogonality error calibration method, device, equipment, medium and product. While considering the contribution of sensitivity error and zero bias error to the measurement error of the fluxgate sensor, the orthogonality parameter can be obtained separately without the need to obtain sensitivity and zero bias error, thereby improving the three-axis orthogonality detection capability and accuracy of the three-axis fluxgate sensor and improving the reliability of the detection results.

[0011] To achieve the above objectives, this application provides the following solutions:

[0012] In a first aspect, the present application provides a method for calibrating the orthogonality error of a three-axis fluxgate sensor, comprising:

[0013] Obtain a magnetic measurement data set of the three-axis fluxgate sensor to be calibrated;

[0014] According to the magnetic survey data set, geometric parameters of the ellipsoid surface where the magnetic survey sampling points are located are fitted to obtain parameter-normalized ellipsoid surface geometric parameters;

[0015] The three-axis fluxgate orthogonality parameter is obtained according to the parameter-normalized ellipsoidal geometric parameters and a pre-constructed three-axis fluxgate orthogonality parameter expression represented by the parameter-normalized ellipsoidal geometric parameters.

[0016] In a second aspect, the present application provides a three-axis fluxgate sensor quadrature error calibration system, comprising:

[0017] A data acquisition module is used to acquire a magnetic measurement data set of a three-axis fluxgate sensor to be calibrated;

[0018] A geometric parameter determination module is used to fit the geometric parameters of the ellipsoid where the magnetic sampling points are located according to the magnetic survey data set to obtain parameter-normalized ellipsoid geometric parameters;

[0019] The orthogonality parameter determination module is used to obtain the three-axis fluxgate orthogonality parameters according to the parameter-normalized ellipsoidal geometric parameters and a pre-constructed three-axis fluxgate orthogonality parameter expression represented by the parameter-normalized ellipsoidal geometric parameters.

[0020] In a third aspect, the present application provides a computer device comprising: 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-mentioned three-axis fluxgate sensor orthogonality error calibration method.

[0021] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned three-axis fluxgate sensor orthogonality error calibration method.

[0022] In a fifth aspect, the present application provides a computer program product, including a computer program, which implements the above-mentioned three-axis fluxgate sensor orthogonality error calibration method when executed by a processor.

[0023] According to the specific embodiments provided in this application, this application has the following technical effects:

[0024] The present application provides a three-axis fluxgate sensor orthogonality error calibration method, device, equipment, medium and product. By constructing a three-axis fluxgate orthogonality parameter expression represented by parameter-normalized ellipsoidal geometric parameters, there is no need to use a total-field magnetometer to obtain the total geomagnetic field intensity, nor is there a need for a non-magnetic turntable to accurately control the posture of the three-axis fluxgate sensor. While considering the contribution of sensitivity and zero-bias error to the fluxgate steering difference, the orthogonality parameter can be obtained separately without the need to obtain sensitivity and zero-bias error. This can substantially improve the three-axis orthogonality detection capability and accuracy of the three-axis fluxgate sensor and improve the reliability of the detection results. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0026] Figure 1 This is the relationship diagram between the non-orthogonal coordinate system and the orthogonal coordinate system of the three-axis fluxgate sensor;

[0027] Figure 2 A schematic flow chart of a method for calibrating the orthogonality error of a three-axis fluxgate sensor provided in one embodiment of the present application;

[0028] Figure 3 A technical flow chart of a method for calibrating the orthogonality error of a three-axis fluxgate sensor provided in one embodiment of the present application;

[0029] Figure 4 The three-component spatial distribution diagram of the sampling points when the three-axis fluxgate sensor to be calibrated is noise-free;

[0030] Figure 5 The total field intensity curve of the magnetic survey sampling point data before (thin line) and after (thick line) compensation is noisy (Gaussian white noise with a standard deviation of 100nT is added to each component);

[0031] Figure 6 The difference curve of the total field intensity between the noisy (Gaussian white noise with a standard deviation of 100nT is added to each component) and the noise-free magnetic survey sampling points;

[0032] Figure 7 This is the three-component spatial distribution diagram of the fluxgate sensor after noise (Gaussian white noise with a standard deviation of 100nT is added to each component) sampling point compensation;

