Iterative linear calibration method of strapdown triaxial cross magnetic array measurement model, program, equipment and storage medium

Abstract

According to the method, a polar decomposition technology is adopted, a measurement matrix of each strapdown triaxial magnetometer is decomposed into a unit orthogonal matrix and a symmetric positive definite matrix, and an ellipsoid equation is adopted for iterative linear least square fitting to obtain equivalent zero offset and the symmetric positive definite matrix of each strapdown triaxial magnetometer; and introducing a virtual coordinate system, calculating a measured data correction value of each strapdown three-axis magnetometer by using orthogonal Prusk decomposition, and further calculating a correction value of a magnetic gradient tensor measured by the strapdown three-axis cross-shaped magnetic array, thereby completing calibration of the strapdown three-axis cross-shaped magnetic array. According to the method, the iterative linear least squares method is adopted, the ellipsoid equation can be solved with high precision, the calibration precision is remarkably improved, the direction of the rotating shaft does not need to be kept stable in the rotating process, and the iterative linear least squares algorithm and the orthogonal Prushing analysis algorithm are small in calculated amount and easy to achieve in engineering. Under the condition that the geomagnetic field model and the magnetic array attitude are provided, calibration can be completed quickly, simply and conveniently, and the method is suitable for practical engineering application.

Description

Technical Field

[0001] The present invention belongs to the technical field of calibration and error correction of magnetic field measurement systems, and in particular relates to an iterative linear calibration method, program, device and storage medium for a strapdown three-axis cross magnetic array measurement model. Background Art

[0002] As a passive detection method, magnetic anomaly detection offers the advantages of speed, low cost, and minimal impact from hydrological and meteorological factors. It is widely used in fields such as UXO detection and mineral resource exploration. Magnetic anomaly detection methods based on magnetic field vectors and their spatial gradients can provide more information about magnetic anomalies, significantly improving detection accuracy and recognition rate. Compared to other three-axis magnetometer array configurations, three-axis cross-magnetic arrays have the lowest theoretical error in measuring magnetic field spatial gradients. To enable rapid magnetic anomaly detection, three-axis cross-magnetic arrays are typically fixed on a carrier such as an aircraft, forming a strapdown three-axis cross-magnetic array. Manufacturing limitations can lead to zero bias, scale factor errors, three-axis orthogonality errors, and alignment errors between different three-axis magnetometers. Furthermore, ferromagnetic materials and electronic devices on the carrier generate interfering magnetic fields, including hard and soft iron fields. Therefore, calibration and error correction of the strapdown three-axis cross-magnetic array are necessary to meet the high-precision measurement requirements of magnetic field vectors and their spatial gradients required for UXO detection.

[0003] Typically, the calibration of a strapdown three-axis cross-magnetic array can be decomposed into single sensor calibration and alignment error calibration. Common methods for solving the measurement model parameters of a strapdown three-axis magnetometer include platform background magnetic interference modeling and solution based on the Tolles-Lawson equation, ellipsoid constraint solution, etc. The Tolles-Lawson equation cannot be applied to all complex magnetic interference measurement environments (Zhang Ning, Zhao Jianyang, Lin Chunsheng, Jia Wendou. Small signal model solution and compensation of helicopter platform background magnetic interference [J]. Journal of Electronics, 2017, 45(1): 83-88). Allen conducted research on magnetic interference compensation for full-tensor magnetic gradiometer systems for underwater unmanned vehicles. This approach converts the magnetic field measured by a reference magnetometer into a current and applies it to a three-dimensional Helmholtz coil outside the other sensors, thereby eliminating the carrier's magnetic interference (Allen GI, Sulzber G, Bono JT, et al. Initial evaluation of the new real-time tracking gradiometer designed for small unmanned underwater vehicles [C]. Proceedings of OCEANS 2005 MTS / IEEE, 2005: 32-40). However, this method requires auxiliary equipment such as magnets, three-dimensional Helmholtz coils, slope film alloys, and conductive plates, making the process complex and costly. Ellipsoid constraint solving is essentially a nonlinear least-squares fitting method. The intelligent optimization algorithm used is sensitive to initial values, making parameter adjustment complex, and the convergence value may be inconsistent, affecting the solution accuracy (Tang Limin. Research on the ill-posedness and algorithm of nonlinear least-squares [D]. Doctoral dissertation, Central South University, 2011). In addition, the ellipsoid constraint solving method is usually difficult to calibrate all the parameters of the strapdown three-axis magnetometer measurement model.

