A method for correcting linear misalignment errors of a triaxial fluxgate sensor array

Abstract

The application discloses a method for correcting linear misalignment error between sensors in a three-axis fluxgate sensor array, aiming at solving the problem of poor consistency of multi-sensor output signals caused by misalignment error between sensors. Firstly, in the case of pure geomagnetic background noise, the sensor array is rotated around the center, and the magnetic signal data of each sensor at different angles is collected; then, an error correction model of each sensor is established, the parameters of the error correction model of each sensor are solved by using the collected geomagnetic background signals at different angles, and the signals measured by each sensor are corrected; a sensor is selected as a reference sensor, a linear misalignment error correction model of other sensors relative to the reference sensor is established, and the model parameters are solved; finally, the measurement data of other sensors are substituted into the linear misalignment error correction model, and the corrected magnetic signal data are obtained. By using the corrected signals for difference or gradient operation, the signal-to-noise ratio of the difference signal or the gradient signal can be improved.

Description

Technical Field

[0001] This invention belongs to the field of error correction technology for geophysical instruments, and relates to a method for correcting measurement data errors of a three-axis fluxgate sensor array. Background Technology

[0002] The three-axis fluxgate sensor has high measurement accuracy and response characteristics, and is used in various fields such as earth information measurement, magnetic anomaly detection, airborne target detection, geological exploration, and terrestrial and underwater archaeology.

[0003] The signals acquired by fluxgate sensors contain more vector information than those from scalar sensors, and can be used for tensor signal calculation and analysis. Therefore, vector magnetic measurement has gradually become a research hotspot in recent years.

[0004] In practical measurement work, triaxial fluxgate sensors exhibit various errors, such as sensitivity errors caused by differences in the sensitivity of the measurement axes, zero-bias errors caused by internal residual magnetism and temperature changes during sensor use, and non-orthogonal errors caused by manufacturing limitations. Furthermore, misalignment issues exist between different sensors during sensor array installation, affecting the acquired signals and leading to inconsistencies. Therefore, correcting these errors is essential to improve the detection capability of fluxgate sensor arrays.

[0005] Most current calibration methods require additional auxiliary equipment, are complex to operate, and are costly. To improve the consistency of signals acquired by sensors in an array, this invention discloses a method for correcting linear misalignment errors in a three-axis fluxgate sensor array. Summary of the Invention

[0006] This invention discloses a method for correcting linear misalignment error in a three-axis fluxgate sensor array. The steps of this correction method are as follows:

[0007] Step 1: Assemble multiple triaxial fluxgate sensors into an array, and rotate each sensor around the center of the array to synchronously collect magnetic signal data at different angles. Let the signal collected by the i-th sensor be B. mi =[B mix B miy B miz ] T B mix B miy B miz These represent the signals collected by the i-th sensor in the X-axis, Y-axis, and Z-axis directions, respectively.

[0008] Step 2: According to Figure 2 An error correction model is established for a single sensor, and the magnetic signal measured by the i-th sensor is B.mi =K i C i B i +b i In the formula, i = 1, 2, ... are sensor numbers, where K i Let C represent the sensitivity inconsistency error matrix of the i-th sensor. i Let B represent the non-orthogonal error matrix of the i-th sensor. i b represents the ideal signal under error-free conditions of the i-th sensor. i K represents the zero-point offset error of the i-th sensor. i C i B i They are represented as follows:

[0009]

[0010] Then the ideal signal of the i-th sensor is B. i =(K i C i ) -1 (B mi -b i If we denote M i =K i C i A i =(M i -1 ) T M i -1 Multiplying both sides of the equation by its transpose on the left yields:

[0011]

[0012] Rewriting the above equation in the general form of an ellipsoidal surface, we get:

[0013]

[0014] In the formula, a, b, c, d, e, f, g, h, i, j are ellipsoidal parameters; the above formula is transformed into an optimization problem of finding the minimum sum of squared arithmetic distances, using the measurement values ​​B of the triaxial sensor at different angles from step 1. mi Solve for and obtain the ellipsoidal parameters a, b, c, d, e, f, g, h, i, j; then obtain the matrix A using the aforementioned ellipsoidal parameters. i and b i They are represented as follows:

[0015] b i =-A i -1 [ghi]T

[0016] From matrix A i Matrix M can be calculated i -1 M i -1 Represented as:

[0017] in

[0018] After obtaining the above parameters, the correction model can be obtained: B i =M i -1 (B mi -b i ); The magnetic signal B collected by the sensor mi Substituting into the above correction model, we obtain the error correction signal B for a single sensor. i ;

[0019] Step 3: Select a sensor as the reference sensor, denoted as sensor 1, according to... Figure 3 Establish a model for linear misalignment error; perform a matrix transformation on the ellipsoid fitted by signals from other sensors to make it coincide with the ellipsoid fitted by the reference sensor signal; the correction signal B1 of sensor 1 and the correction signal B2 of sensor 2 have the relationship B1 = PB2 + Q, where P and Q are respectively:

[0020]

[0021] Substituting the single-sensor calibration result obtained in step 2 into the above relational expression, we obtain the equations for matrices P and Q:

[0022] C1 -1 K1 -1 (B m1 -b1)=PC2 -1 K2 -1 (B m2 -b2)+Q

[0023] Solving the above equations, we can calculate the rotation matrix P and the offset matrix Q, thus obtaining the linear misalignment error correction model of sensor 2 relative to sensor 1: B cal_2 =PC2 -1 K2 -1 (B m2 -b2)+Q;

[0024] By repeating the above process, the linear misalignment error correction model for other sensors i relative to reference sensor 1 can be obtained:

[0025] Bcal_i =P i C i -1 K i -1 (B mi -b i )+Q i

[0026] Where P i Q i B represents the rotation matrix and offset matrix of the i-th sensor relative to sensor 1, respectively. cal_i This is the result after correcting the linear misalignment error of the i-th sensor relative to the reference sensor 1;

[0027] Step 4: Convert the signals B collected by the other sensors mi Substituting the linear misalignment error correction models obtained in step 3 relative to the reference sensor 1, we can obtain the results of linear misalignment error correction for each sensor with sensor 1 as the reference.

[0028] The advantages of this invention are:

[0029] 1. Compared with traditional correction methods, the present invention does not require the assistance of devices such as gyroscopes and GPS.

[0030] 2. This invention relies on the collected data for correction, making it easy to implement.

[0031] 3. This invention uses the ellipsoid fitting method to correct linear misalignment error, solves the inconsistency problem between signals collected by different sensors in the sensor array, and reduces the alignment requirements during sensor installation. Attached Figure Description

[0032] Figure 1 Flowchart of the calibration method;

[0033] Figure 2 A schematic diagram of the error correction model for a single sensor;

[0034] Figure 3 This is a schematic diagram of the error correction model between two sensors; Detailed Implementation

[0035] To make the technical solution of the present invention clearer, the present invention will be further described in detail below with reference to specific examples and the accompanying drawings. It should be noted that similar or identical parts are referred to by the same reference numerals in the drawings or description. Implementations not shown or described in the drawings are forms known to those skilled in the art.

[0036] This invention provides a method for calibrating a three-axis fluxgate sensor without the need for additional equipment. The implementation steps of this calibration method are as follows:

[0037] Step 1: Assemble multiple triaxial fluxgate sensors into an array, and rotate each sensor around the center of the array to synchronously collect magnetic signal data at different angles. Let the signal collected by the i-th sensor be B. mi =[B mix B miy B miz ] T B mix B miy B miz These represent the signals collected by the i-th sensor in the X-axis, Y-axis, and Z-axis directions, respectively.