[0033] Figure 8 A schematic diagram of the functional modules of a three-axis fluxgate sensor orthogonality error calibration system provided in one embodiment of the present application. DETAILED DESCRIPTION

[0034] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0035] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0036] The three-axis fluxgate sensor measures the projection value of the spatial magnetic field vector in each axis direction. Let OXYZ be the three-axis orthogonal coordinate system, and the projection values ​​of the spatial magnetic field vector on its three axes OX, OY, and OZ are B x 、B y 、B z Assume that OX1Y1Z1 is the non-orthogonal coordinate system formed by the three axes of the three-axis fluxgate sensor to be tested. The origins of the two coordinate systems coincide with each other. The projection values ​​of the spatial magnetic field vector on 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 that OZ and OZ1 are coaxial, OY1 is located in the OYZ plane, the angle between OY1 and OY is γ, the angle between OX1 and the OXY plane is β, and the angle between the projection of OX1 on the OXY plane and the OX axis is α, as shown in the following example: Figure 1 α, β, and γ are the three-axis fluxgate orthogonality parameters.

[0037] In an exemplary embodiment, the present application first constructs a three-axis fluxgate orthogonality parameter expression represented by parameter-normalized ellipsoidal geometric parameters, and the construction process includes the following steps 1 to 6.

[0038] Step 1: construct a three-axis fluxgate sensor error model, which includes quadrature error, sensitivity error, and zero bias error.

[0039] The first step in calibrating a three-axis fluxgate sensor is to build an error model. The inherent errors of a three-axis fluxgate sensor include three-axis orthogonality error, sensitivity error, and zero bias error. The error model of a three-axis fluxgate sensor that combines these three errors is:

[0040] F=SPB+O (1)

[0041] Where B=[B x By B z ] T is the orthogonal three-component vector of the spatial magnetic field, F=[F x F y F z ] T is the output vector of the three-axis fluxgate sensor, the superscript T represents the matrix transpose, P is the orthogonality error coefficient matrix, S is the sensitivity error coefficient matrix, and O is the zero bias error coefficient matrix.

[0042] according to Figure 1 The coordinate transformation relationship in , the orthogonality error coefficient matrix P can be written as:

[0043]

[0044] Theoretically, when the same magnetic field is applied to the three axes of a three-axis fluxgate sensor, its output values ​​should be consistent. However, in reality, the sensitivity between the three axes may be inconsistent due to differences in the amplification and conditioning circuits, resulting 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 with sensitivity error is proportional to the actual magnetic field value. Assume that the sensitivity of the three axes of the three-axis fluxgate sensor is S x 、S y 、S z , then the sensitivity error coefficient matrix S in formula (1) can be written as:

[0045]

[0046] The three-axis fluxgate sensor has three-axis core remanence and zero-point offset of the internal circuit, which is equivalent to superimposing a fixed magnetic field on the three axes of the three-axis fluxgate sensor, causing the three-axis output value to offset and generate zero-bias error. Assume that the zero bias of the three axes of the three-axis fluxgate sensor is O x , O y , O z , then the zero bias error coefficient matrix O in formula (1) can be written as:

[0047]

[0048] According to the three-axis fluxgate sensor error model shown in formula (1), the three-component vector B of the spatial magnetic field can be expressed by the output vector F of the three-axis fluxgate sensor as follows:

[0049] B=P -1 S -1 (FO) (5)

[0050] If the error parameters of the three-axis fluxgate sensor are known, the magnetic measurement sampling point data can be compensated according to the above formula to correct the steering error, thereby obtaining accurate environmental magnetic field information.

[0051] Step 2: Based on the condition that the total magnetic field modulus is constant and according to the three-axis fluxgate sensor error model, determine the ellipsoidal surface equation form of the three components of the three-axis fluxgate sensor output value.