[0004] The main methods for calibrating alignment errors are: 1) Optical correction method, which uses a regular hexahedral optical prism and an orthogonal optical system for correction (Lassahn MP, Trenkler G. Vectorial calibration of 3D magnetic fieldsensor arrays [J]. IEEE transactions on instrumentation and measurement, 1995, 44 (2): 360-362). This method requires very high accuracy of the initial coordinate system of the optical system and the optical prism; 2) Rotational alignment method, which uses the constant magnetic field in the direction of the rotation axis of the non-magnetic turntable to model and solve the alignment error. This method requires high accuracy and placement of the non-magnetic turntable; 3) Geomagnetic reference method, which obtains heading information and refers to local geomagnetic data to calibrate the alignment error (Wu Yongliang, Wang Tianmiao, Liang Jianhong. Field error correction method for three-axis magnetometer of micro-UAV [J]. Acta Aeronautica Sinica, 2011, 32 (2): 330-336). However, this method is also difficult to operate. In summary, most calibration methods use a large amount of measurement data under different postures to estimate error parameters through nonlinear fitting, and often use three-dimensional Helmholtz coils to obtain vector references, which is costly and not conducive to engineering implementation. Summary of the Invention

[0005] The object of the present invention is to provide an iterative linear calibration method, program, device and storage medium for a strapdown three-axis cross magnetic array measurement model.

[0006] An iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model comprises the following steps:

[0007] In the calibration area, a high-precision scalar magnetometer is used to obtain the geomagnetic field modulus of the calibration area;

[0008] Mounting a strapdown three-axis cross magnetic array on a three-axis turntable, adjusting the turntable to a horizontal level, and aligning a measuring axis of the strapdown three-axis cross magnetic array with a rotation axis of the turntable; the strapdown three-axis cross magnetic array includes four sets of strapdown three-axis magnetometers;

[0009] The strapdown three-axis cross magnetic array is rotated around the three axes of the three-axis turntable in sequence, and the measurement values ​​of the geomagnetic field by the strapdown three-axis cross magnetic array are recorded at certain angles to obtain a geomagnetic field measurement data sequence;

[0010] The polar decomposition technique is used to decompose the measurement matrix of each strapdown three-axis magnetometer into a unit orthogonal matrix and a symmetric positive definite matrix. The ellipsoidal equation is used to iteratively fit the linear least squares to obtain the equivalent zero bias and symmetric positive definite matrix of each strapdown three-axis magnetometer.

[0011] A virtual coordinate system is introduced, and the orthogonal Prouck decomposition is used to calculate the correction value of the measurement data of each strapdown three-axis magnetometer. Then, the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array is calculated to complete the calibration of the strapdown three-axis cross magnetic array.

[0012] Furthermore, in the calibration area, a high-precision scalar magnetometer is used to obtain the geomagnetic field modulus of the calibration area. The strapdown three-axis cross magnetic array is rotated around the x-axis, y-axis, and z-axis of the three-axis turntable in sequence, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at each angle. The measurement values ​​of the geomagnetic field by the strapdown three-axis cross magnetic array are recorded at certain angles to obtain the geomagnetic field measurement data sequence.

[0013] Furthermore, according to the geomagnetic field measurement data sequence Construct the measurement matrix K of each strapdown three-axis magnetometer k ;

[0014]

[0015] Furthermore, the iterative linear least squares fitting using the ellipsoidal surface equation is specifically as follows:

[0016] Step 1: Set the convergence threshold ε k , initialize the number of iterations t = 0, initialize the linear least squares solution

[0017]

[0018] Among them, u k (t)=[a k (t)b k (t)c k (t)d k (t)e k (t)f k (t)p k (t)q k (t)r k (t)] T ; [α] N×1 represents an N×1 column vector whose elements are all α;

[0019] Step 2: Calculate the equivalent zero bias of each strapdown three-axis magnetometer

[0020]

[0021] Step 3: Update the linear least squares solution

[0022]

[0023] Step 4: If Then let t=t+1 and return to step 2;

[0024] Otherwise, stop the iteration according to Perform step 2 once to obtain the equivalent zero bias of each strapdown three-axis magnetometer and matrix A k (t+1), let That is the equivalent zero bias of each strapdown three-axis magnetometer.

