Strapdown three-axis cross magnetic array self-calibration method applied to unknown reference magnetic field, program, equipment and storage medium

Abstract

According to the method, a target function of three-direction equivalent zero offset and real number deflection matrixes of the strapdown three-axis magnetometer is constructed, an overdetermined equation set related to the Euler angle of the strapdown three-axis magnetometer is constructed, the solving problem of the target function and the overdetermined equation set is converted into a constraint optimization problem, a sequential quadratic programming algorithm is adopted for solving, a telescopic factor is introduced, and the Euler angle of the strapdown three-axis magnetometer is obtained. And calculating a correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array, and completing self-calibration of the strapdown three-axis cross magnetic array under the condition that the reference magnetic field is unknown. According to the method, all parameters of the strapdown three-axis cross magnetic array measurement model can be automatically and accurately calibrated under the condition that a reference magnetic field vector model is not provided, a calibration link of alignment errors does not exist, and a high-precision three-axis magnetometer or a scalar magnetometer does not need to be used for measuring the reference magnetic field vector model in the calibration process. The method does not have an iterative process and mathematical approximation, so that an iterative calculation initial value does not need to be provided, and the calibration algorithm is rapid and high in precision.

Description

Technical Field

[0001] The present invention belongs to the technical field of field measurement system calibration, and in particular relates to a strapdown three-axis cross magnetic array self-calibration method, program, device and storage medium applied in an unknown reference magnetic field. Background Art

[0002] The magnetic field is a widespread physical field in nature. Accurate measurement of the magnetic field and its gradient holds significant scientific significance and application value in scientific research, geological and mineral exploration, and life sciences. A three-axis cross-magnetic array, formed by a symmetrical arrangement of four three-axis magnetometers, is an excellent configuration for measuring the magnetic gradient tensor. The measurement outputs of the four three-axis magnetometers can also be used to calculate the magnetic field vector, magnetic field intensity, and its gradient. In practical applications, three-axis cross-magnetic arrays are often strapped down to a carrier or carrier, forming a strapdown three-axis magnetic cross array. However, alignment misalignment between the sensor coordinate system and the measurement coordinate system is inevitably caused by various factors. Furthermore, imperfect sensor manufacturing technology results in inherent instrument errors such as three-axis non-orthogonality, inter-axis scale factor deviation, and zero bias in the three-axis magnetometers. Furthermore, the carrier and its surroundings also contain interfering magnetic fields, such as hard and soft iron fields. Therefore, calibration and error correction of the strapdown three-axis cross-magnetic array are necessary to improve its measurement accuracy.

[0003] Aiming at the three-axis non-orthogonality, inter-axis scale factor deviation, 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); Chi Cheng et al. used the total least squares method to estimate the three-axis non-orthogonality, inter-axis scale factor deviation, zero bias and alignment error between sensors of the three-axis fluxgate magnetometer cross array, and obtained experimental results that the calibration effect was better than the least squares estimation method (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); Sui Yangyi et al. took the magnetic gradient tensor system as a whole and used the two rotation invariants of the magnetic gradient tensor for calibration (Yangyi et al. Sui, Shibin Liu, Zhijian Zhou, Yanzhang Wang, and Defu Cheng. Invariant calibration of magnetic tensor gradiometers [J]. IEEE Magnetic Letters, 2017, 8: 650-5105), but did not consider the configuration of the magnetic gradient tensor system and its fundamental error factors. Yin Gang et al. proposed a two-step linear calibration method for the magnetic gradient tensor system for the orthogonal output of the reference platform. The calibration model was not mathematically simplified (Yin G, Zhang Y, Fan H, et al. Linear calibration method of magnetic gradient tensor system [J]. Measurement, 2014, 56: 8-18). However, the three alignment error angles obtained by rotating the two axes belong to different calibration order relationships, resulting in mismatched parameter estimates.Pang Hongfeng et al. used the main platform frame and the vertical platform to obtain the alignment error of the three-axis magnetometer array (Hongfeng Pang, Mengchun Pan, Wei Qu, et al. Misalignment error suppression between host frame and magnetic sensor array [J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1-7). They also established a nonlinear integrated calibration model for the three-axis cross magnetic array and used the magnetic field vector for calibration (Hongfeng Pang, Mengchun Pan, Chengbiao Wan, Jinfei Chen, Xuejun Zhu, Feilu Luo. 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), but it is necessary to use a more complex magnetic field generating device to generate an accurate magnetic vector field as a calibration reference. The above calibration methods only correct the instrument error and alignment deviation in the three-axis magnetometer array, and do not consider the influence of the interfering magnetic field.