[0052] In a constant magnetic field environment, the three orthogonal components of the spatial magnetic field vector B can be considered to remain unchanged, that is, the total magnetic field modulus |B| is constant. After squared and expanded, formula (5) is obtained to obtain the three components of the output value F of the three-axis fluxgate sensor. x 、F y 、F z The quadratic surface equation is as follows:

[0053] a1(F x -O x ) 2 +a2(F y -O y ) 2 +a3(F z -O z ) 2 +2a4(F x -O x )(F y -O y )+2a5(F x -O x )(F z -O z )+2a6(F y -O y )(F z -O z )-|B| 2 =0 (6)

[0054] Among them, a i (i=1,2,…6) are the geometric parameters of the quadratic surface.

[0055] In a constant magnetic field environment, the spatial rotation sampling points of the three-axis fluxgate sensor are distributed on an ellipsoidal surface. Therefore, the above quadratic surface equation is actually an ellipsoidal surface equation. At this time, a i (i=1,2,…6) are the geometric parameters of the ellipsoid.

[0056] Step 3: construct a magnetic measurement vector stripped of the zero bias error based on the magnetic measurement data and zero bias error of the three-axis fluxgate sensor.

[0057] Step 4: According to the magnetic measurement vector of the stripped zero bias error, the ellipsoidal surface equation form is converted into a matrix form expressed by the magnetic measurement vector of the stripped zero bias error, and combined with the three-axis fluxgate sensor error model, the ellipsoidal surface geometric parameter expression represented by the orthogonality parameter and the sensitivity parameter is obtained.

[0058] In a constant magnetic field environment, if the position of the three-axis fluxgate sensor is kept fixed and a series of measurement values ​​F generated by changes in the fluxgate posture are collected, the error parameters can be inverted through ellipsoid fitting or least squares methods based on the constant total magnetic field modulus |B| to achieve three-axis fluxgate sensor error calibration.

[0059] However, this method requires the simultaneous calculation of the orthogonality, sensitivity, and bias error of the three-axis fluxgate sensor. It is unable to independently invert the orthogonality error while also considering the contribution of sensitivity and bias error to the fluxgate steering error, which increases the computational complexity of the orthogonality inversion problem. Furthermore, this method typically requires the use of a high-precision total-field magnetometer to measure the total field strength of the ambient magnetic field. However, the ambient magnetic field is not uniform and constant, and measurement deviations between magnetometers vary due to the manufacturing process. This makes it difficult to accurately determine the total field strength at the location of the three-axis fluxgate sensor being calibrated, inevitably introducing errors in the orthogonality calibration.

[0060] From the derivation of the formula, we note that the orthogonality error primarily determines the angle between the ellipsoid's semi-axis and the orthogonal coordinate axes. For the ellipsoid surface fitted by the fluxgate's three-component sampling points, the angle between the ellipsoid's semi-axis and the orthogonal coordinate axes depends on the ellipsoid's geometric parameters. Therefore, theoretically, the orthogonality error expression can be derived from the inherent relationship between the ellipsoid's geometric parameters.

[0061] Let F c =FO=[F x -O x F y -O y F z -O z ] T =[F cx F cy F cz ] T (7)

[0062] Among them, F cx 、F cy 、F cz is the magnetic measurement vector F after stripping the bias error c The three components of . Then the ellipsoidal surface equation of formula (6) can be written in the following matrix form:

[0063] F c T EF c -|B|2 =0 (8)

[0064] Among them, E is the ellipsoidal geometric parameter matrix,

[0065] Taking the square of formula (5) and combining it with formula (7) we can get:

[0066] |B| 2 =B T B=F c T (P -1 S -1 ) T P -1 S -1 F c (9)

[0067] After finishing, we can get:

[0068] F c T (P -1 S -1 ) T P -1 S -1 F c -|B| 2 =0 (10)

[0069] Combining formula (8) and formula (10), we can get:

[0070] E=(P -1 S -1 ) T P -1 S -1 (11)

[0071] From formula (2), we can get:

[0072]

[0073] From formula (3), we can get:

[0074]

[0075] Substituting formula (12) and formula (13) into formula (11), after a series of derivations, the expression of the ellipsoidal geometric parameters represented by the orthogonality parameter and the sensitivity parameter can be obtained:

[0076]

[0077] Step 5: Eliminate the sensitivity parameter from the ellipsoidal geometric parameter expression represented by the orthogonality parameter and the sensitivity parameter according to the ratio between the ellipsoidal geometric parameters, and obtain an expression containing only the orthogonality parameter and the ellipsoidal geometric parameters.

