A method for spatial target positioning based on rotating permanent magnets

Abstract

A spatial target positioning method based on a rotating permanent magnet: a permanent magnet is placed on a turntable that can rotate at a constant speed, and the permanent magnet can rotate at a fixed rate; a cross-shaped magnetometer array is composed of 5 magnetometers with exactly the same parameters, and the 0th magnetometer is used as the target point; the plane where the permanent magnet is located is parallel to the plane where the cross-shaped magnetometer array is located and maintains a certain distance. The permanent magnet magnetic field signal is received by the cross-shaped magnetometer array, and the received permanent magnet magnetic field signal is sent to a data processing device for data processing; most of the geomagnetic field and environmental magnetic field are filtered out, and useful sinusoidal magnetic field vector signals are extracted; the gradient tensor matrix is ​​calculated using the cross-shaped magnetometer array and the Euler deconvolution equation of the magnetic field is used to obtain the 0th magnetometer, that is, the single-point positioning of the Euler deconvolution equation of the target point. The present invention adopts a rotating permanent magnet to solve the problem that the traditional positioning algorithm cannot provide a magnetic field signal, adopts an error gradient matrix to reduce the error of the gradient tensor in principle, and can effectively improve the accuracy of the magnetic positioning system.

Description

Technical Field

[0001] The invention relates to a space target positioning technology, and in particular to a space target positioning method based on a rotating permanent magnet. Background Art

[0002] At present, there are many means and methods for positioning, but many positioning methods are easily interfered with and cannot be applied in special occasions. Indoors, underground, underwater and some other complex environments, many navigation and positioning methods cannot be used in these environments. Radio navigation systems can ensure the approach and landing of aircraft, but the signal is very easy to be interfered with. Satellite navigation can achieve high-precision positioning, but it cannot receive signals in special occasions such as indoors. Magnetic field signals have the advantages of strong penetration and strong anti-interference ability, and can be used in special occasions such as indoors and underground. Therefore, the use of magnetic signals for navigation and positioning has great development potential.

[0003] Permanent magnets can generate artificial magnetic field signals in space. When the permanent magnet is stationary in space, the magnetic field signal is also fixed. If the permanent magnet rotates at a fixed rate, a magnetic field signal similar to a sine wave can be generated. Therefore, artificial magnetic field signals can be used to achieve positioning. There are currently many different methods for magnetic signal positioning. Among them, the gradient tensor method is the most widely used because of its relatively simple calculation. However, many research methods use the finite difference method when solving the magnetic gradient tensor matrix using the magnetometer array, and ignore the quadratic elements of the differential formula, which inevitably leads to measurement errors of the gradient tensor.

[0004] Assuming that the center point of the permanent magnet is located at the origin of the three-dimensional coordinate system in space, the three components of the magnetic field at any point in the coordinate system with the permanent magnet as the origin can be expressed as:

[0005]

[0006] Among them, B1, B2, and B3 represent the magnitude of the magnetic field of the permanent magnet on the x, y, and z axes respectively; m x 、m y 、 m z represents the component size of the permanent magnet magnetic moment on the x, y, and z axes respectively; x, y, and z represent the coordinate values ​​of the target point (in the present invention, the 0th magnetometer in the cross-shaped magnetometer array is taken as the target point) on the x, y, and z axes of the three-dimensional coordinate system in space; r represents the distance from the target point to the origin of the coordinate axis; u0 is a constant with a size of 4π×10 -7 .

[0007] When the permanent magnet rotates at a constant angular velocity in the xy plane, the magnetic moment of the permanent magnet also rotates at a constant angular velocity. Therefore, the magnetic moment of the rotating permanent magnet can be expressed as:

[0008]

[0009] Where w is the angular velocity of the permanent magnet, is the initial phase of permanent magnet rotation, m xy is m x and m y Vector overlay.