[0004] 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 a magnetic tensor detection system carrier [J]. Chinese Journal of Geophysics, 2016, 59(1): 311-317). However, its error model ignores high-order small quantities above the second order. Yu et al. used a standard magnetic source of a rectangular bar magnet to generate a known magnetic field at different positions to perform least squares calibration of a three-axis fluxgate magnetometer cube array, but did not obtain the alignment error (Xiangqian Yu, YongFu Wang, Chijie Xiao, et al. A practicable method for calibrating a magnetic sensor array [J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1007106). Guo et al. established a unified measurement model for MEMS magnetometer arrays and proposed an adaptive Kalman filter to estimate the unknown parameters of the model (Zetao Guo, Tao Zhang, Xiuli Ning, et al. Research on the calibrated method for MEMS magnetometer arrays [C]. 2020 IEEE / ION Position, Location and Navigation Symposium: 740-745, April 2020). However, the adaptive Kalman filter is sensitive to initial conditions and noise. Yu Zhentao et al. established a carrier magnetic interference model for a tetrahedron magnetic gradient tensor system and compensated for the carrier magnetic interference by using the constraint relationship between the elements of the magnetic gradient tensor (Yu Zhentao, Lv Junwei, Bi Bo, Zhou Jing. Carrier magnetic interference compensation method for a tetrahedron magnetic gradient tensor system [J]. Acta Physica Sinica, 2014, 63(11): 110702). However, it is necessary to solve a high-dimensional optimization problem, and the calculation results are sensitive to the initial parameters and are prone to falling into local optimal solutions. At the calibration point, the reference magnetic field vector modulus is usually constant. To avoid the need for precise measurement of the reference magnetic field vector modulus, a three-axis magnetometer calibration method that does not require the reference magnetic field vector modulus has been proposed in the literature (Huang Yu, Wu Lihua, Jiang Haili, Lv Zhenchuan, Qi Ruiyun. A method for identifying and correcting the total error parameters of a three-axis magnetometer that is independent of the geomagnetic field: China, [P]. 2019-02-26). However, this method can only calibrate the error of the three-axis magnetometer itself and does not include the interfering magnetic field of the strapdown three-axis magnetometer platform. Summary of the Invention

[0005] The purpose of the present invention is to provide a strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field, which can calibrate all parameters of the strapdown three-axis cross magnetic array model without measuring the reference magnetic field and does not require additional steps to calibrate the alignment error.

[0006] A strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field comprises the following steps:

[0007] In the calibration area, a strapdown three-axis cross magnetic array is mounted on the table of a three-axis turntable, the table of the three-axis turntable is adjusted to be horizontal, and the measuring axis of the strapdown three-axis cross magnetic array is aligned with the rotation axis of the turntable; the strapdown three-axis cross magnetic array includes four sets of strapdown three-axis magnetometers;

[0008] 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 three sets of geomagnetic field measurement data sequences;

[0009] The three sets of measurement data sequences were divided equally and then integrated into two sets of data sequences with the same number of elements. The squared absolute difference of the norm between the two sets of data sequences was used as the objective function of the equivalent zero bias and real skew matrix of the three directions of the strapdown three-axis magnetometer. The constrained optimization problem corresponding to the objective function was solved using the sequential quadratic programming algorithm, and the estimated values ​​of the equivalent zero bias of the three directions of the four strapdown three-axis magnetometers were obtained.

[0010] By performing a difference operation between the two data series, an overdetermined system of equations for the Euler angles of the strapdown three-axis magnetometer is constructed. The solution of the overdetermined system of equations is transformed into a constrained optimization problem and solved using a sequential quadratic programming algorithm. The estimated values ​​of the Euler angles of the four strapdown three-axis magnetometers are obtained.