[0078] According to formula (14), we can get i The ratio between them (i=1,2,…6) eliminates the sensitivity parameter in the relationship, such as Eliminate S x 、S y , thus removing the influence of sensitivity parameter coupling in the orthogonality calculation and obtaining an expression containing only the orthogonality parameter and the ellipsoidal geometric parameters:

[0079]

[0080] Among them, λ and μ are two auxiliary calculation parameters.

[0081] Step 6: normalize the ellipsoidal geometric parameters in the expression containing only the orthogonality parameters and the ellipsoidal geometric parameters to obtain a three-axis fluxgate orthogonality parameter expression represented by the parameter-normalized ellipsoidal geometric parameters.

[0082] The ellipsoidal surface equation of formula (6) can be further expanded as follows:

[0083]

[0084]

[0085] where a 10 >0.

[0086] Let d i =a i / a 10 (17)

[0087] Where i = 1, 2, ... 10, the geometric parameters of the ellipsoid can be normalized to obtain the parameter-normalized ellipsoid equation:

[0088] Γ(A,v)=A T v=0 (18)

[0089] Where A=[d1,d2,d3,d4,d5,d6,d7,d8,d9,-1] T is the geometric parameter vector of the parametric normalized ellipsoid, is the auxiliary vector of magnetic data.

[0090] Substituting formula (17) into formula (15), we can finally obtain the geometric parameters d of the normalized ellipsoid surface iThe expression of the three-axis fluxgate orthogonality parameter represented by (i=1,2,…6) is:

[0091]

[0092] In an exemplary embodiment, Figure 2 As shown, a method for calibrating the orthogonality error of a three-axis fluxgate sensor is provided. The method is executed by a computer device, and specifically can be executed by a computer device such as a terminal or a server alone, or can be executed by a terminal and a server together. The method for calibrating the orthogonality error of a three-axis fluxgate sensor includes the following steps 201 to 203.

[0093] Step 201: Acquire a magnetic measurement data set of a three-axis fluxgate sensor to be calibrated.

[0094] Specifically, a three-axis fluxgate sensor to be calibrated is placed in a constant magnetic field with a gentle gradient, and the position of the three-axis fluxgate sensor to be calibrated is kept unchanged. With the induction unit of the three-axis fluxgate sensor to be calibrated as the center point, the three-axis fluxgate sensor to be calibrated is controlled to rotate at a uniform speed (such as rotating around three sensitive axes in sequence for one circle or rotating freely at a uniform speed in any direction), and multiple groups (at least 9 groups) of three-component magnetic measurement data with different rotation postures are collected to obtain a magnetic measurement data set.

[0095] Step 202 : fitting the geometric parameters of the ellipsoid where the magnetic sampling points are located according to the magnetic survey data set to obtain parameter-normalized ellipsoid geometric parameters.

[0096] In practice, various nonlinear optimization methods such as the least squares method can be used to fit the geometric parameters of the ellipsoid where the magnetic sampling points are located. Here, the least squares method is used as an example to solve the geometric parameters of the normalized ellipsoid.

[0097] According to the algebraic fitting method that defines the fitting error distance by algebraic distance, the jth group of three-component magnetic data F j =[F xj ,F yj ,F zj The algebraic distance between ] and the ellipsoid Γ(A,v)=0 can be expressed as Γ(A,v j ) indicates that, where F xj is the x-axis magnetic data of the jth group of three-component magnetic data in the magnetic data set, F yj is the y-axis magnetic data of the jth group of three-component magnetic data in the magnetic data set, F zj is the z-axis magnetic data of the jth group of three-component magnetic data in the magnetic data set, n is the number of groups of three-component magnetic data in the magnetic data set, v jis the auxiliary vector of the jth group of three-component magnetic data. The constraint condition is that the sum of the squares of the algebraic distances between the set of n groups of three-component magnetic data and the ellipsoid Γ(A,v)=0 is minimized, and n≥9. The least squares method can be used to solve the geometric parameters of the parameterized ellipsoid, that is:

[0098]

[0099] Where V is the geomagnetic matrix,

[0100] When the partial derivative of the above formula with respect to A is equal to 0, the minimum value can be obtained. Taking the partial derivative of the above formula with respect to A, we can get:

[0101] V T VA=O 10×1 (twenty one)

[0102] Among them, O 10×1 is a zero matrix with 10 rows and 1 column. The geomagnetic matrix V and the geometric parameter vector A of the parameter normalized ellipsoid are divided into blocks as follows:

[0103]

[0104] Among them, V1 is the first sub-matrix in the geomagnetic matrix, V2 is the second submatrix in the geomagnetic matrix, which is an n-row, 1-column matrix with all elements set to 1. A1 is the geometric parameter vector of the parametrically normalized ellipsoid, A1 = [d1 d2 d3 d4 d5 d6 d7 d8 d9] T , A2=[-1] T Then formula (21) can be written as:

[0105]

[0106] The derivation and arrangement can be obtained:

[0107]

[0108] Obviously, It is a reversible square matrix. Multiply both ends of the above formula by the left After finishing, we can get:

[0109]

[0110] Specifically, the geomagnetic matrix is ​​constructed based on the magnetic survey data set and formula (22), and the parameter normalized ellipsoid geometric parameter vector is obtained according to formula (25).

[0111] Step 203 : obtaining the three-axis fluxgate orthogonality parameter according to the parameter-normalized ellipsoidal geometric parameters and a pre-constructed three-axis fluxgate orthogonality parameter expression represented by the parameter-normalized ellipsoidal geometric parameters.

[0112] This application proposes a new method for calibrating orthogonality errors using ellipsoid fitting, by deriving a relationship between the geometric parameters of the ellipsoid surface at the magnetic sampling point and the orthogonality parameters. This method is simple and easy to implement, requiring neither a total-field magnetometer to obtain the total geomagnetic field intensity nor a non-magnetic turntable to precisely control the attitude of a three-axis fluxgate sensor. While accounting for the contributions of sensitivity and bias errors to the fluxgate steering error, this method can independently determine the orthogonality error, eliminating the need for sensitivity and bias errors. This method can substantially improve the three-axis orthogonality detection capability and accuracy of the three-axis fluxgate sensor, enhancing the reliability of the test results.

[0113] The effectiveness, inversion accuracy and robustness of the technical solution of the present application are verified by an example below.

[0114] The sensitivity parameters S of the three axes of the three-axis fluxgate sensor to be calibrated are x 、S y 、S z Set them to 1.00, 0.94, and 1.04 respectively, and the zero bias parameters of the three axes are O x , O y , O z They are set to -100nT, 100nT, and 0 respectively; the theoretical values ​​of the orthogonality parameters of the three axes are set as shown in the second row of Table 1, the maximum absolute value of the angular deviation is set to 10°, and they are set to be greater than 0°, less than 0°, and close to 0° respectively, in order to fully test the applicability of the technical solution of the present application to the inversion of orthogonality errors in different ranges.

[0115] Table 1 Theoretical values ​​of orthogonality parameters, inversion results of this application without noise and with noise

[0116] Orthogonality parameter α / ° β / ° γ / ° Maximum absolute error / ° Theoretical value 10.0 -10.0 1.0 Noise-free data inversion 10.0000 -10.0000 1.0000 0.0000 Noise data inversion (standard deviation is 10nT) 10.0052 -10.0051 1.0040 0.0052 Noise data inversion (standard deviation is 50nT) 10.0205 -9.9931 1.0083 0.0205 Noise data inversion (standard deviation is 100nT) 9.9732 -9.9655 1.0310 0.0345 Noise data inversion (standard deviation is 500nT) 10.1280 -10.0201 1.3016 0.3016

[0117] The three-axis fluxgate sensor to be calibrated is placed in a constant geomagnetic field with a total magnetic field modulus of 45000nT. The sensing unit of the three-axis fluxgate sensor to be calibrated is rotated as the center point to perform spherical uniform sampling. The azimuth angle ranges from 0° to 360°, the pitch angle ranges from 0° to 180°, and the rotation angle interval is 20°. Figure 4 The three-component spatial distribution of the sampling points of the noise-free three-axis fluxgate sensor to be calibrated is shown. As can be seen, due to the errors of the three-axis fluxgate sensor to be calibrated, the sampling points are evenly distributed on an ellipsoid rather than a theoretical sphere, and the angle between the ellipsoid's semi-axis and the orthogonal coordinate axes is not zero.