[0025] Furthermore, the symmetric positive definite matrix of the strapdown three-axis magnetometer is The calculation method is:

[0026] make The matrix A′ k Diagonalize to get the orthogonal matrix C k , using the matrix A′ k The eigenvalue matrix of Compute positive definite matrices

[0027]

[0028] Among them, τ k1 ,τ k2 ,…,τ kn is the matrix A′ k The eigenvalue of .

[0029] Furthermore, the virtual coordinate system is introduced and the correction value of the measurement data of each strapdown three-axis magnetometer is calculated using orthogonal Prouck decomposition, specifically:

[0030] Introduce a set of virtual coordinate systems a k , construct virtual measurement data

[0031]

[0032] make The matrix Perform singular value decomposition to obtain the matrix The left singular matrix and right singular matrices

[0033]

[0034] in, is a matrix The diagonal matrix of the singular values ​​of ;

[0035] Calculate the correction value of the measurement data of each strapdown three-axis magnetometer

[0036]

[0037] in,

[0038] Furthermore, the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array The calculation method is:

[0039]

[0040] Among them, L x L is the array baseline length of the strapdown three-axis cross magnetic array in the x direction, y is the array baseline length of the strapdown three-axis cross magnetic array in the y direction.

[0041] A computer device / equipment / system includes a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the iterative linear calibration method of the strapdown three-axis cross magnetic array measurement model.

[0042] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the iterative linear calibration method for the strapdown three-axis cross magnetic array measurement model.

[0043] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the iterative linear calibration method for the strapdown three-axis cross magnetic array measurement model.

[0044] The beneficial effects of the present invention are:

[0045] The present invention achieves high-precision calibration of a strapdown three-axis cross-magnetic array by introducing polar decomposition and a virtual coordinate system and employing an iterative linear least-squares fitting method for an ellipsoid. The present invention employs an iterative linear least-squares method to solve the ellipsoid equation with high precision, significantly improving calibration accuracy. The present invention is simple to operate and does not require maintaining the direction of the rotation axis stable during rotation, simplifying the operational process. The iterative linear least-squares algorithm and orthogonal Prucker analysis algorithm require minimal computational effort and are easily implemented in engineering applications. Given a geomagnetic field model and the magnetic array's attitude, the present invention can quickly and easily complete calibration, making it suitable for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a diagram of the magnetic sensor configuration of a strapdown three-axis cross magnetic array.

[0047] Figure 2 This is a block diagram of the measurement of the Earth's magnetic field using a strapdown three-axis cross magnetic array and its error correction.

[0048] Figure 3 It is the overall flow chart of the present invention.

[0049] Figure 4 3 is a graph showing the relationship between the relative error of the measurement model parameters and the standard deviation of the geomagnetic model error in an embodiment of the present invention.

[0050] Figure 5 3 is a graph showing the relationship between the absolute error of the geomagnetic gradient tensor and the standard deviation of the geomagnetic model error in an embodiment of the present invention.

[0051] Figure 6 3 is a graph showing the relationship between the relative error of the measurement model parameters and the standard deviation of the magnetic measurement noise in an embodiment of the present invention.

[0052] Figure 7 3 is a graph showing the relationship between the absolute error of the geomagnetic gradient tensor and the standard deviation of the magnetic measurement noise in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be further described below with reference to the accompanying drawings.

