Iterative linear least square calibration method of strapdown triaxial cross magnetic array for measuring horizontal modulus gradient of magnetic field, program, equipment and storage medium

Abstract

The method comprises the following steps of: decomposing a measurement matrix of each strapdown triaxial magnetometer into a unit orthogonal matrix and a symmetric positive definite matrix by utilizing the characteristic that a magnetic field modulus is independent of the unit orthogonal matrix and adopting a polar decomposition technology, and obtaining an equivalent zero offset and the symmetric positive definite matrix of each strapdown triaxial magnetometer by adopting ellipsoid equation iteration linear least square fitting; a virtual coordinate system is introduced, a vector modulus value correction value of measurement data of each strapdown triaxial magnetometer is calculated, a correction value of a magnetic field horizontal modulus gradient is further obtained, and calibration of the strapdown triaxial cross magnetic array is completed. According to the method, the ellipsoid equation is solved with high precision by adopting the iterative linear least square method, the strapdown three-axis cross magnetic array does not need to be accurately rotated, high-precision calibration can be carried out under the condition of providing the geomagnetic field modulus, and the operation is simple and convenient; the iterative linear least square algorithm is simple, the calculation amount is small, and engineering implementation is easy.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetic field measurement system calibration, and in particular relates to an iterative linear least squares calibration method, program, device and storage medium for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field. 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, making it the current mainstream approach for UXO detection. Because the gradient measurement of the magnetic anomaly modulus is unaffected by diurnal variations in the magnetic field, it improves magnetic survey accuracy and provides more information in different directions, enhancing the resolution and interpretation of magnetic anomalies. This effectively increases the scale, thereby expanding the exploration range and reducing costs. Compared to high-precision scalar magnetometers such as optically pumped magnetometers, high-precision vector magnetometers such as three-axis fluxgates offer advantages in size, weight, and price. Therefore, the use of a three-axis cross magnetic array to measure the horizontal gradient of the magnetic anomaly modulus is suitable. To enable rapid magnetic anomaly detection, a three-axis cross magnetic array is typically fixed on a carrier such as an aircraft, forming a strapdown three-axis cross magnetic array. Manufacturing limitations can lead to errors in the three-axis magnetometer's zero bias, scale factor, orthogonality, and alignment 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, it is necessary to calibrate and correct the errors of the strapdown three-axis cross magnetic array to meet the requirements of UXO detection for high-precision measurement of the magnetic field modulus gradient.

[0003] Generally speaking, the calibration of a strapdown three-axis cross magnetic array can be decomposed into the calibration of a single three-axis magnetometer and the calibration of the alignment error. Common methods for solving the measurement model parameters of a strapdown three-axis magnetometer include the platform background magnetic interference modeling and solution based on the Tolles-Lawson equation, the TWO-STEP method, the estimation algorithm based on the ellipsoid constraint, and various intelligent optimization algorithms. The platform background magnetic interference compensation algorithm based on the Tolles-Lawson equation uses eight-heading learning flight data to solve the model parameters. It is only suitable for weak interference compensation and has a poor effect on strong interference compensation (Zhang Ning, Zhao Jianyang, Lin Chunsheng, Jia Wendou. Solution and compensation of small signal model of helicopter platform background magnetic interference [J]. Journal of Electronics, 2017, 45(1): 83-88). The least squares estimation results of the TWO-STEP method are sensitive to noise and gross errors, and the pathological state of the system often causes the solution to be unstable. The intelligent optimization algorithm is sensitive to the initial value, the parameter adjustment is relatively complex, and the convergence value may be inconsistent each time. The least squares fitting results used in the ellipsoid constraint solving method are sensitive to the initial point, and inaccurate initial points affect the solution accuracy (Tang Limin. Research on the ill-posedness and algorithm of nonlinear least squares [D]. Doctoral dissertation of Central South University, 2011).