[0010] Therefore, the three-component expression of the magnetic field of the rotating permanent magnet can be obtained:

[0011]

[0012] in The process parameters c1, c2, c3, c4, c5, c6, c7, c8, c9 are (3x 2 -r 2 )m xy 、3xym xy 、3xzm z 、3xym xy 、(2y 2 -x 2 -z 2 )m xy 、3yzm z 、3xzm xy 、3yzm xy 、(2z 2 -x 2 -y 2 )m z .

[0013] According to the above formula, the general expression of the three components of the magnetic field of the rotating permanent magnet is:

[0014]

[0015] Where i = 1, 2, 3, B i Indicates the magnitude of the three components of the magnetic field, B1, B2, and B3.

[0016] Therefore, the above formula can be expressed as a sine function:

[0017]

[0018] Where θ represents the phase of the synthetic signal, and a represents the amplitude of the synthetic signal.

[0019] It can be seen from the above formula that the signal generated by the rotating permanent magnet is a sinusoidal modulated signal.

[0020] The component change rate of the three components of magnetic induction intensity in three directions is the first-order magnetic gradient tensor matrix. The first-order magnetic gradient tensor matrix has a total of 9 elements, as shown below:

[0021]

[0022] G represents the gradient tensor matrix, B represents the magnetic field vector, and B xx , B xy , B xz Respectively represent the size of the components of B1 on the x, y, and z axes, B yx , B yy , B yz Respectively represent the size of the components of B2 on the x, y, and z axes, B zx , B zy , B zz Respectively represent the size of the components of B3 on the x, y, and z axes, B x , B y , B z They represent the magnitude of the magnetic field of the permanent magnet on the x, y, and z axes respectively.

[0023] According to the divergence and gradient of the magnetic source being zero, the following conclusions can be drawn:

[0024]

[0025] Put the permanent magnet on the turntable. The center point of the permanent magnet is the origin of the three-dimensional coordinate system. When the permanent magnet rotates at a constant angular velocity, the gradient tensor matrix also rotates together. Referring to the calculation method of the magnetic field of the rotating permanent magnet, the theoretical expression of the five independent elements of the gradient tensor of the rotating permanent magnet can be obtained as follows:

[0026]

[0027] Since the cross-shaped magnetometer array model has the highest accuracy in the planar magnetometer model, the cross-shaped magnetometer array is used to calculate the gradient tensor matrix. Figure 1 As shown, a new coordinate system x1-o1-y1 is established, wherein the x1-y1 plane is parallel to the xy plane, the x1 axis is parallel to the x axis, and the y1 axis is parallel to the y axis. The cross-shaped magnetometer array is composed of 5 magnetometers with identical parameters, wherein the center point of the 0th magnetometer is at the origin, the 1st magnetometer is arranged at the positive half axis of the x1 axis, the 2nd magnetometer is arranged at the positive half axis of the y1 axis, the 3rd magnetometer is arranged at the negative half axis of the x1 axis, and the 4th magnetometer is arranged at the negative half axis of the y1 axis. The 1st, 2nd, 3rd, and 4th magnetometers are at the same distance from the 0th magnetometer. As mentioned above, the 0th magnetometer is taken as the target point.

[0028] According to the two-point method derivation principle, the five independent gradient tensor elements of the 0th magnetometer can be obtained as follows:

[0029]

[0030] in Indicates the x-axis magnetic field value of the first magnetometer, Respectively represent the x, y, and z axis magnetic field magnitude values ​​of the second magnetometer, Respectively represent the x-axis and z-axis magnetic field magnitude values ​​of the third magnetometer, They respectively represent the x-, y-, and z-axis magnetic field magnitude values ​​of the 4th magnetometer.

[0031] like Figure 2 As shown, the permanent magnet with its center point located at the origin of the turntable rotates clockwise at a constant angular velocity on the xy plane of the turntable, and the modulated magnetic signal is received by the cross-shaped magnetometer array in space, thereby realizing the positioning of the 0th magnetometer relative to the three-dimensional coordinate system in space with the permanent magnet as the origin.