[0054] The present invention includes alignment errors within a strapdown three-axis magnetometer measurement model, performs polar decomposition on the square matrix in each strapdown three-axis magnetometer measurement model, and obtains a unit orthogonal matrix and a symmetric positive definite matrix. An iterative linear least squares algorithm is used to achieve high-precision solution of the ellipsoidal surface equation, and the solution of the linearized equation group is used as the initial point for solving the nonlinear equation group to calculate the symmetric positive definite matrix. A set of virtual coordinate systems is then introduced, and the unit orthogonal matrix is ​​solved using the orthogonal Prucker decomposition based on the posture of the strapdown three-axis cross magnetic array. The advantages of the present invention are that the iterative linear least squares method is used to solve the ellipsoidal surface equation with high precision, and there is no need to maintain the rotation axis direction stable during the rotation of the strapdown three-axis cross magnetic array. High-precision calibration can be performed under the condition of providing the geomagnetic field model and the magnetic array posture, and the operation is simple. The iterative linear least squares algorithm and the orthogonal Prucker analysis algorithm are relatively simple, have a small amount of calculation, and are easy to implement in engineering.

[0055] Due to manufacturing process limitations, the three-axis magnetometer itself has zero bias, scale factor error, and three-axis orthogonality error. There is also alignment error between the three-axis magnetometer and the carrier. These errors are collectively referred to as the inherent errors of the three-axis magnetometer array. In addition, ferromagnetic materials and electronic devices on the carrier generate interfering magnetic fields such as hard iron fields and soft iron fields, as well as magnetic measurement noise, further affecting measurement accuracy.

[0056] Considering the two types of errors, the intrinsic error of the three-axis cross magnetic array and the interference magnetic field, the measurement model of the strapdown three-axis cross magnetic array is established in the carrier coordinate system as follows:

[0057]

[0058] Where, is the reference magnetic field of the kth strapdown triaxial magnetometer The measured output, is the Earth's magnetic field or other constant external magnetic field, D k 、 and are the measurement matrix, equivalent zero bias and magnetic measurement noise of the kth strapdown three-axis magnetometer, is the direction cosine matrix from the reference coordinate system r to the carrier coordinate system b.

[0059] From formula (1), we can get the expression of the reference magnetic field in the carrier coordinate system as follows:

[0060]

[0061] Where:

[0062]

[0063] Formula (2) is also the error correction formula of the kth strapdown three-axis magnetometer.

[0064] The real symmetric reversible matrix Ω k Uniquely decomposed into a 3rd order real unit orthogonal matrix Q k and the 3rd order real positive definite matrix S k ,Right now:

[0065] Ω k =Q k S k (4)

[0066] Substituting formula (4) into formula (2) yields:

[0067]

[0068] Where:

[0069]

[0070] Then order:

[0071]

[0072] Then formula (5) can be written as:

[0073]

[0074] The influence of noise on calibration accuracy can be analyzed theoretically. For N measurement values, ignoring noise, we can obtain the following equation (11):

[0075] K k u k (t) = (1-χ 2k (t)) N ,k=1,2,…,N (12)

[0076] Where:

[0077] χ 2k (t) = (X 0k (t)) T A k (t)X 0k (t) (13)

[0078]

[0079] u k (t)=[a k (t) b k (t) c k (t) d k (t) e k (t) f k (t) p k (t) q k (t) r k (t)] T (15)

[0080] The magnetic field used for calibration is usually larger than the equivalent zero bias, hard iron magnetic field and soft iron magnetic field. Therefore, the magnetic field data can be considered as X after standardization. 0k All elements in are less than 1.

[0081] Let the number of iterations t = 0, and set χ 2k Substituting (t)=0 into equation (12) yields the linear least squares solution:

[0082]

[0083] Substituting equation (16) into equations (6) and (8), we get A k (t) and

[0084] Calculate χ according to formula (13) 2k (t), and then substitute it into formula (12) to obtain Update the approximate least squares solution. Repeat this process until ε k is a given small positive number.

[0085] The above iterative calculation Substitute into formula (6) and formula (8) respectively to obtain A k and

[0086] Calculated using the geomagnetic field model By A k The value of According to the properties of the ellipsoid equation, A k ′ is a real symmetric positive definite matrix, so we get:

[0087]

[0088] Where C k Diagonalization A k ′The obtained orthogonal matrix, τ k1 ,τ k2 ,…,τ kn A k The eigenvalues ​​of ′ are all positive.