[0004] In order to solve the three-axis orthogonality error, scale factor error, zero bias and alignment error between sensors, Li Qingzhu et al. proposed a two-step linear correction method without mathematical simplification (Li Qingzhu, Li Zhining, Zhang Yingtang, et al. Two-step linear correction of planar cross magnetic gradient tensor system [J]. Chinese Journal of Scientific Instrument, 2017, 38(9): 2232-2242). In the face of the three-axis fluxgate magnetometer cross array, Chi Cheng et al. used the total least squares method to estimate the three-axis orthogonality error, scale factor error, zero bias and alignment error between sensors. Although the total least squares method is better than the traditional least squares method, the calculation process is also more complicated (Cheng Chi, Dan Wang, Ronghua Tao, et al. Error calibration of cross magnetic gradient tensor system with total least-squares method [J]. Mathematical Problems in Engineering, 2023, 2023: 6974834). Hongfeng Pang et al. established a nonlinear integrated calibration model for a three-axis cross magnetic array and used magnetic field vectors for calibration (Hongfeng Pang, Mengchun Pan, Chengbiao Wan, et al. Integrated compensation of magnetometer array magnetic distortion field and improvement of magnetic object localization [J]. IEEE Transactions on Geoscience and Remote Sensing, 2014, 52(9): 5670-5676). However, this method requires the use of a complex magnetic field generator to generate an accurate magnetic vector field as a calibration reference. Furthermore, these calibration methods only correct for instrument errors and alignment errors in a three-axis magnetometer array and do not consider the influence of interfering magnetic fields. Combining the influence of hard iron magnetic field and soft iron magnetic field, Zhang Guang et al. established a carrier magnetic gradient tensor compensation model and proposed a carrier-integrated linear compensation method for the magnetic gradient tensor system (Zhang Guang, Zhang Yingtang, Yin Gang, et al. A magnetic tensor compensation method for the carrier of a magnetic tensor detection system [J]. Chinese Journal of Geophysics, 2016, 59(1): 311-317). However, its error model ignores high-order small quantities above the second order. Summary of the Invention

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

[0006] An iterative linear least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field 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 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;

[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 method to obtain the equivalent zero bias and symmetric positive definite matrix of each strapdown three-axis magnetometer. A virtual coordinate system is introduced to calculate the vector modulus correction value of the measurement data of each strapdown three-axis magnetometer, and then the correction value of the horizontal modulus gradient of the magnetic field is obtained to complete the calibration of the strapdown three-axis cross magnetic array.

[0011] 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.

[0012] Furthermore, according to the geomagnetic field measurement data sequence Construct the measurement matrix K of each strapdown three-axis magnetometer k ;

[0013]

[0014] Furthermore, the iterative linear least squares fitting using the ellipsoidal surface equation is specifically as follows:

[0015] Step 1: Set the convergence threshold ε k , initialize the number of iterations t = 0, initialize the linear least squares solution

[0016]

[0017] 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;

[0018] Step 2: Calculate the equivalent zero bias of each strapdown three-axis magnetometer

[0019]

[0020] Step 3: Update the linear least squares solution

[0021]

[0022] Step 4: If Then let t=t+1 and return to step 2;

[0023] 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.

[0024] Furthermore, the symmetric positive definite matrix of the strapdown three-axis magnetometer is The calculation method is:

[0025] 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

[0026]

[0027] Among them, τ k1 ,τ k2 ,…,τ kn is the matrix A′ k The eigenvalue of .

[0028] Furthermore, the introduction of the virtual coordinate system a k , calculate the measurement data of each strapdown three-axis magnetometer Vector modulus correction value Specifically:

[0029]

[0030] Furthermore, the correction value of the horizontal modulus gradient of the magnetic field and The calculation method is:

[0031]

[0032] 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.

[0033] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the iterative linear least squares calibration method of the strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of the magnetic field.

[0034] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the iterative linear least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field.

[0035] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the iterative linear least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field.

[0036] The beneficial effects of the present invention are:

[0037] The present invention introduces a set of virtual coordinate systems, performs polar decomposition on the measurement matrix of each strapdown three-axis cross-magnetic array, and calibrates it using an iterative linear least squares fitting algorithm for the ellipsoid. The present invention uses an iterative linear least squares method to solve the ellipsoid equation with high precision, eliminating the need for precise rotation of the strapdown three-axis cross-magnetic array. High-precision calibration can be performed while providing the geomagnetic field modulus, and the operation is simple. The iterative linear least squares algorithm is relatively simple, requires little computation, and is easy to implement in engineering. The present invention can easily, quickly, and accurately calibrate a strapdown three-axis cross-magnetic array used for measuring the horizontal modulus gradient of the magnetic field. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1This is a diagram of the three-axis magnetic sensor configuration of the strapdown three-axis cross magnetic array.

