An aeromagnetic compensation method for vector magnetic field sensor based on small signal model

Abstract

The present invention discloses an aeromagnetic compensation method for a vector magnetic field sensor based on a small signal model, the steps of which include: using an unmanned aerial vehicle magnetic survey system to fly multiple survey lines to obtain magnetic field data for each survey line; preprocessing the obtained magnetic field data to filter out high-frequency interference magnetic fields in the magnetic field data; using a high-pass filter to extract platform interference magnetic fields in the magnetic field data; establishing a linear equation group of compensation parameters based on a small signal compensation model; solving the linear equation group using a least squares method to determine the compensation parameters; and applying the compensation parameters to the aeromagnetic compensation of a vector magnetic field sensor. The aeromagnetic compensation method for a vector magnetic field sensor can realize effective aeromagnetic compensation of a vector magnetic field sensor without the need for additional sensors or a rotating magnetic field sensor system, and has low requirements for a flight platform.

Description

Technical Field

[0001] The invention relates to an aeromagnetic compensation method for a vector magnetic field sensor, in particular to an aeromagnetic compensation method for a vector magnetic field sensor based on a small signal model. Background Art

[0002] In recent years, the magnetic field variable system based on drones has received extensive attention and has been widely used in shallow resource exploration, archaeology and underground ferromagnetic target detection. The drone magnetic measurement system realizes the measurement of spatial magnetic field variables by loading scalar magnetic field sensors, vector magnetic field sensors or two sensors, so as to invert the characteristics, positioning and identification of magnetic anomaly targets. In actual work, the interference magnetic field generated by the drone platform will be superimposed on the spatial magnetic field signal, resulting in the quality of drone magnetic measurement data being lower than that of ground magnetic measurement, resulting in large data measurement errors and inaccurate measurements. Therefore, aeromagnetic compensation is indispensable. At present, the aeromagnetic compensation technology based on scalar magnetic field sensors is more mature, and the aeromagnetic compensation method based on vector magnetic field sensors has many difficulties. The existing vector sensor aeromagnetic compensation models are all based on the fact that the modulus value of the measured magnetic field signal in the compensation operation is a constant. However, the measurement result of the magnetic field sensor fixed on the drone is the superposition of the geomagnetic field and the platform interference magnetic field. The platform interference magnetic field is closely related to the maneuver and attitude of the system. Therefore, even if the center position of the drone magnetic measurement system is fixed, its measurement result is still time-varying, resulting in residual errors in the traditional compensation method. Summary of the invention

[0003] Purpose of the invention: To address the problem of interference of the magnetic field generated by the platform on the measured spatial magnetic field during aeromagnetic measurement, an aeromagnetic compensation method for a vector magnetic field sensor based on a small signal model is provided, which can achieve effective aeromagnetic compensation of the vector magnetic field sensor without the need for additional sensors or a rotating magnetic field sensor system, and has low requirements for the flight platform.

[0004] Technical solution: The aeromagnetic compensation method of a vector magnetic field sensor based on a small signal model of the present invention comprises the following steps:

[0005] Step 1: The UAV flies multiple survey lines in a local area, and the platform magnetic measurement system obtains the magnetic field data of each survey line;

[0006] Step 2, preprocessing the acquired magnetic field data to filter out high-frequency interference magnetic fields in the magnetic field data;

[0007] Step 3, construct a high-pass filter, and use the high-pass filter to extract the platform interference magnetic field in the magnetic field data;

[0008] Step 4, establishing a linear equation group of compensation parameters according to the small signal compensation model;

[0009] Step 5, solving the linear equations using the least square method to determine the compensation parameters;

[0010] Step 6: Apply the compensation parameters to the aeromagnetic compensation of the vector magnetic field sensor.

[0011] Furthermore, in step 1, there are at least three survey lines, and magnetic field data of N sampling points are obtained on each survey line.

[0012] Furthermore, in step 2, during preprocessing, a low-pass filter is used to preprocess the acquired magnetic field data.