[0011] Based on the estimated values ​​of the Euler angles of four sets of strapdown three-axis magnetometers, the estimated value of the unit orthogonal matrix is ​​calculated. The scaling factor is introduced, and the correction value of the measurement data of the four sets of strapdown three-axis magnetometers is calculated. Then, the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array is calculated, completing the self-calibration of the strapdown three-axis cross magnetic array under unknown reference magnetic field.

[0012] Furthermore, 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 of the strapdown three-axis cross magnetic array are recorded at certain angles to obtain three sets of geomagnetic field measurement data sequences, specifically:

[0013] The strapdown three-axis cross magnetic array is rotated around the x-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. x ={m kxa|k=1,2,3,4;a=1,2,...,2n x}; k represents the index of the strapdown three-axis magnetometer;

[0014] The strapdown three-axis cross magnetic array is rotated around the y-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. y ={m kyb |k=1,2,3,4;b=1,2,...,2n y};

[0015] The strapdown three-axis cross magnetic array is rotated around the z-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. z ={m kzc |k=1,2,3,4;c=1,2,...,2n z}.

[0016] Furthermore, the three groups of measurement data sequences are divided equally and then integrated into two groups of data sequences with the same number of elements, specifically:

[0017] The measurement data sequence M x Divide equally into M xF With M xB :

[0018]

[0019] The measurement data sequence M y Divide equally into M yF With M yB :

[0020]

[0021] The measurement data sequence M z Divide equally into M zF With M zB :

[0022]

[0023] M xF 、M yF 、M zF Integrate into data sequence M F ={M xF ,M yF ,M zF}, M xB 、M yB 、MzB Integrate into data sequence M B ={M xB ,M yB ,M zB}, after integration:

[0024]

[0025] Furthermore, the objective function of the equivalent zero bias and real skew matrix in three directions of the strapdown three-axis magnetometer is specifically:

[0026] make Construct the objective function;

[0027]

[0028] Among them, ω k1 、ω k2 、ω k3 、ω k4 、ω k5 ∈(-1,1); is the equivalent zero bias of the kth strapdown three-axis magnetometer in the x, y, and z directions;

[0029] Use the sequential quadratic programming algorithm to solve the constrained optimization problem corresponding to the objective function:

[0030]

[0031] in, x ki is x k The i-th element of

[0032] Solve the constrained optimization problem and get x k Estimated value of The equivalent zero bias of the strapdown three-axis magnetometer in three directions is The real skew matrix is

[0033] Furthermore, the overdetermined set of equations for the Euler angles of the strapdown three-axis magnetometer is specifically:

[0034]

[0035] Convert the problem of solving the overdetermined system of equations into a constrained optimization problem:

[0036]

[0037] The sequential quadratic programming algorithm is used to solve the problem and obtain the estimated Euler angles of the four sets of strapdown three-axis magnetometers. and

[0038] Furthermore, the estimated value of the unit orthogonal matrix is ​​calculated based on the estimated values ​​of the Euler angles of the four sets of strapdown three-axis magnetometers.

[0039]

[0040] Introducing the scaling factor λ k :

[0041]

[0042] Calculate the correction values ​​of the measurement data of four sets of strapdown three-axis magnetometers

[0043]

[0044] in,

[0045] Furthermore, the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array is calculated Completed the self-calibration of the strapdown three-axis cross magnetic array under unknown reference magnetic field;

[0046]

[0047] 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.

[0048] 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 above-mentioned strapdown three-axis cross magnetic array self-calibration method applied to an unknown reference magnetic field.

[0049] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the strapdown three-axis cross magnetic array self-calibration method applied to an unknown reference magnetic field.

[0050] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the strapdown three-axis cross magnetic array self-calibration method applied to an unknown reference magnetic field.

[0051] The beneficial effects of the present invention are:

[0052] The present invention can autonomously and accurately calibrate all parameters of a strapdown three-axis cross-magnetic array measurement model without providing a reference magnetic field vector modulus. This eliminates the calibration process that could lead to alignment errors, and eliminates the need for a high-precision three-axis magnetometer or scalar magnetometer to measure the reference magnetic field vector modulus. The present invention eliminates the need for iterative calculations and mathematical approximations, eliminating the need for initial values. The calibration algorithm is fast and highly accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a diagram of the three-axis magnetometer configuration of a strapdown three-axis cross magnetic array.

[0054] 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.