[0039] Figure 2 This is a block diagram of the measurement of the horizontal modulus gradient of the Earth's magnetic field by a strapdown three-axis cross magnetic array and its error correction.

[0040] Figure 3 It is the overall flow chart of the present invention.

[0041] Figure 4 is the absolute error of the geomagnetic horizontal modulus gradient in the embodiment of the present invention and σ VM The relationship curve diagram.

[0042] Figure 5 is the absolute error of the geomagnetic horizontal modulus gradient in the embodiment of the present invention and σ SM The relationship curve diagram.

[0043] Figure 6 3 is a graph showing the relationship between the absolute error of the geomagnetic horizontal modulus gradient and the number of sampling points in each rotation direction in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention will be further described below with reference to the accompanying drawings.

[0045] Generally speaking, the accuracy of the ellipsoid constraint solution method is affected by inaccurate initial points, the algorithm is complex, and engineering implementation is difficult. Since the measurement matrix of the strapdown three-axis magnetometer is a square matrix, the present invention introduces a set of virtual coordinate systems and performs a square matrix pole decomposition on each strapdown three-axis magnetometer to obtain a unit orthogonal matrix and a symmetric positive definite matrix. Since the unit orthogonal matrix does not affect the measurement of the magnetic field modulus, it is only necessary to calibrate the symmetric positive definite matrix corresponding to the strapdown three-axis cross magnetic array to improve the accuracy of its measurement of the horizontal magnetic field modulus gradient. The present invention uses an iterative linear least squares algorithm to achieve high-precision solution of the ellipsoid equation, using the solution of the linearized equation system as the initial point for solving the nonlinear equation system, thereby calculating the symmetric positive definite matrix. The advantages of the present invention are: the iterative linear least squares method solves the ellipsoid equation with high precision, does not require the rotation axis direction to be stable during the rotation of the strapdown three-axis cross magnetic array, can perform high-precision calibration under the condition of providing the geomagnetic field modulus, and is simple to operate; the iterative least squares algorithm is relatively simple, has a small computational workload, and is easy to implement in engineering.

[0046] Due to manufacturing limitations, each triaxial magnetometer has inherent zero bias, scale factor error, and triaxial quadrature error. There is also alignment error between the triaxial magnetometer and the platform it is mounted on. This error is attributed to the inherent errors of the triaxial magnetometer array. Furthermore, ferromagnetic materials and electronic devices on the carrier generate interfering magnetic fields, such as hard and soft iron fields, that differ from the magnetic field being measured.

[0047] Taking into account the two types of errors, namely the three-axis cross magnetic array’s own error and the interference magnetic field of the carrying platform, the measurement model of the strapdown three-axis cross magnetic array is established in the carrier coordinate system as follows:

[0048]

[0049] Where, is the reference magnetic field of the kth strapdown triaxial magnetometer The measured output, It can be the geomagnetic field of the calibration ground or other constant external magnetic field, D k =C SFk C NOk C Mk (E3+C SIk ) is the measurement matrix of the kth strapdown three-axis magnetometer, C SFk is the scale factor matrix of the kth sensor, C NOk is the three-axis orthogonal error matrix of the k-th strapdown three-axis magnetometer, C Mk is the three-axis alignment error matrix formed between the k-th strapdown three-axis magnetometer and the carrying platform, E3 is the third-order unit matrix, C SIk is the soft iron magnetic field matrix at the kth strapdown triaxial magnetometer, is the direction cosine matrix from the reference coordinate system r to the carrier coordinate system b, is the equivalent zero bias of the kth strapdown three-axis magnetometer, is the hard iron magnetic field at the kth strapdown triaxial magnetometer, is the sensor bias of the kth strapdown three-axis magnetometer, is the measurement noise of the kth strapdown tri-axis magnetometer.