[0032] According to the Euler deconvolution equation of the magnetic field, the single-point positioning equation of the 0th magnetometer can be obtained as:

[0033]

[0034] At present, most methods for solving the magnetic gradient tensor matrix use the finite difference principle. However, the finite difference ignores the quadratic elements of the differential formula and the attenuation of the magnetic field of the permanent magnet is not a linear relationship, which will inevitably lead to measurement errors of the gradient tensor, thereby reducing the accuracy of magnetic positioning. Summary of the invention

[0035] In view of the problems existing in the prior art, the present invention proposes a spatial target positioning method based on a rotating permanent magnet, specifically:

[0036] Place the permanent magnet on a turntable that can rotate at a constant speed. Assume that the center point of the permanent magnet is located at the origin o of the three-dimensional coordinate system oxyz in space. The permanent magnet can rotate at a fixed speed.

[0037] Then the three components of the magnetic field at any point in the coordinate system with the permanent magnet as the origin can be expressed as:

[0038]

[0039] Among them, B1, B2, and B3 represent the magnitude of the magnetic field of the permanent magnet on the x, y, and z axes respectively; m x 、m y 、 m zrepresents the magnitude of the components of the permanent magnet’s magnetic moment on the x, y, and z axes respectively; x, y, and z represent the coordinates of the target point on the x, y, and z axes of the three-dimensional coordinate system in space respectively; r represents the distance from the target point to the origin of the coordinate axis; u0 is a constant with a size of 4π×10 -7 ;

[0040] The cross-shaped magnetometer array is composed of 5 magnetometers with exactly the same parameters. A new coordinate system o1x1y1 is established with the center of the 0th magnetometer as the origin, where the x1-y1 plane is parallel to the xy plane, the x1 axis is parallel to the x axis, and the y1 axis is parallel to the y axis; the first magnetometer is arranged on the positive half axis of the x1 axis, the second magnetometer is arranged on the positive half axis of the y1 axis, the third magnetometer is arranged on the negative half axis of the x1 axis, and the fourth magnetometer is arranged on the negative half axis of the y1 axis;

[0041] According to the two-point method derivation principle, the five independent gradient tensor elements of the 0th magnetometer are obtained as follows:

[0042]

[0043] Among them B xx , B xy , B xz Respectively represent the size of the components of B1 on the x, y, and z axes, B yy , B yz Respectively represent the magnitude of the component of B2 on the y and z axes; B1, B2, B3 represent the magnitude of the magnetic field of the permanent magnet on the x, y, z axes; Indicates the x-axis magnetic field value of the first magnetometer, Respectively represent the x, y, and z axis magnetic field magnitude values ​​of the second magnetometer, Respectively represent the x-axis and z-axis magnetic field magnitude values ​​of the third magnetometer, They respectively represent the x-, y-, and z-axis magnetic field magnitude values ​​of the 4th magnetometer.

[0044] According to the divergence and gradient of the magnetic source being zero, the following conclusions can be drawn:

[0045]

[0046] When the cross-shaped magnetometer array solves the gradient tensor matrix, point B is the actual measurement position of the cross-shaped magnetometer array and point D is the theoretical position of the gradient tensor. Since the attenuation of the magnetic field is not a linear relationship, there must be errors in the calculation in principle.

[0047] Therefore, it is necessary to introduce the gradient tensor error matrix; in actual measurement, the measured value of the gradient tensor G T Denoted as:

[0048]

[0049] Among them, G T G T represents the actual measured value of the gradient tensor, G represents the gradient tensor matrix, g1, g2, g3, g4, g5, g6, g7, g8, g9 represent the row and column elements of the error gradient tensor respectively;

[0050] Assume that the following equations hold:

[0051]