[0013] Furthermore, in step 3, the specific steps of using a high-pass filter to extract the platform interference magnetic field in the magnetic field data are:

[0014] Set the magnetic field data of the nth sampling point of the vector magnetic field sensor for:

[0015]

[0016] In the formula, is the measured geomagnetic field vector at the nth sampling point, is the measured geomagnetic field vector at the first sampling point, R(n) represents the transformation matrix between the coordinate system of the vector magnetic field sensor at the nth (n≥1) sampling point and the coordinate system of the vector magnetic field sensor at the first sampling point, and satisfies

[0017] is the inductive interference magnetic field caused by the soft iron material in the drone at the nth sampling point, is the induced interference magnetic field caused by the soft iron material in the drone at the first sampling point, and satisfies A is the coefficient matrix of the interference magnetic field caused by soft iron, which is a symmetric matrix;

[0018] is the constant interference magnetic field generated by the drone at the nth sampling point, is the constant interference magnetic field generated by the drone at the first sampling point, and is set satisfy

[0019] Since the platform interference magnetic field is much smaller than the geomagnetic field, the modulus of the magnetic field signal measured by the vector magnetic field is approximately the projection of the geomagnetic field modulus superimposed on the platform interference magnetic field in the geomagnetic field direction. Therefore, the modulus of the magnetic field signal at the nth sampling point satisfies:

[0020]

[0021] In the formula, ‖‖ represents the L2 norm, is the unit vector of the geomagnetic field vector at the nth sampling point; combined with equations (1) and (2), the platform interference magnetic field extracted by the high-pass filter is obtained as follows:

[0022]

[0023] Furthermore, in step 4, the specific steps of establishing a linear equation group of compensation parameters according to the small signal compensation model are:

[0024] According to the Rodriguez rotation formula, R(n) is calculated according to and Estimated to be:

[0025]

[0026] In the formula,

[0027] Since the induced interference magnetic field and constant interference magnetic field generated by the UAV platform are much smaller than the geomagnetic field vector Therefore, in formula (2) Approximately equal to then The approximate result is:

[0028]

[0029] In the formula, B mx (n), B my (n) and B mz (n) are the output results of the vector magnetic field sensor at the nth (n=1, 2, ..., N) sampling point, thereby converting formula (3) into a linear equation of compensation parameters, and writing the linear equation in vector form as follows:

[0030]

[0031] In the formula, vector

[0032] Furthermore, in step 5, the specific steps of determining the compensation parameters using the least squares method are:

[0033] Obtain the N sampling point data obtained from the compensation flight, and then form a series of linear equations according to formula (6):

[0034] PX c =B h (7)

[0035] Where, X c is the compensation parameter, X c =[α xx α xy αxz α yy α yz α zz b x b y b z ] T ,definition p 1 、p 2 , ... and p N Respectively represent the vectors at the 1st, 2nd, ... and Nth sampling points, and define …and They respectively represent the signals of the magnetic field measured at the (n=1, 2, …, N)th sampling point after high-pass filtering;

[0036] Then P and B h Calculate the compensation parameter X of the system c for:

[0037] X c =(P T P) -1 P T B h (8)

[0038] Where P T is the transpose of P.

[0039] Furthermore, in step 6, the specific steps of applying the compensation parameters to the aeromagnetic compensation of the vector magnetic field sensor are:

[0040] Determine the compensation parameter X according to formula (8): c After that, the compensation magnetic field signal is obtained for:

[0041]

[0042] Compared with the prior art, the present invention has the following beneficial effects: (1) The compensation scheme proposed in the present invention does not require additional sensors, and only requires a single vector magnetic field sensor to achieve self-compensation; (2) The compensation flight in the compensation scheme proposed in the present invention is simpler than the compensation flight specified in the existing compensation scheme, and does not require a rotating magnetic field sensor system, and has low requirements for the flight platform; (3) The compensation performance of the compensation scheme proposed in the present invention is better than that of the traditional compensation scheme. The existing compensation scheme is generally based on estimating the compensation parameters of the system based on the constant modulus of the magnetic field signal measured by the vector magnetic field sensor during the compensation flight. However, in actual applications, the attitude of the flight platform will continue to change during the flight, and the measured modulus of the magnetic field signal is a changing parameter, resulting in a large residual in the magnetic field after compensation in the prior art. The small signal compensation model proposed in the present invention derives a mathematical model between the attitude change of the flight platform and the platform interference magnetic field, which overcomes the problem caused by the assumption that the modulus of the magnetic field signal remains unchanged, and the compensation performance is better than that of the existing compensation scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic flow chart of the small signal magnetic compensation method of the present invention;

[0044] Figure 2 A schematic diagram of the flight trajectory of the UAV magnetic measurement system of the present invention;

[0045] Figure 3 A schematic diagram of the platform interference magnetic field before and after compensation in the compensation flight of the present invention;