[0089] Ignoring magnetic measurement noise, a set of virtual coordinate systems a is introduced k , such that:

[0090]

[0091] According to the attitude of the strapdown three-axis cross magnetic array, combined with the geomagnetic field model, it is calculated use and calculate right Perform singular value decomposition to obtain:

[0092]

[0093] Then we get the virtual coordinate system a k Transform to carrier coordinate system b k The unit orthogonal matrix, Q k The values ​​are:

[0094]

[0095] Substituting equations (17) and (20) into equation (4), we can obtain Ω k , and then according to formula (3) we get the measurement matrix D k .

[0096] The position and attitude of the strapdown three-axis cross magnetic array required for the calculation of the geomagnetic field model can be obtained from the output results of the strapdown inertial navigation system or the position and attitude measurement system.

[0097] Based on the above theoretical derivation, an iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model in the present invention includes the following steps:

[0098] Step 1: In the calibration area, use a high-precision scalar magnetometer to obtain the geomagnetic field modulus of the calibration area Mount the strapdown three-axis cross magnetic array on the table of the three-axis turntable, adjust the table of the three-axis turntable to a horizontal level, and align the measurement axis of the strapdown three-axis cross magnetic array with the rotation axis of the turntable to obtain the array baseline length L of the strapdown three-axis cross magnetic array in the x direction. x The array baseline length L in the y direction y ; The strapdown three-axis cross magnetic array includes four sets of strapdown three-axis magnetometers;

[0099] Step 2: Rotate the strapdown three-axis cross magnetic array 360° around the turntable's x-axis, y-axis, and z-axis in sequence, and record the measurement value of the geomagnetic field at each angle. Get the geomagnetic field measurement data sequence

[0100] Step 3: Set a small positive number ε k , initialize the number of iterations t = 0, initialize the linear least squares solution

[0101]

[0102] in, u k (t)=[a k (t)b k (t)c k (t)d k (t)e k (t)f k (t)p k (t)q k (t)r k (t)] T ; [α] N×1 represents an N×1 column vector whose elements are all α;

[0103] Step 4: Calculate the equivalent zero bias of each strapdown three-axis magnetometer

[0104]

[0105] Step 5: Update the linear least squares solution

[0106]

[0107] Step 6: If Then let t=t+1 and return to step 4;

[0108] Otherwise, stop the iteration according to Perform step 4 once to obtain the equivalent zero bias of each strapdown three-axis magnetometer and matrix A k (t+1), let

[0109] Step 7: Make The matrix A′ k Diagonalize to get the orthogonal matrix C k , using the matrix A′ k The eigenvalue matrix of Compute positive definite matrices

[0110]

[0111] Among them, τ k1 ,τ k2 ,…,τ kn is the matrix A′ k The eigenvalues ​​of are all positive;

[0112] Step 8: Introduce a set of virtual coordinate systems a k , construct virtual measurement data

[0113]

[0114] Step 9: Make The matrix Perform singular value decomposition to obtain the matrix The left singular matrix and right singular matrices

[0115]

[0116] in, is a matrix The diagonal matrix of the singular values ​​of ;

[0117] Step 10: Calculate the correction value of the measurement data of each strapdown three-axis magnetometer

[0118]

[0119] in,

[0120] Step 11: Calculate the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array Completed the calibration of the strapdown three-axis cross magnetic array;

[0121]

[0122] Example 1:

[0123] The present invention provides an iterative linear calibration method for strapdown three-axis cross-magnetic array model parameters. By performing polar decomposition on the measurement matrix of each strapdown three-axis cross-magnetic array, introducing a virtual coordinate system, and employing an ellipsoidal iterative linear least squares fitting method, high-precision calibration of the zero bias and the measurement matrix is ​​achieved. The method has the advantages of using an iterative linear least squares method to solve the ellipsoidal equation with high precision, eliminating the need to maintain a stable rotation axis during rotation of the strapdown three-axis cross-magnetic array. The method can be easily, quickly, and accurately calibrated provided the geomagnetic field model and the magnetic array's attitude are provided, making it suitable for practical engineering applications. Furthermore, the iterative linear least squares and orthogonal Prucker analysis algorithms are relatively simple, computationally inefficient, and easy to implement.