[0055] Figure 3 It is the overall flow chart of the present invention.

[0056] Figure 4 3 is a graph showing the relationship between the relative calibration error and the measurement noise standard deviation in an embodiment of the present invention.

[0057] Figure 5 3 is a graph showing the relationship between the geomagnetic field measurement error and the measurement noise standard deviation in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The present invention will be further described below with reference to the accompanying drawings.

[0059] Due to manufacturing limitations, the three-axis magnetometer itself has zero bias, scale factor error, three-axis orthogonality error, and alignment error between the three-axis magnetometer and the carrier. These errors are attributed to the inherent errors of the three-axis magnetometer array. Furthermore, ferromagnetic materials and electronic devices on the carrier generate interfering magnetic fields, such as hard iron fields, soft iron fields, and interference noise, which are different from the magnetic field being measured.

[0060] There is a carrier interference magnetic field in the actual working environment. In order to calibrate the measurement model parameters of the strapdown three-axis cross magnetic array, the present invention establishes a unified measurement model under the carrier coordinate system framework. Based on the characteristic of the constant reference magnetic field, a strapdown three-axis cross magnetic array self-calibration method applied to an unknown reference magnetic field is proposed. By introducing a scaling factor, this calibration method can calibrate all the parameters of the strapdown three-axis cross magnetic array measurement model without the reference magnetic field vector modulus. The advantage of this calibration method is that it does not require the use of a high-precision three-axis magnetometer or scalar magnetometer to measure the reference magnetic field during the calibration process, and the calibration algorithm does not require any mathematics, so the calibration accuracy is high; the alignment errors between different three-axis magnetometers are unified into the measurement model, and no additional calibration of the alignment error is required.

[0061] Combining 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 as follows:

[0062]

[0063] Where, is the reference magnetic field B of the kth strapdown triaxial magnetometer r The measured output, B r 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 system interference noise of the kth strapdown three-axis magnetometer.

[0064] Without considering the system interference noise, the reference magnetic field in the carrier coordinate system is expressed as follows from formula (1):

[0065]

[0066] Where, The influence of noise on calibration accuracy can be analyzed through simulation experiments. Equation (2) is also the error correction formula for the kth strapdown three-axis magnetometer.

[0067] The real matrix Ω k Decomposed into a 3rd order real unit orthogonal matrix Q k and the 3rd order real upper triangular matrix R k ,Right now:

[0068] Ω k =Q k R k (3)

[0069] According to the physical meaning of the measurement model shown in formula (2), Q k It reflects the transformation matrix between two orthogonal coordinate systems, which can be expressed as the Euler angle ψ k ,θ k and γ k To express, the Euler angle ψ k ,θ k and γ k Represent the heading angle, pitch angle and roll angle respectively, that is:

[0070]

[0071] Real upper triangular matrix R k Can be expressed as:

[0072]

[0073] Where λ k is the scaling factor, in general, 0<λ k <2,-1<ω ki <1,i=1,2,…,5。

[0074] The strapdown three-axis cross magnetic array is rotated around the x-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. x ={m kxa |k=1,2,3,4;a=1,2,...,2n x}; k represents the index of the strapdown three-axis magnetometer;

[0075] The strapdown three-axis cross magnetic array is rotated around the y-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. y ={m kyb |k=1,2,3,4;b=1,2,...,2n y};

[0076] The strapdown three-axis cross magnetic array is rotated around the z-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. z ={m kzc |k=1,2,3,4;c=1,2,...,2n z}.

[0077] The measurement data sequence M x Divide equally into M xF With MxB :

[0078]

[0079] The measurement data sequence M y Divide equally into M yF With M yB :

[0080]

[0081] The measurement data sequence M z Divide equally into M zF With M zB :

[0082]

[0083] M xF 、M yF 、M zF Integrate into data sequence M F ={M xF ,M yF ,M zF}, M xB 、M yB 、M zB Integrate into data sequence M B ={M xB ,M yB ,M zB}, after integration:

[0084]

[0085] The two sets of data series and Substituting into equation (2), the optimal error parameter should minimize the squared absolute difference of the norm between the two groups of measurement sequences. That is, the objective function J k Can be set to:

[0086]

[0087] Since the objective function J k Taking the minimum value is equivalent to taking the minimum value of the objective function shown in formula (7), and the matrix R k ′ and equivalent bias The optimal value of should make formula (7) take the minimum value.