[0118] The orthogonality parameters of the noise-free magnetic survey data were inverted using the method of the present application, wherein the least squares method was used to fit the parameters to normalize the ellipsoid. The orthogonality parameters obtained by inversion are shown in the third row of Table 1. It can be seen that the inversion results of the three-axis orthogonality parameters are completely consistent with the theoretical values, which illustrates the effectiveness, accuracy and precision of the method of the present application.

[0119] In actual magnetic measurement, there will be environmental magnetic noise, so it is necessary to test the robustness of the proposed method. Therefore, Gaussian white noise with a standard deviation of 100nT is added to the noise-free three-component sampling point data to obtain the noisy three-component magnetic measurement data of the three-axis fluxgate sensor to be calibrated. The total field strength curve is as follows: Figure 5 As shown by the thin line, it can be seen that the total field intensity curve at this time has a large fluctuation relative to the total field modulus of 45000nT, and the fluctuation amplitude can reach 6000nT. The total field intensity difference curve of the noisy and noise-free magnetic measurement sampling points is shown in Figure 6 As shown in the figure, the maximum difference in total field intensity caused by noise is nearly 300nT, which poses a challenge to the accurate inversion of the orthogonality of the three-axis fluxgate sensor.

[0120] The method of the present application is used to invert the orthogonality parameters of noisy data with a standard deviation of 100nT. The results are shown in the sixth row of Table 1. It can be seen that when the maximum fluctuation of the total field intensity caused by noise can reach 300nT, the maximum absolute deviation of the three-axis orthogonality parameters is 0.0345°. The results are accurate and stable, reflecting the robustness of the method of the present application.

[0121] Using the theoretical value of the total geomagnetic field intensity at the location of the three-axis fluxgate sensor, the traditional ellipsoid fitting method was used to invert the orthogonality parameters of the noisy data. It was found that the orthogonality parameters obtained by the method of the present application and the traditional ellipsoid fitting method were basically consistent, which reflects the stability of the method of the present application; however, the method of the present application does not require the use of the total geomagnetic field intensity, which reflects the advantages of the method of the present application.

[0122] According to formula (5), the orthogonality parameter and the theoretical values ​​of sensitivity and bias parameters obtained by the inversion method of this application are used to compensate the magnetic survey data with a standard deviation of 100nT Gaussian white noise to correct the magnetic survey steering error. The total field intensity change curve of the sampling point after compensation is as follows: Figure 5 As shown by the thick line. It can be seen that compared with the total field intensity curve before compensation shown by the thin line, the total field intensity after compensation is close to the total field modulus value of 45000nT, the curve fluctuation is significantly reduced, and the fluctuation amplitude is no more than 300nT. This amplitude is equivalent to the maximum difference in the total field intensity caused by noise, indicating that the remaining total field intensity fluctuation after compensation should be caused by the objective existence of environmental noise; the spatial distribution of the three components of the sampling points after compensation is shown as follows Figure 7 As shown, it can be seen that the basic distribution is on a sphere, which once again demonstrates the effectiveness of the method of the present application.

[0123] To further verify the robustness of the method of the present application under different noise levels, Gaussian white noise with standard deviations of 10nT, 50nT, 100nT, and 500nT was added to the three-component data of the noise-free sampling points, respectively, to obtain noisy three-component magnetic survey data with different noise levels. The three-axis orthogonality of the noisy three-component magnetic survey data with different noise levels was inverted using the method of the present application, and the results are shown in Table 1. It can be seen that when the standard deviation of the Gaussian white noise of each component of the three-component data is 10nT, the maximum absolute deviation of the three-axis orthogonality parameter is only about 0.0052°; when the standard deviation of the Gaussian white noise is 50nT, the maximum absolute deviation of the three-axis orthogonality parameter is only about 0.0205°, both demonstrating the stability and accuracy of the method of the present application. In the extreme case, when the standard deviation of the Gaussian white noise of each component of the three-component data is 500nT, the maximum absolute deviation of the three-axis orthogonality parameter is still only about 0.3°, fully demonstrating the robustness of the inversion of the method of the present application under low signal-to-noise ratio conditions.