[0124] The block diagram of the measurement error correction process of the geomagnetic field and geomagnetic gradient tensor by the strapdown three-axis cross magnetic array is as follows: Figure 2 As shown, the geomagnetic field measured by the kth strapdown triaxial magnetometer is The correction value of the geomagnetic field measurement data in the carrier coordinate system is

[0125] Calibration measurement matrix D k The relative error ε Dk Defined as:

[0126]

[0127] Where, is the measurement matrix D k The estimated value of ||·|| F Represents the Frobenius norm of the matrix.

[0128] Calibration of equivalent zero bias The relative error ε B0k Defined as:

[0129]

[0130] Where, is the equivalent bias The estimated value of , ||·|| represents the 2-norm of the vector.

[0131] by and They represent the measured value and the corrected value of the geomagnetic gradient tensor respectively, and define the geomagnetic gradient tensor of the strapdown three-axis cross magnetic array before and after error correction. The absolute measurement errors are:

[0132]

[0133] Assume that at the calibration point, the x, y and z components of the geomagnetic field are and Array baseline length L x and L y The measurement matrices of the four strapdown three-axis magnetometers are: and The equivalent zero biases are: and The unit is μT. The effectiveness and accuracy of the present invention are verified through simulation experiments.

[0134] The strapdown three-axis cross magnetic array rotates uniformly around the three axes of the carrier and performs data sampling. The number of sampling points in each rotation direction is 180. The magnetic measurement noise of each axis is zero-mean and independent Gaussian white noise. Through 50 Monte Carlo simulations, under the given conditions of the standard deviation of the magnetic measurement noise, the relationship curve between the relative error of the strapdown three-axis cross magnetic array measurement model and the standard deviation of the geomagnetic model error is obtained as shown in the figure below. Figure 4 As shown, Figure 4 (a) is the curve showing the change of relative error of the measurement matrix of four strapdown three-axis magnetometers (A, B, C, D). Figure 4 (b) is the variation curve of the relative error of the equivalent zero bias of the four strapdown three-axis magnetometers. Figure 4 It can be seen that the method proposed in the present invention can accurately and completely calibrate the measurement model parameters of the strapdown three-axis magnetic array. Within the standard deviation range of the geomagnetic model error in the figure, its relative error increases with the increase of the standard deviation of the geomagnetic model error.

[0135] When the standard deviation of the magnetic noise of the strapdown three-axis magnetometer σ VM When the value is 10nT, the absolute error of the geomagnetic gradient tensor measured by the strapdown three-axis cross magnetic array before and after calibration is as follows: Figure 5 (a) and Figure 5 As shown in (b), by comparison, it is found that the calibration method of the present invention can greatly improve the accuracy of measuring the geomagnetic gradient tensor by the strapdown three-axis magnetic array.

[0136] When the standard deviation of the geomagnetic model error is 5nT, the relationship curve between the relative error of the strapdown three-axis cross magnetic array measurement model and the standard deviation of the magnetic measurement noise is obtained by 50 Monte Carlo simulations. Figure 6 As shown, Figure 6 (a) is the curve showing the change of relative error of the measurement matrix of four strapdown three-axis magnetometers (A, B, C, D). Figure 6(b) is the variation curve of the relative error of the equivalent zero bias of the four strapdown three-axis magnetometers. Figure 6 It can be seen that the method proposed in the present invention can accurately and completely calibrate the measurement model parameters of the strapdown three-axis magnetic array. Within the range of the magnetic measurement noise standard deviation shown in the figure, its relative error increases with the increase of the magnetic measurement noise standard deviation. The relationship between the absolute error of the geomagnetic gradient tensor measured by the strapdown three-axis cross magnetic array before and after calibration and the magnetic measurement noise standard deviation is shown in the figure. Figure 6 (a) and Figure 6 As shown in (b), by comparison, it is found that the calibration method of the present invention can greatly improve the accuracy of measuring the geomagnetic gradient tensor by the strapdown three-axis magnetic array.