[0088]

[0089] make

[0090] make Expanding formula (7) yields

[0091]

[0092] Use the sequential quadratic programming algorithm to solve the following constrained optimization problem, and get x k Estimates

[0093]

[0094] Where, x ki 、x kui and x lui x k 、x ku and x kl The i-th element, x ku =[1,1,1,1,1,1,1,1], x kl =[-1,-1,-1,-1,-1,-1,-1,-1].

[0095] because Then we have:

[0096]

[0097] Where, is the average calculation result of the magnetic field measurement data.

[0098] From equations (5) and (10), we can get the scaling factor:

[0099]

[0100] When the strapdown three-axis cross magnetic array rotates around the axis of the mounting platform, the component value of the reference magnetic field on the rotating axis remains unchanged.

[0101]

[0102] By M F With M B The difference operation of , we can get:

[0103]

[0104] Combining equations (15), (16) and (17), we can get the Euler angle ψ k ,θ k and γ k The overdetermined set of equations is transformed into the constrained optimization problem shown in formula (18).

[0105]

[0106] The sequential quadratic programming algorithm is used to solve the constrained optimization problem shown in Equation (18), and ψ k ,θ k and γ k Estimated value of and Will and Substituting into formula (4) we can obtain the unit orthogonal matrix Q k Estimated value of

[0107] Based on the above content, the present invention provides a strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field, comprising the following steps:

[0108] Step 1: If Figure 1 As shown, in the calibration area, the strapdown three-axis cross magnetic array is installed on the table of the three-axis turntable. The table of the three-axis turntable is adjusted to be horizontal and the measurement axis of the strapdown three-axis cross magnetic array is aligned with the rotation axis of the turntable. The array baseline length L of the strapdown three-axis cross magnetic array in the x direction is obtained. 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; Figure 1 The three-axis magnetometers A, B, C and D are placed at x b axis and y b axis and are denoted by subscripts 1, 2, 3, and 4 respectively.

[0109] Step 2: Rotate the strapdown three-axis cross magnetic array around the three axes of the three-axis turntable in sequence, and record the measurement values ​​of the geomagnetic field of the strapdown three-axis cross magnetic array at a certain angle to obtain three sets of geomagnetic field measurement data sequences M x 、M y 、M z , calculate the average

[0110] Step 3: Transform the measurement data sequence M x 、M y 、M z After integration, it is divided into two groups of sequences M with the same number of elements F and M B ;

[0111] Step 4: Make Construct the objective function;

[0112]

[0113] Use the sequential quadratic programming algorithm to solve the constrained optimization problem corresponding to the objective function and obtain xk Estimated value of

[0114]

[0115] in, x ki is x k The i-th element of

[0116] The equivalent zero bias of the strapdown three-axis magnetometer in three directions is The real skew matrix is

[0117]

[0118] Step 5: Calculate the scaling factor λ k ;

[0119]

[0120] Step 6: Overdetermined equations for the Euler angles of the strapdown triaxial magnetometer:

[0121]

[0122] Convert the problem of solving the overdetermined system of equations into a constrained optimization problem:

[0123]

[0124] The sequential quadratic programming algorithm is used to solve the problem and obtain the estimated Euler angles of the four sets of strapdown three-axis magnetometers. and

[0125] Step 7: Based on the estimated value of Euler angle and Estimated value of the unit orthogonal matrix

[0126]

[0127] Step 8: Calculate the correction value of the measurement data of each strapdown three-axis magnetometer

[0128]

[0129] in,

[0130] Step 9: Calculate the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array Completed the self-calibration of the strapdown three-axis cross magnetic array under unknown reference magnetic field;

[0131]

[0132] Example 1:

[0133] By taking advantage of the fact that the vector modulus of the reference magnetic field (geomagnetic field) remains unchanged during the rotation calibration, the measurement model parameters of the strapdown three-axis cross magnetic array are self-calibrated, and then the error of the measured magnetic field is corrected using the self-calibrated measurement model parameters. The block diagram of the strapdown three-axis cross magnetic array geomagnetic field measurement 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 carrier coordinate system is A flow chart of a strapdown three-axis cross magnetic array self-calibration method applied to an unknown reference magnetic field is shown in the following figure. Figure 3 shown.