[0052] where r x+ 、r y+ 、r x- 、r y- Respectively represent the distances from the 1st, 2nd, 3rd, and 4th magnetometers in the cross magnetometer array to the permanent magnet, x, y, and z represent the coordinates of the 0th magnetometer on the x, y, and z axes of the three-dimensional coordinate system in space, d represents the distances from the 1st, 2nd, 3rd, and 4th magnetometers in the cross magnetometer array to the 0th magnetometer, and a and b represent the distance deviations from the positions of the 1st and 3rd magnetometers on the x1 axis and the 2nd and 4th magnetometers on the y1 axis during actual measurement to the positions of the 1st and 3rd magnetometers and the 2nd and 4th magnetometers of the cross magnetometer array established with a fixed distance d;

[0053] Then the five independent elements of the gradient tensor error matrix are expressed as:

[0054]

[0055] in

[0056] According to the Euler deconvolution equation of the magnetic field, the single-point positioning equation of the 0th magnetometer is obtained as follows:

[0057]

[0058] Among them, B xx , B xy B xz Respectively represent the size of the components of B1 on the x, y, and z axes, B yx , B yy , B yz Respectively represent the size of the components of B2 on the x, y, and z axes, B zx , B zy , B zz Respectively represent the component size of B3 on the x, y, and z axes;

[0059] In the specific solution, the 3*3 matrix The specific solutions of the parameters in are as follows: Using the data of the first, second, third, and fourth magnetometers, according to formula (2), we can solve B xx , B xy , B xz , B yy , B yz , then according to formula (3), solve B yx , B zx B zy , B zz ,and It can be obtained directly through the 0th magnetometer.

[0060] In a specific embodiment of the present invention, a Butterworth filter and harmonic wavelet transform are used to process data of a useful sinusoidal magnetic field vector signal; the center sampling frequency of the Butterworth filter is 4 Hz, the passband is 0.2, and the stopband is 0.4; the permanent magnet rotates at a constant speed of 4 rad / s, and the electromagnetic field in the experimental environment changes at a frequency of 50 Hz.

[0061] In another specific embodiment of the present invention, the permanent magnet is a cuboid with a length of 9.6 cm, a width of 4.7 cm, and a height of 1.7 cm.

[0062] The spatial target positioning method based on rotating permanent magnets proposed in the present invention is one of the few rotating magnetic field positioning methods. The use of rotating permanent magnets solves the problem that the traditional gradient tensor method cannot produce magnetic field signals. In view of the fact that there must be errors in solving the gradient tensor using the two-point method, the error gradient matrix is ​​used to reduce the error in principle and can effectively improve the accuracy of the magnetic positioning system. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a schematic diagram of a cross-shaped measurement array;

[0064] Figure 2 This is a diagram of the rotating permanent magnet positioning system;

[0065] Figure 3 This is the error analysis diagram of the cross-shaped magnetometer array;

[0066] Figure 4 This is a diagram of the error compensation idea of ​​the cross-shaped magnetometer array;

[0067] Figure 5 This is a physical picture of a permanent magnet;

[0068] Figure 6 This is a real picture of the non-magnetic turntable;

[0069] Figure 7 This is a physical picture of the cross-shaped magnetometer array;

[0070] Figure 8 It is the waveform diagram of the measured signal of the magnetic field signal;

[0071] Fig. 9 It is the original waveform of the measured signal;

[0072] Fig.10 Filter waveform diagram for measured signal;

[0073] Fig.11 This is the waveform diagram processed by harmonic wavelet transform. DETAILED DESCRIPTION

[0074] like Figure 3 As shown, point B is the actual measurement position of the cross-shaped magnetometer array, and point D is the theoretical position of the gradient tensor. The cross-shaped magnetometer array solves the derivative based on the two-point method, and the attenuation of the magnetic field is not a linear relationship. Therefore, the cross-shaped magnetometer array actually solves the gradient tensor matrix at point B, while for permanent magnets, the gradient tensor value at point D should be solved. Therefore, using the cross-shaped magnetometer array model to measure the gradient tensor matrix must have errors in principle.

[0075] In order to improve the positioning accuracy of space targets using artificial magnetic signals, the present invention proposes a space target positioning method based on a rotating permanent magnet, which can extract the magnetic field signal of the permanent magnet to achieve the positioning of the space target.