[0137] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. An iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model, characterized by: In the calibration area, a high-precision scalar magnetometer is used to obtain the geomagnetic field modulus of the calibration area; Mounting a strapdown three-axis cross magnetic array on a three-axis turntable, adjusting the turntable to a horizontal level, and aligning a measurement axis of the strapdown three-axis cross magnetic array with a rotation axis of the turntable; the strapdown three-axis cross magnetic array includes four sets of strapdown three-axis magnetometers; The strapdown three-axis cross magnetic array is rotated around the three axes of the three-axis turntable in sequence, and the measurement values ​​of the geomagnetic field by the strapdown three-axis cross magnetic array are recorded at certain angles to obtain a geomagnetic field measurement data sequence; The polar decomposition technique is used to decompose the measurement matrix of each strapdown three-axis magnetometer into a unit orthogonal matrix and a symmetric positive definite matrix. The ellipsoidal equation is used to iteratively fit the linear least squares to obtain the equivalent zero bias and symmetric positive definite matrix of each strapdown three-axis magnetometer. A virtual coordinate system is introduced, and the orthogonal Prouck decomposition is used to calculate the correction value of the measurement data of each strapdown three-axis magnetometer. Then, the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array is calculated to complete the calibration of the strapdown three-axis cross magnetic array.

2. The iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model according to claim 1, characterized in that: In the calibration area, a high-precision scalar magnetometer is used to obtain the geomagnetic field modulus of the calibration area. The strapdown three-axis cross magnetic array is rotated around the x-axis, y-axis, and z-axis of the three-axis turntable in sequence, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at each angle. The measurement values ​​of the geomagnetic field by the strapdown three-axis cross magnetic array are recorded at certain angles to obtain the geomagnetic field measurement data sequence.

3. The iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model according to claim 2, characterized in that: According to the geomagnetic field measurement data series Construct the measurement matrix K of each strapdown three-axis magnetometer k ; 4. The iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model according to claim 3, characterized in that: The iterative linear least squares fitting using the ellipsoid equation is specifically as follows: Step 1: Set the convergence threshold ε k , initialize the number of iterations t = 0, initialize the linear least squares solution Among them, u k (t)=[a k (t)b k (t)c k (t)d k (t)e k (t)f k (t)p k (t)q k (t)r k (t)] T ; [α] N×1 represents an N×1 column vector whose elements are all α; Step 2: Calculate the equivalent zero bias of each strapdown three-axis magnetometer Step 3: Update the linear least squares solution Step 4: If Then let t=t+1 and return to step 2; Otherwise, stop the iteration according to Perform step 2 once to obtain the equivalent zero bias of each strapdown three-axis magnetometer and matrix A k (t+1), let That is the equivalent zero bias of each strapdown three-axis magnetometer.

5. The iterative linear calibration method of a strapdown three-axis cross magnetic array measurement model according to claim 4, characterized in that: The symmetric positive definite matrix of the strapdown three-axis magnetometer The calculation method is: make The matrix A′ k Diagonalize to get the orthogonal matrix C k , using the matrix A′ k The eigenvalue matrix of Compute positive definite matrices Among them, τ k1 ,τ k2 ,…,τ kn is the matrix A′ k The eigenvalue of .

6. The iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model according to claim 5, characterized in that: The virtual coordinate system is introduced and the orthogonal Prouck decomposition is used to calculate the measurement data correction value of each strapdown three-axis magnetometer, specifically: Introduce a set of virtual coordinate systems a k , construct virtual measurement data make The matrix Perform singular value decomposition to obtain the matrix The left singular matrix and right singular matrices in, is a matrix The diagonal matrix of the singular values ​​of ; Calculate the correction value of the measurement data of each strapdown three-axis magnetometer in, 7. The iterative linear calibration method for a strapdown three-axis cross magnetic array measurement model according to claim 6, characterized in that: Correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array The calculation method is: Among them, L x L is the array baseline length of the strapdown three-axis cross magnetic array in the x direction, y is the array baseline length of the strapdown three-axis cross magnetic array in the y direction.

8. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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