[0134] Calibration measurement matrix D k The relative error ε Dk Defined as

[0135]

[0136] Where, is the measurement matrix D k The estimated value of ||·|| F Represents the Frobenius norm of the matrix.

[0137] Calibration of equivalent zero bias The relative error ε B0k Defined as

[0138]

[0139] Where, is the equivalent bias The estimated value of , ||·|| represents the 2-norm of the vector.

[0140] The kth strapdown three-axis magnetometer measures the Earth's magnetic field vector in the carrier coordinate system before and after error correction. The absolute measurement errors are δB Ek and Their definitions are:

[0141]

[0142] 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

[0143]

[0144] Assume that at the calibration point, the x, y and z components of the geomagnetic field are and L x and L y The measurement matrices of the four strapdown three-axis magnetometers (A, B, C, and D) that constitute the magnetic array are and The equivalent zero biases are and The unit is μT.

[0145] The strapdown three-axis 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 measurement noise of each axis is independent Gaussian white noise with a mean of 0 and a standard deviation of σ. The relationship curve between the relative error of the strapdown three-axis magnetic array measurement model parameters and the standard deviation of the measurement noise is obtained by 50 Monte Carlo simulations. Figure 4 As shown, Figure 4 (a) is the curve showing the relationship between the relative error of the measurement matrix of four strapdown three-axis magnetometers (A, B, C, D) and the noise standard deviation. Figure 4 (b) is the curve of the relative error of the equivalent zero bias of the four strapdown three-axis magnetometers (A, B, C, D) versus the standard deviation of the noise. Figure 4 It can be seen that the method proposed in the present invention can calibrate the measurement model parameters of the strapdown three-axis magnetic array more accurately and completely. Within the noise standard deviation range shown in the figure, the relative error increases with the increase of the noise standard deviation.

[0146] When the noise standard deviation σ is 200nT, the absolute errors of the four strapdown three-axis magnetometers (A, B, C, D) in measuring the geomagnetic field vector and its gradient tensor before and after calibration are as follows: Figure 5 shown. Figure 5 (a) is the absolute error of the geomagnetic field vector measured by A and B. The black and red lines are the absolute errors of the geomagnetic field vector measured by A before and after calibration, respectively. The blue and green lines are the absolute errors of the geomagnetic field vector measured by B before and after calibration, respectively. Figure 5 Middle (b) is the absolute error of the geomagnetic field vector measured by C and D. The black and red lines are the absolute errors of the geomagnetic field vector measured by C before and after calibration, respectively. The blue and green lines are the absolute errors of the geomagnetic field vector measured by D before and after calibration, respectively. Figure 5Figure (c) shows the absolute error of the geomagnetic field gradient tensor measured by a strapdown three-axis magnetic array. The black and red lines represent the absolute error of the geomagnetic field gradient tensor measured by the magnetic array before and after calibration, respectively. This comparison reveals that the self-calibration method of the present invention significantly improves the measurement accuracy of the magnetic field vector and its gradient tensor using a strapdown three-axis magnetic array.

[0147] 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. A strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field, characterized by: In the calibration area, a strapdown three-axis cross magnetic array is mounted on the table of a three-axis turntable, the table of the three-axis turntable is adjusted to be horizontal, and the measuring axis of the strapdown three-axis cross magnetic array is aligned with the 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 three sets of geomagnetic field measurement data sequences; The three sets of measurement data sequences were divided equally and then integrated into two sets of data sequences with the same number of elements. The squared absolute difference of the norm between the two sets of data sequences was used as the objective function of the equivalent zero bias and real skew matrix of the three directions of the strapdown three-axis magnetometer. The constrained optimization problem corresponding to the objective function was solved using the sequential quadratic programming algorithm, and the estimated values ​​of the equivalent zero bias of the three directions of the four strapdown three-axis magnetometers were obtained. By performing a difference operation between the two data series, an overdetermined system of equations for the Euler angles of the strapdown three-axis magnetometer is constructed. The solution of the overdetermined system of equations is transformed into a constrained optimization problem and solved using a sequential quadratic programming algorithm. The estimated values ​​of the Euler angles of the four strapdown three-axis magnetometers are obtained. Based on the estimated values ​​of the Euler angles of four sets of strapdown three-axis magnetometers, the estimated value of the unit orthogonal matrix is ​​calculated. The scaling factor is introduced, and the correction value of the measurement data of the four sets of strapdown three-axis magnetometers is calculated. Then, the correction value of the magnetic gradient tensor measured by the strapdown three-axis cross magnetic array is calculated, completing the self-calibration of the strapdown three-axis cross magnetic array under unknown reference magnetic field.