[0076] like Figure 4 As shown, in order to reduce this measurement error in principle, the measurement baseline is moved so that the point measured by the cross-shaped magnetometer array is closer to point D of the theoretical value.

[0077] Therefore, the gradient tensor error matrix is ​​introduced. In actual measurement, the measured value of the gradient tensor G T Recorded as

[0078]

[0079] Among them, G T represents the actual measured value of the gradient tensor, G represents the gradient tensor matrix, g1, g2, g3, g4, g5, g6, g7, g8, and g9 represent the row and column elements of the error gradient tensor, respectively.

[0080] Assume that the following equations hold:

[0081]

[0082] where r x+ 、r y+ 、r x- 、r y-represents the distance from the 1st, 2nd, 3rd, 4th magnetometer in the cross magnetometer array to the permanent magnet, x, y, z represent the coordinates of the 0th magnetometer on the x, y, z axes of the three-dimensional coordinate system, d represents the distance from the 1st, 2nd, 3rd, 4th magnetometer to the 0th magnetometer in the cross magnetometer array, a and b represent the distance deviation from the positions of the 1st and 3rd magnetometer on the x1 axis and the 2nd and 4th magnetometer on the y1 axis during actual measurement to the 1st and 3rd magnetometer and the 2nd and 4th magnetometer of the cross magnetometer array established with a fixed distance d, wherein the fixed distance d represents the distance from the 1st, 2nd, 3rd, 4th magnetometer to the 0th magnetometer in the cross magnetometer array.

[0083] Then the five independent elements of the gradient tensor error matrix can be expressed as:

[0084]

[0085] in B xx , B xy , B xz Respectively represent the size of the components of B1 on the x, y, and z axes, B yy , B yz Respectively represent the size of the components of B2 on the y and z axes.

[0086] In order to verify the anti-interference ability of the algorithm, this experiment was conducted in a laboratory with many electrical appliances, and random points were selected for positioning experiments. The position of the fixed non-magnetic turntable remains unchanged, and the relative position of the non-magnetic turntable and the measurement array is changed by changing the position of the measurement array. The permanent magnet is fixed in the center of the non-magnetic turntable, that is, the center of the permanent magnet coincides with the center of the non-magnetic turntable. The speed of the non-magnetic turntable is set to 4r / s. In order to examine the positioning effect from different angles, three variables are defined: relative distance error, azimuth angle, and pitch angle. The specific calculation formula is as follows:

[0087]

[0088]

[0089]

[0090] Where Ep, Et, and Er represent the azimuth angle, pitch angle, and relative distance errors of the 0th magnetometer relative to the permanent magnet, respectively.

[0091] In order to more easily distinguish the magnetic field generated by the permanent magnet, the experiment uses a rotating permanent magnet model for positioning experiments. Figure 5 As shown in the figure, this experiment uses a rectangular permanent magnet with a length of 9.6 cm, a width of 4.7 cm, and a height of 1.7 cm. Figure 6As shown in the figure, the permanent magnet rotates uniformly on the turntable at a constant angular velocity of 4 rad / s. Figure 7 As shown, at another point on the plane which is parallel to the xy plane in space and the x1 axis is parallel to the x axis, and the y1 axis is parallel to the y axis, there is a cross magnetometer to receive the permanent magnet magnetic field signal, and then send the received permanent magnet magnetic field signal to the computer for processing.