[0050] From formula (1), the reference magnetic field in the carrier coordinate system is expressed as:

[0051]

[0052] Where, The real 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:

[0053] Ω k =Q k S k (3)

[0054] Substituting formula (3) into formula (2), we get:

[0055]

[0056] Formula (4) is also the error correction formula for measuring the magnetic field modulus of the k-th strapdown three-axis magnetometer.

[0057] From formula (4), we can get:

[0058]

[0059] Where:

[0060]

[0061] Then order:

[0062]

[0063] Then formula (5) can be written as:

[0064]

[0065] The influence of noise on calibration accuracy can be analyzed theoretically. For N measurement values, ignoring noise, we can obtain the following equation (11):

[0066] K k u k (t) = (1-χ 2k (t)) N ,k=1,2,…,N (12)

[0067] Where:

[0068] χ 2k (t) = (X 0k (t)) T A k (t)X 0k (t) (13)

[0069]

[0070] 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)

[0071] 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.

[0072] Let the number of iterations t = 0, and set χ 2k Substituting (t)=0 into equation (12) yields the linear least squares solution:

[0073]

[0074] Substituting equation (16) into equations (6) and (8), we get A k (t) and

[0075] Calculate χ according to formula (13) 2k (t), and then substitute it into formula (12) to obtain Thus the approximate least squares solution is updated. This process is repeated until ε k is a given small positive number.

[0076] The above iterative calculation Substitute into formula (6) and formula (8) respectively to obtain A k and

[0077] The modulus of the Earth's magnetic field is measured using a high-precision scalar magnetometer 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:

[0078]

[0079] Where C k Diagonalization A k ′The obtained orthogonal matrix, τ k1 ,τ k2 ,…,τ kn A k The eigenvalues ​​of ′ are all positive.

[0080] Ignoring measurement noise, a set of virtual coordinate systems a is introduced k , such that:

[0081]

[0082] Will Substituting into formula (18), we can get the measured value of the magnetic field modulus of the k-th strapdown triaxial magnetometer:

[0083] Based on the above theoretical derivation, the present invention provides an iterative linear least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field, which specifically includes the following steps:

[0084] 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;

[0085] 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

[0086] Step 3: Set a small positive number ε k , initialize the number of iterations t = 0, initialize the linear least squares solution

[0087]

[0088] 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;

[0089] Step 4: Calculate the equivalent zero bias of each strapdown three-axis magnetometer

[0090]

[0091] Step 5: Update the linear least squares solution

[0092]

[0093] Step 6: If Then let t=t+1 and return to step 4;

[0094] 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

[0095] 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

[0096]

[0097] Among them, τ k1 ,τ k2 ,…,τ kn is the matrix A′ k The eigenvalues ​​of are all positive;

[0098] Step 8: Introduce virtual coordinate system a k , calculate the measurement data of each strapdown three-axis magnetometer Correction value of the vector modulus

[0099]

[0100] Step 9: Calculate the correction value of the horizontal modulus gradient of the magnetic field and Completed the calibration of the strapdown three-axis cross magnetic array;

[0101]

[0102] Example 1:

[0103] The present invention aims to provide an iterative linear least squares calibration method for a strapdown three-axis cross-magnetic array for measuring the horizontal modulus gradient of a magnetic field. By utilizing the characteristic that the magnetic field modulus is independent of the unit orthogonal matrix, a virtual coordinate system and polar decomposition techniques are introduced to decompose the measurement matrix of each strapdown three-axis magnetometer into a unit orthogonal matrix and a symmetric positive definite matrix. High-precision calibration is achieved by using an iterative linear least squares fit of the ellipsoidal equation. The method has the advantages of using an iterative linear least squares algorithm to solve the ellipsoidal equation with high precision, eliminating the need to maintain a stable rotation axis direction during the rotation of the strapdown three-axis cross-magnetic array, enabling high-precision calibration under the condition of providing the geomagnetic field modulus, and being simple to operate. Furthermore, noise sensitivity is reduced through iterative optimization, and the iterative linear least squares algorithm has low complexity, small computational effort, and is easy to implement in engineering.