[0038] Step 2: According to Figure 2 An error correction model is established for a single sensor, and the magnetic signal measured by the i-th sensor is B. mi =K i C i B i +b i In the formula, i = 1, 2, ... are sensor numbers, where K i Let C represent the sensitivity inconsistency error matrix of the i-th sensor. i Let B represent the non-orthogonal error matrix of the i-th sensor. i b represents the ideal signal under error-free conditions of the i-th sensor. i K represents the zero-point offset error of the i-th sensor. i C i B i They are represented as follows:

[0039]

[0040] Then the ideal signal of the i-th sensor is B. i =(K i C i ) -1 (B mi -b i If we denote M i =K i C i A i =(M i -1 ) T M i -1 Multiplying both sides of the equation by its own transpose on the left yields:

[0041]

[0042] Rewriting the above equation in the general form of an ellipsoidal surface, we get:

[0043]

[0044] In the formula, a, b, c, d, e, f, g, h, i, j are ellipsoidal parameters; the above formula is transformed into an optimization problem of finding the minimum sum of squared arithmetic distances, using the measurement values ​​B of the triaxial sensor at different angles from step 1. mi That is, to find the parameter p that minimizes the following expression:

[0045] D(p)=(Sp) T (Sp), where

[0046] p = [abc 2d 2e 2f 2g 2h 2i j] T ,

[0047]

[0048] The above equation is transformed into an equality constraint, and its minimum value is solved using the Lagrange method to obtain the ellipsoidal parameters a, b, c, d, e, f, g, h, i, j; then, matrix A is obtained using the aforementioned ellipsoidal parameters. i and b i :

[0049] b i =-A i -1 [ghi] T ;

[0050] And because of M i It can be represented in the following form:

[0051]

[0052] Then M i -1 It can be represented as:

[0053]

[0054] Since the angular deviation caused by non-orthogonal error is generally less than ±3°, m 11 ,m 22 ,m 33 Satisfy m 11 >0, m 22 >0, m 33 >0, It can be represented as

[0055]

[0056] Matrix M can be obtained from the above formula. i -1 ,in This leads to the correction model: B i =M i -1 (B mi -b i ); The magnetic signal B collected by the sensor mi Substituting into the above correction model, we obtain the error correction signal B for a single sensor. i ;

[0057] Step 3: Select a sensor as the reference sensor, denoted as sensor 1, and establish a model for the linear misalignment error; perform a matrix transformation on the ellipsoid fitted by the signals acquired by other sensors to make it coincide with the ellipsoid fitted by the reference sensor signal; the correction signal B1 of sensor 1 and the correction signal B2 of sensor 2 have the relationship B1 = PB2 + Q, where P and Q are respectively:

[0058]

[0059] Substituting the single-sensor calibration result obtained in step 2 into the above relation, we obtain the equation for matrices P and Q: C1 -1 K1 -1 (B m1 -b1)=PC2 -1 K2 -1 (B m2 Solve the above equations to calculate the rotation matrix P and the offset matrix Q, thus obtaining the linear misalignment error correction model of sensor 2 relative to sensor 1.

[0060] By repeating the above process, the linear misalignment error correction model for other sensors i relative to reference sensor 1 can be obtained:

[0061] B cal_i =P i C i -1 K i -1 (B mi -b i )+Q i

[0062] Where P i Q i B represents the rotation matrix and offset matrix of the i-th sensor relative to sensor 1, respectively. cal_i This is the result after correcting the linear misalignment error of the i-th sensor relative to the reference sensor 1;

[0063] Step 4: Convert the signals B collected by the other sensors mi Substituting the linear misalignment error correction models obtained in step 3 relative to the reference sensor 1, we can obtain the results of linear misalignment error correction for each sensor with sensor 1 as the reference.

[0064] The present embodiment has been described in detail above with reference to the accompanying drawings. Based on the above description, those skilled in the art should have a clear understanding of the method for correcting linear misalignment error of a three-axis fluxgate sensor array disclosed in this invention.

[0065] In summary, this invention performs error correction on signals acquired by a sensor array. Compared to traditional correction methods, this method does not require additional auxiliary equipment and can directly utilize the signals from the sensor array itself to complete the patterning work, thus reducing testing costs. Through correction, the consistency of signals from various sensors can be enhanced, noise in the differential and gradient signals of the sensor array can be reduced, and the signal-to-noise ratio can be improved.