[0124] Based on the same inventive concept, embodiments of the present application also provide a three-axis fluxgate sensor orthogonality error calibration system for implementing the aforementioned three-axis fluxgate sensor orthogonality error calibration method. The solution provided by this system is similar to the solution described in the aforementioned method. Therefore, the specific limitations of one or more of the following three-axis fluxgate sensor orthogonality error calibration system embodiments can be found in the above-described limitations of the three-axis fluxgate sensor orthogonality error calibration method and are not further elaborated here.

[0125] In an exemplary embodiment, Figure 8 As shown, a three-axis fluxgate sensor orthogonality error calibration system is provided, including: a data acquisition module 801 , a geometric parameter determination module 802 and an orthogonality parameter determination module 803 .

[0126] The data acquisition module 801 is used to acquire a magnetic measurement data set of a three-axis fluxgate sensor to be calibrated.

[0127] The geometric parameter determination module 802 is used to fit the geometric parameters of the ellipsoid where the magnetic sampling points are located according to the magnetic survey data set to obtain parameter-normalized ellipsoid geometric parameters.

[0128] The orthogonality parameter determination module 803 is used to obtain the three-axis fluxgate orthogonality parameters according to the parameter-normalized ellipsoidal geometric parameters and the pre-constructed three-axis fluxgate orthogonality parameter expression represented by the parameter-normalized ellipsoidal geometric parameters.

[0129] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0130] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0131] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0132] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0133] In this application, all actions to obtain signals, information or data are carried out in compliance with the relevant data protection laws and policies of the country where they are located and with the authorization given by the owner of the corresponding device.

[0134] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0135] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0136] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, 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.

[0137] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for calibrating the orthogonality error of a three-axis fluxgate sensor, characterized in that: The method comprises: Obtain a magnetic measurement data set of the three-axis fluxgate sensor to be calibrated; According to the magnetic survey data set, geometric parameters of the ellipsoid surface where the magnetic survey sampling points are located are fitted to obtain parameter-normalized ellipsoid surface geometric parameters; The three-axis fluxgate orthogonality parameter is obtained according to the parameter-normalized ellipsoidal geometric parameters and a pre-constructed three-axis fluxgate orthogonality parameter expression represented by the parameter-normalized ellipsoidal geometric parameters.

2. The method for calibrating the orthogonality error of a three-axis fluxgate sensor according to claim 1, wherein: Obtain the magnetic measurement data set of the three-axis fluxgate sensor to be calibrated, including: The three-axis fluxgate sensor to be calibrated is placed in a constant magnetic field and its position is kept unchanged. The three-axis fluxgate sensor to be calibrated is controlled to rotate at a constant speed with its induction unit as the center point, and multiple sets of three-component magnetic measurement data with different rotation postures are collected to obtain a magnetic measurement data set.

3. The orthogonality error calibration method of a three-axis fluxgate sensor according to claim 1, characterized in that: The least squares method is used to fit the geometric parameters of the ellipsoid where the magnetic sampling points are located.

4. The method for calibrating the orthogonality error of a three-axis fluxgate sensor according to claim 1, wherein: According to the magnetic survey data set, the geometric parameters of the ellipsoid where the magnetic survey sampling points are located are fitted to obtain the parameter-normalized ellipsoid geometric parameters, specifically including: According to the magnetic survey data set, a geomagnetic matrix is ​​constructed: V = [V1 V2]; wherein V is the geomagnetic matrix, V1 is the first sub-matrix in the geomagnetic matrix, F xj is the x-axis magnetic data of the jth group of three-component magnetic data in the magnetic data set, F yj is the y-axis magnetic data of the jth group of three-component magnetic data in the magnetic data set, F zj is the z-axis magnetic data of the jth group of three-component magnetic data in the magnetic data set, n is the number of groups of three-component magnetic data in the magnetic data set, V2 is the second submatrix in the geomagnetic matrix, which is an n-row and 1-column matrix with all elements being 1; According to the geomagnetic matrix, the formula Determine the geometric parameters of the parametric normalized ellipsoid; where A1 is the parametric normalized ellipsoid geometric parameter vector, A1 = [d1 d2 d3 d4 d5 d6 d7 d8 d9] T , d1~d9 are the geometric parameters of the parametric normalized ellipsoid, and the superscript T represents the matrix transpose.