2. The strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field according to claim 1, characterized in that: 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 a certain angle to obtain three sets of geomagnetic field measurement data sequences, specifically: The strapdown three-axis cross magnetic array is rotated around the x-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. x ={m kxa |k=1,2,3,4;a=1,2,...,2n x }; k represents the index of the strapdown three-axis magnetometer; The strapdown three-axis cross magnetic array is rotated around the y-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. y ={m kyb |k=1,2,3,4;b=1,2,...,2n y }; The strapdown three-axis cross magnetic array is rotated around the z-axis of the three-axis turntable, and the measurement value of the geomagnetic field by the strapdown three-axis cross magnetic array is recorded at a certain angle. The total number of measured values ​​is an even number, and the measurement data sequence M is obtained. z ={m kzc |k=1,2,3,4;c=1,2,...,2n z }.

3. The strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field according to claim 2, characterized in that: After the three sets of measurement data sequences are equally divided, they are integrated into two sets of data sequences with the same number of elements, specifically: The measurement data sequence M x Divide equally into M xF With M xB : M xF ={m kxpF |k=1,2,3,4;p=1,2,...,n x }, M xB ={m kxpB |k=1,2,3,4;p=1,2,...,n x }, The measurement data sequence M y Divide equally into M yF With M yB : M yF ={m kyqF |k=1,2,3,4;q=1,2,...,n y }, M yB ={m kyqB |k=1,2,3,4;q=1,2,...,n y }, The measurement data sequence M z Divide equally into M zF With M zB : M zF ={m kzrF |k=1,2,3,4;r=1,2,...,n z }, M zB ={m kzrB |k=1,2,3,4;r=1,2,...,n z }, M xF 、M yF 、M zF Integrate into data sequence M F ={M xF ,M yF ,M zF }, M xB 、M yB 、M zB Integrate into data sequence M B ={M xB ,M yB ,M zB }, after integration: M F ={m kjF |k=1,2,3,4;j=1,2,...,n x +n y +n z }, M B ={m kjB |k=1,2,3,4;j=1,2,...,n x +n y +n z }, 4. The strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field according to claim 3, characterized in that: The objective function of the equivalent zero bias and real skew matrix of the strapdown three-axis magnetometer in three directions is specifically: make Construct the objective function; Among them, ω k1 、ω k2 、ω k3 、ω k4 、ω k5 ∈(-1,1); is the equivalent zero bias of the kth strapdown three-axis magnetometer in the x, y, and z directions; Use the sequential quadratic programming algorithm to solve the constrained optimization problem corresponding to the objective function: in, x ki is x k The i-th element of Solve the constrained optimization problem and get x k Estimated value of The equivalent zero bias of the strapdown three-axis magnetometer in three directions is The real skew matrix is 5. The strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field according to claim 4, characterized in that: The overdetermined set of equations for the Euler angles of the strapdown three-axis magnetometer is specifically: Convert the problem of solving the overdetermined system of equations into a constrained optimization problem: The sequential quadratic programming algorithm is used to solve the problem and obtain the estimated Euler angles of the four sets of strapdown three-axis magnetometers. and 6. The strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field according to claim 5, characterized in that: Calculate the estimated value of the unit orthogonal matrix based on the estimated values ​​of the Euler angles of four sets of strapdown triaxial magnetometers Introducing the scaling factor λ k : in, Calculate the correction values ​​of the measurement data of four sets of strapdown three-axis magnetometers in, 7. The strapdown three-axis cross magnetic array self-calibration method for an unknown reference magnetic field according to claim 6, characterized in that: Calculating the correction value of the magnetic gradient tensor measured by a strapdown three-axis cross magnetic array Completed the self-calibration of the strapdown three-axis cross magnetic array under unknown reference magnetic field; 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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