[0104] The block diagram of the strapdown three-axis cross magnetic array measurement of the horizontal modulus gradient of the Earth's magnetic field and its error correction process is shown in the figure. 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 virtual coordinate system is

[0105] The absolute measurement errors of the kth strapdown triaxial magnetometer on the Earth's magnetic field modulus before and after error correction are and Their definitions are:

[0106]

[0107] The absolute measurement errors of the horizontal modulus gradient of the Earth's magnetic field before and after error correction by the strapdown three-axis cross magnetic array are defined as follows:

[0108]

[0109] 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 are all 0.4m, and the measurement matrices of the four strapdown three-axis magnetometers (A, B, C, and D) are and The equivalent zero biases are and The unit is μT.

[0110] The strapdown three-axis cross magnetic array rotates uniformly around the three axes of the carrier and performs data sampling. The measurement noise of each axis is independent Gaussian white noise with a mean of 0 and a standard deviation of σ. VM , ε k =10 -4 When the number of sampling points in each rotation direction is 180, the measurement noise of the scalar magnetometer is Gaussian white noise, with a mean and standard deviation of 0 and 1nT respectively. The absolute error of the geomagnetic horizontal modulus gradient obtained by 50 Monte Carlo simulations is related to σ VM The relationship curve between Figure 4 As shown, the black line is the absolute error curve of the geomagnetic horizontal modulus gradient measured by the strapdown three-axis cross magnetic array before calibration, and the blue line is the absolute error curve of the geomagnetic horizontal modulus gradient measured by the strapdown three-axis cross magnetic array after calibration. Figure 4 It can be seen that the absolute error after calibration is much smaller than the absolute error before calibration; before calibration, the absolute error of the geomagnetic horizontal modulus gradient increases with the increase of the measurement noise standard deviation; after calibration, the absolute error of the geomagnetic horizontal modulus gradient increases linearly with the increase of the measurement noise standard deviation.

[0111] When the number of sampling points in each rotation direction is 180, the noise standard deviation σ of the strapdown three-axis magnetometer is VM When the value is 10nT, the absolute error of the geomagnetic horizontal modulus gradient obtained by 50 Monte Carlo simulations is SM The relationship curve between Figure 5 As shown, the black line is the absolute error curve of the strapdown three-axis cross magnetic array measuring the geomagnetic horizontal modulus gradient before calibration, and the blue line is the absolute error curve of the strapdown three-axis cross magnetic array measuring the geomagnetic horizontal modulus gradient after calibration. Figure 5 The results show that the absolute error after calibration is much smaller than the absolute error before calibration, and the absolute error increases with σ SM The increase has not changed much.

[0112] When σ VM and σ SM When the values ​​are 10nT and 1nT respectively, the relationship curve between the absolute error of the geomagnetic horizontal modulus gradient and the number of sampling points in each rotation direction obtained by 50 Monte Carlo simulations is shown in the figure below. Figure 6 As shown. Figure 6 It can be seen that the absolute error after calibration is much smaller than the absolute error before calibration, and the absolute errors before and after calibration are less affected by the number of sampling points.

[0113] By comparison, it is found that the calibration method of the present invention can greatly improve the measurement accuracy of the horizontal modulus gradient of the magnetic field measured by the strapdown three-axis magnetic array.

[0114] 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 least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field, 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 method to obtain the equivalent zero bias and symmetric positive definite matrix of each strapdown three-axis magnetometer. A virtual coordinate system is introduced to calculate the vector modulus correction value of the measurement data of each strapdown three-axis magnetometer, and then the correction value of the horizontal modulus gradient of the magnetic field is obtained to complete the calibration of the strapdown three-axis cross magnetic array.

2. The iterative linear least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field 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 least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field 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 least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field 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 least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field 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 least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field according to claim 5, characterized in that: The introduction of the virtual coordinate system a k , calculate the measurement data of each strapdown three-axis magnetometer Vector modulus correction value Specifically:

7. The iterative linear least squares calibration method for a strapdown three-axis cross magnetic array for measuring the horizontal modulus gradient of a magnetic field according to claim 6, characterized in that: Correction value of the horizontal modulus gradient of the magnetic field and 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.

Images