5. The method for calibrating the orthogonality error of a three-axis fluxgate sensor according to claim 1, wherein: The expression of the three-axis fluxgate orthogonality parameter expressed by the geometric parameters of the parametric normalized ellipsoid is: Among them, α, β, and γ are the three-axis fluxgate orthogonality parameters, α represents the angle between the projection of OX1 on the OXY plane and the OX axis, β represents the angle between OX1 and the OXY plane, γ represents the angle between OY1 and the OY axis, OXYZ is the three-axis orthogonal coordinate system, OX1Y1Z1 is the non-orthogonal coordinate system formed by the three axes of the three-axis fluxgate sensor to be measured, OZ and OZ1 are coaxial, OY1 is located in the OYZ plane, λ and μ are two auxiliary calculation parameters, and d1 to d6 are the geometric parameters of the parameter normalized ellipsoid.

6. The method for calibrating the orthogonality error of a three-axis fluxgate sensor according to claim 1, wherein: The process of constructing the expression of the three-axis fluxgate orthogonality parameter represented by the geometric parameters of the parametric normalized ellipsoid includes: Constructing a three-axis fluxgate sensor error model; the three-axis fluxgate sensor error model includes orthogonality error, sensitivity error and zero bias error; Based on the condition that the total magnetic field modulus is constant and according to the three-axis fluxgate sensor error model, determining the ellipsoidal surface equation form for the three components of the three-axis fluxgate sensor output value; According to the magnetic measurement data and zero bias error of the three-axis fluxgate sensor, a magnetic measurement vector stripped of the zero bias error is constructed; According to the magnetic measurement vector of the stripping zero bias error, the ellipsoidal surface equation form is converted into a matrix form expressing the magnetic measurement vector of the stripping zero bias error, and combined with the three-axis fluxgate sensor error model, an ellipsoidal surface geometric parameter expression represented by an orthogonality parameter and a sensitivity parameter is obtained; Eliminating the sensitivity parameter from the ellipsoidal surface geometric parameter expression represented by the orthogonality parameter and the sensitivity parameter according to the ratios between the ellipsoidal surface geometric parameters, thereby obtaining an expression containing only the orthogonality parameter and the ellipsoidal surface geometric parameters; The ellipsoidal geometric parameters in the expression containing only the orthogonality parameter and the ellipsoidal geometric parameters are normalized to obtain the orthogonality parameter expression of the three-axis fluxgate represented by the parameter-normalized ellipsoidal geometric parameters.

7. A three-axis fluxgate sensor orthogonality error calibration system, applied to the three-axis fluxgate sensor orthogonality error calibration method according to any one of claims 1 to 6, characterized in that: The system comprises: A data acquisition module is used to acquire a magnetic measurement data set of a three-axis fluxgate sensor to be calibrated; A geometric parameter determination module is used to fit the geometric parameters of the ellipsoid where the magnetic sampling points are located according to the magnetic survey data set to obtain parameter-normalized ellipsoid geometric parameters; The orthogonality parameter determination module is used to obtain the three-axis fluxgate orthogonality parameters according to the parameter-normalized ellipsoidal geometric parameters and a pre-constructed three-axis fluxgate orthogonality parameter expression represented by the parameter-normalized ellipsoidal geometric parameters.

8. A computer device comprising: 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 orthogonality error calibration method for a three-axis fluxgate sensor according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the orthogonality error calibration method of a three-axis fluxgate sensor according to any one of claims 1 to 6 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the orthogonality error calibration method of a three-axis fluxgate sensor according to any one of claims 1 to 6 is implemented.

Images