[0066] The specific implementation examples described above further illustrate the purpose, technical solution, and beneficial effects of the present invention in detail. It should be noted that the above descriptions are merely specific implementation examples of the present invention and should not be used to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of correcting for linear misalignment errors of a triaxial fluxgate sensor array, characterized by, The implementation steps are as follows: Step 1: Multiple triaxial fluxgate sensors are arranged in an array, each sensor rotates around the center of the array, and the magnetic signal data at different angles are collected synchronously, and the signal collected by the i-th sensor is denoted as B mi = [B mix B miy B miz ] T , B mix , B miy , B miz , respectively, represent the signals collected by the i-th sensor in the X, Y, and Z directions. Step 2: Establish an error correction model for a single sensor. Let the magnetic signal measured by the i-th sensor be B. mi =K i C i B i +b i In the formula, i = 1, 2, ... are sensor numbers, and K i Let C represent the sensitivity inconsistency error matrix of the i-th sensor. i Let B represent the non-orthogonal error matrix of the i-th sensor. i b represents the ideal signal under error-free conditions of the i-th sensor. i Let B represent the zero-point offset error of the i-th sensor, then the ideal signal of the i-th sensor is B. i =(K i C i ) -1 (B mi -b i If we denote M i =K i C i A i =(M i -1 ) T M i -1 Multiplying both sides of the equation by its transpose on the left yields: The above formula is rewritten into the general form of an ellipsoid surface, that is: a(B mix ) 2 +b(B miy ) 2 +c(B miz ) 2 +2d(B mix B miy )+2e(B mix B miz ) + 2f(B miy B miz + 2g(B mix + 2h(B miy + 2i(B miz + j = 0 Wherein a, b, c, d, e, f, g, h, i, j are ellipsoid parameters; the above formula is converted into an optimization solving problem of minimum arithmetic distance square sum, and the measured values B of the three-axis sensor in step 1 at different angles are used mi , ellipsoid parameters a, b, c, d, e, f, g, h, i, j are solved and obtained; then the matrix A i and b i are obtained through the above ellipsoid parameters, so that the matrix M i is obtained -1 , and then a correction model: B i =M i -1 (B mi -b i ) is obtained; the magnetic signal B mi collected by the sensor is substituted into the above correction model, so that the error correction signal B i of the single sensor is obtained; Step 3: select one sensor as a reference sensor, denoted as sensor 1, and establish a model of linear misalignment error; make the ellipsoid fitted by signals of other sensors matrix transform so as to coincide with the ellipsoid fitted by signals of the reference sensor; there is a relationship of B1=PB2+Q between the correction signal B1 of the sensor 1 and the correction signal B2 of the sensor 2, and the correction result of the single sensor obtained in step 2 is substituted into the above relationship to obtain an equation about the matrix P and Q as follows: C1 -1 K1 -1 (B m1 -b1)=PC2 - 1 K2 -1 (B m2 -b2)+Q Solving the above equations, the rotation matrix P and the offset matrix Q are calculated, i.e. the linear misalignment error correction model of sensor 2 relative to sensor 1 is obtained: B cal_2 = PC2 -1 K2 -1 (B m2 -b2)+ Q The above process in this step is repeated to obtain the linear misalignment error correction model of other sensors i relative to sensor 1: B cal_i = P i C i -1 K i -1 (B mi -b i )+ Q i where P i , Q i represent the rotation matrix and offset matrix of the i-th sensor relative to sensor 1, respectively, and B cal_i is the result of the linear misalignment error correction of the i-th sensor relative to sensor 1. Step 4: Signal B collected by other individual sensors mi By substituting the linear misalignment error correction model of each individual sensor relative to sensor 1 obtained in Step 3, the result of linear misalignment error correction of each individual sensor with sensor 1 as the reference can be obtained.

2. The method of claim 1, wherein, The sensitivity inconsistency error matrix K in step 2 i , the quadrature error matrix C i , the zero offset error matrix b i are respectively: The parameter matrix A in step 2 i is: According to the general form of the ellipsoid surface formula, the zero point offset error matrix b i may also be expressed as: b i = -A i -1 [g h i] T The computed matrix M i -1 is: wherein 3. The method of claim 1, wherein, The matrices P, Q described in step 3 are respectively: B m1 , B m2 The specific values of B m1 , B m2 are substituted into the following equation: M1 -1 (B m1 -b1) = PM2 -1 (B m2 -b2) + Q Then, the specific values of the matrices P and Q are obtained according to the above equation.

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