[0092] The Butterworth filter and the harmonic wavelet filter are used to process the permanent magnet magnetic field signal successively. The central sampling frequency of the Butterworth filter is 4 Hz, the passband is 0.2, and the stopband is 0.4. Since the permanent magnet rotates at a constant speed of 4 rad / s, and the electromagnetic field in the experimental environment changes at a frequency of 50 Hz, most of the geomagnetic field and environmental magnetic field can be filtered out by the Butterworth filter, and the filtered permanent magnet magnetic field signal is output. Next, the filtered permanent magnet magnetic field signal is extracted by the harmonic wavelet filter. Since the analysis bandwidth of the harmonic wavelet filter for the permanent magnet magnetic field signal gradually decreases from high frequency to low frequency in a 1 / 2 relationship, the low-frequency part of the permanent magnet magnetic field signal is divided more finely, and the resolution of the low-frequency magnetic field vector signal is high, which is conducive to the extraction of characteristic magnetic field signals. Therefore, the harmonic wavelet filter can be used to extract useful sinusoidal magnetic field vector signals from the magnetic field data.

[0093] The cross-shaped magnetometer array consists of 5 magnetometers. Taking one of the magnetometers as an example, the distribution of the modulated magnetic field signal obtained in the experiment is as follows: Figure 8 As shown, the trends of the modulated magnetic field signals of the other four magnetometers are similar.

[0094] exist Figure 8 In the embodiment, the magnetic field components in the x-axis direction and the y-axis direction have sinusoidal wave characteristics, but due to the large fluctuation of the magnetic field in the z-axis direction, the total magnetic field signal actually obtained is unstable.

[0095] Since the magnetic field generated by the permanent magnet has the properties of a sine wave, the Butterworth filter is used to process the permanent magnet magnetic field signal received by the magnetometer. The original permanent magnet magnetic field signal before processing is as follows: Fig. 9 As shown, the filtered permanent magnet magnetic field signal is as follows Fig.10 shown.

[0096] Since the rotation speed of the non-magnetic turntable needs an acceleration process to reach a constant value, the permanent magnet magnetic field signal after filtering is unstable at the beginning. However, when the rotation speed is constant, the Butterworth filter can filter out the permanent magnet magnetic field signal better and obtain a filtered permanent magnet magnetic field signal with good effect.

[0097] Since the harmonic wavelet transform has a high resolution for low-frequency magnetic field vector signals, the harmonic wavelet filter is used to process the permanent magnet magnetic field signal again. The processing results are as follows: Fig.11 shown.

[0098] Since the analysis bandwidth of the harmonic wavelet filter for the permanent magnet magnetic field signal gradually decreases from high frequency to low frequency in a 1 / 2 relationship, the period of the filtered permanent magnet magnetic field signal is halved.

[0099] The spatial target positioning method based on rotating permanent magnets proposed in the present invention is one of the few rotating magnetic field positioning methods. The use of rotating permanent magnets solves the problem that the traditional gradient tensor method cannot produce magnetic field signals. In view of the fact that there must be errors in solving the gradient tensor using the two-point method, the error gradient matrix is ​​used to reduce the error in principle and can effectively improve the accuracy of the magnetic positioning system.

Claims

1. A spatial target positioning method based on a rotating permanent magnet, characterized in that: Specifically Place the permanent magnet on a turntable that can rotate at a constant speed. Assume that the center point of the permanent magnet is located at the origin o of the three-dimensional coordinate system oxyz in space. The permanent magnet can rotate at a fixed speed. Then the three components of the magnetic field at any point in the coordinate system with the permanent magnet as the origin can be expressed as: Among them, B1, B2, and B3 represent the magnitude of the magnetic field of the permanent magnet on the x, y, and z axes respectively; m x 、m y 、m z represents the magnitude of the components of the permanent magnet’s magnetic moment on the x, y, and z axes respectively; x, y, and z represent the coordinates of the target point on the x, y, and z axes of the three-dimensional coordinate system in space respectively; r represents the distance from the target point to the origin of the coordinate axis; u0 is a constant with a size of 4π×10 -7 ; The cross-shaped magnetometer array is composed of 5 magnetometers with exactly the same parameters. A new coordinate system o1x1y1 is established with the center of the 0th magnetometer as the origin, where the x1-y1 plane is parallel to the xy plane, the x1 axis is parallel to the x axis, and the y1 axis is parallel to the y axis; the first magnetometer is arranged on the positive half axis of the x1 axis, the second magnetometer is arranged on the positive half axis of the y1 axis, the third magnetometer is arranged on the negative half axis of the x1 axis, and the fourth magnetometer is arranged on the negative half axis of the y1 axis; According to the two-point method derivation principle, the five independent gradient tensor elements of the 0th magnetometer are obtained as follows: Among them B xx , B xy , B xz Respectively represent the size of the components of B1 on the x, y, and z axes, B yy , B yz Respectively represent the magnitude of the component of B2 on the y and z axes; B1, B2, B3 represent the magnitude of the magnetic field of the permanent magnet on the x, y, z axes; Indicates the x-axis magnetic field value of the first magnetometer, Respectively represent the x, y, and z axis magnetic field magnitude values ​​of the second magnetometer, Respectively represent the x-axis and z-axis magnetic field magnitude values ​​of the third magnetometer, They respectively represent the x-, y-, and z-axis magnetic field magnitude values ​​of the 4th magnetometer. According to the divergence and gradient of the magnetic source being zero, the following conclusions can be drawn: When the cross-shaped magnetometer array solves the gradient tensor matrix, point B is the actual measurement position of the cross-shaped magnetometer array and point D is the theoretical position of the gradient tensor. Since the attenuation of the magnetic field is not a linear relationship, there must be errors in the calculation in principle. Therefore, it is necessary to introduce the gradient tensor error matrix; in actual measurement, the measured value of the gradient tensor G T Denoted as: Among them, G T G T represents the actual measured value of the gradient tensor, G represents the gradient tensor matrix, g1, g2, g3, g4, g5, g6, g7, g8, g9 represent the row and column elements of the error gradient tensor respectively; Assume that the following equations hold: where r x+ 、r y+ 、r x- 、r y- Respectively represent the distances from the 1st, 2nd, 3rd, and 4th magnetometers in the cross magnetometer array to the permanent magnet, x, y, and z represent the coordinates of the 0th magnetometer on the x, y, and z axes of the three-dimensional coordinate system in space, d represents the distances from the 1st, 2nd, 3rd, and 4th magnetometers in the cross magnetometer array to the 0th magnetometer, and a and b represent the distance deviations from the positions of the 1st and 3rd magnetometers on the x1 axis and the 2nd and 4th magnetometers on the y1 axis during actual measurement to the positions of the 1st and 3rd magnetometers and the 2nd and 4th magnetometers of the cross magnetometer array established with a fixed distance d; Then the five independent elements of the gradient tensor error matrix are expressed as: in According to the Euler deconvolution equation of the magnetic field, the single-point positioning equation of the 0th magnetometer is obtained as follows: Among them, B xx , B xy , B xz Respectively represent the size of the components of B1 on the x, y, and z axes, B yx , B yy , B yz Respectively represent the size of the components of B2 on the x, y, and z axes, B zx , B zy , B zz Respectively represent the component size of B3 on the x, y, and z axes; In the specific solution, the 3*3 matrix The specific solutions of the parameters in are as follows: Using the data of the 1st, 2nd, 3rd, and 4th magnetometers, according to formula (2), we can solve B xx , B xy , B xz , B yy , B yz , then according to formula (3), solve B yx , B zx , B zy , B zz ,and It can be obtained directly through the 0th magnetometer.

2. The method for spatial target positioning based on rotating permanent magnets according to claim 1, characterized in that: The Butterworth filter and harmonic wavelet transform are used to process the useful sinusoidal magnetic field vector signal. The center sampling frequency of the Butterworth filter is 4 Hz, the passband is 0.2, and the stopband is 0.4; the permanent magnet rotates at a constant speed of 4 rad / s, and the electromagnetic field in the experimental environment changes at a frequency of 50 Hz.

3. The method for spatial target positioning based on rotating permanent magnets according to claim 1, characterized in that: The permanent magnet is a cuboid with a length of 9.6 cm, a width of 4.7 cm, and a height of 1.7 cm.

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