[0046] Figure 4 It is a schematic diagram of the platform interference magnetic field before and after compensation in the test flight of the present invention;

[0047] Figure 5 It is a schematic diagram of the total magnetic field of the measuring line before and after the SSM compensation of the present invention;

[0048] Figure 6 It is a schematic diagram of the superposition of the geomagnetic field and the platform interference magnetic field of the present invention. DETAILED DESCRIPTION

[0049] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0050] Embodiment 1:

[0051] like Figure 1 As shown, the aeromagnetic compensation method of a vector magnetic field sensor based on a small signal model disclosed in the present invention comprises the following steps:

[0052] Step 1: In a local area, a drone flies multiple survey lines, and the magnetic field data of each survey line is obtained through the drone platform magnetic measurement system;

[0053] Step 2, downloading the acquired magnetic field data, and preprocessing the acquired magnetic field data to filter out high-frequency interference magnetic fields in the magnetic field data;

[0054] Step 3, construct a high-pass filter, and use the high-pass filter to extract the platform interference magnetic field in the magnetic field data;

[0055] Step 4, establishing a linear equation group of compensation parameters according to the small signal compensation model;

[0056] Step 5, solving the linear equations using the least square method to determine the compensation parameters;

[0057] Step 6: Apply the compensation parameters to the aeromagnetic compensation of the vector magnetic field sensor.

[0058] Furthermore, in step 1, there are at least three survey lines, preferably five survey lines, and magnetic field data of N sampling points are obtained on each survey line, and the number of sampling points N is at least 9.

[0059] Furthermore, in step 2, during preprocessing, a low-pass filter is used to preprocess the acquired magnetic field data.

[0060] Furthermore, in step 3, the specific steps of using a high-pass filter to extract the platform interference magnetic field in the magnetic field data are:

[0061] Set the magnetic field data of the nth sampling point of the vector magnetic field sensor for:

[0062]

[0063] In the formula, is the measured geomagnetic field vector at the nth sampling point, is the measured geomagnetic field vector at the first sampling point, R(n) represents the transformation matrix between the coordinate system of the vector magnetic field sensor at the nth (n≥1) sampling point and the coordinate system of the vector magnetic field sensor at the first sampling point, and satisfies

[0064] is the inductive interference magnetic field caused by the soft iron material in the drone at the nth sampling point, is the induced interference magnetic field caused by the soft iron material in the drone at the first sampling point, and satisfies A is the coefficient matrix of the interference magnetic field caused by soft iron, which is a symmetric matrix;

[0065] is the constant interference magnetic field generated by the drone at the nth sampling point, is the constant interference magnetic field generated by the drone at the first sampling point, and is set satisfy

[0066] The measurement result of the vector magnetic field sensor is the superposition of the geomagnetic field and the platform interference magnetic field, such as Figure 6 As shown in the figure, since the platform interference magnetic field is much smaller than the geomagnetic field, the modulus of the magnetic field signal measured by the vector magnetic field is approximately the geomagnetic field modulus superimposed on the projection of the platform interference magnetic field in the geomagnetic field direction. Therefore, the modulus of the magnetic field signal at the nth sampling point satisfies:

[0067]

[0068] In the formula, ‖‖ represents the L2 norm, is the unit vector of the geomagnetic field vector at the nth sampling point; combined with equations (1) and (2), the platform interference magnetic field extracted by the high-pass filter is obtained as follows:

[0069]

[0070] Furthermore, in step 4, the specific steps of establishing a linear equation group of compensation parameters according to the small signal compensation model are:

[0071] According to the Rodriguez rotation formula, R(n) is calculated according to and Estimated to be:

[0072]

[0073] In the formula,

[0074] Since the induced interference magnetic field and constant interference magnetic field generated by the UAV platform are much smaller than the geomagnetic field vector Therefore, in formula (2) Approximately equal to then The approximate result is:

[0075]

[0076] In the formula, B mx (n), B my (n) and B mz (n) are the output results of the vector magnetic field sensor at the nth (n=1, 2, ..., N) sampling point, thereby converting formula (3) into a linear equation of compensation parameters, and writing the linear equation in vector form as follows:

[0077]

[0078] In the formula, vector

[0079] Furthermore, in step 5, the specific steps of determining the compensation parameters using the least squares method are:

[0080] According to formula (6), in order to determine the compensation parameters of the system, it is necessary to determine and vector p n .in, It is the raw data of the vector magnetic field sensor to compensate for the platform interference magnetic field during flight. After high-pass filtering, we get According to equations (4), (5) and the measurement results of the vector magnetic field sensor, the vector p can be determined n , obtain the N sampling point data obtained from the compensation flight, and then form a series of linear equations according to formula (6):

[0081] PX c =B h (7)

[0082] Where, X c is the compensation parameter, X c =[α xx α xy α xz α yy α yz α zz b x b y b z ] T ,definition p 1 、p 2 , ... and p N Respectively represent the vectors at the 1st, 2nd, ... and Nth sampling points, and define …and They respectively represent the signals of the magnetic field measured at the (n=1, 2, …, N)th sampling point after high-pass filtering;

[0083] Then P and B h Calculate the compensation parameter X of the system c for:

[0084] X c =(P T P) -1 P T B h (8)

[0085] Where P T is the transpose of P.

[0086] Furthermore, in step 6, the specific steps of applying the compensation parameters to the aeromagnetic compensation of the vector magnetic field sensor are:

[0087] Determine the compensation parameter X according to formula (8): c After that, the compensation magnetic field signal is obtained for:

[0088]

[0089] like Figure 2 The results of field experiments using the specific implementation of the present invention are shown in FIG. The UAV flies 10 measurement lines with a length of 17 m and a measurement line interval of 1 m. The large “×” is the flight starting point of the UAV, the curve connected by the small “×” is the compensation flight data, and the curve connected by the “o” is the test flight data.

[0090] like Figure 3 As shown, the traditional vector magnetic field sensor compensation method SCM and the small signal model-based compensation method SSM are used to process the data of the compensation flight and the test flight.

[0091] like Figure 4 As shown in Figure 2, the magnetic field still has residual error after the traditional SCM compensation, and the root mean square error after compensation is 4.54nT. The magnetic field residual after the SSM compensation method based on the small signal model is 1.94nT, and the compensation performance is improved by 57.26%. Figure 4 It can be seen that the performance of the compensation method SSM based on the small signal model is consistent with the experimental results of the compensation flight, which is better than the traditional SCM compensation algorithm.

[0092] like Figure 5 As shown in the figure, the magnetic measurement system flies a horizontal line above a target and collects the magnetic field signal above it. Figure 5 It can be seen that the comparison of the total magnetic field signal before and after the proposed SSM compensation is adopted.

[0093] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. An aeromagnetic compensation method for a vector magnetic field sensor based on a small signal model, characterized in that: The steps include: Step 1: The UAV flies multiple survey lines in a local area, and the platform magnetic measurement system obtains the magnetic field data of each survey line; Step 2, preprocessing the acquired magnetic field data to filter out high-frequency interference magnetic fields in the magnetic field data; Step 3, construct a high-pass filter, and use the high-pass filter to extract the platform interference magnetic field in the magnetic field data; Step 4, establishing a linear equation group of compensation parameters according to the small signal compensation model; Step 5, solving the linear equations using the least square method to determine the compensation parameters; Step 6, applying the compensation parameters to the aeromagnetic compensation of the vector magnetic field sensor; In step 4, the specific steps of establishing the linear equations of compensation parameters according to the small signal compensation model are: According to the Rodriguez rotation formula, R(n) is calculated according to and Estimated to be: In the formula, The induced interference magnetic field and constant interference magnetic field generated by the UAV platform are much smaller than the geomagnetic field vector In formula (2) Approximately equal to The approximate result is: In the formula, B mx (n), B my (n) and B mz (n) are the output results of the vector magnetic field sensor at the nth (n=1, 2, ..., N) sampling point, thereby converting formula (3) into a linear equation of compensation parameters, and writing the linear equation in vector form as follows: In the formula, vector 2. The aeromagnetic compensation method of a vector magnetic field sensor based on a small signal model according to claim 1, characterized in that: In step 1, there are at least three survey lines, and magnetic field data of N sampling points are obtained on each survey line.

3. The aeromagnetic compensation method of a vector magnetic field sensor based on a small signal model according to claim 1, characterized in that: In step 2, during preprocessing, a low-pass filter is used to preprocess the acquired magnetic field data.

4. The aeromagnetic compensation method of a vector magnetic field sensor based on a small signal model according to claim 1, characterized in that: In step 3, the specific steps of using a high-pass filter to extract the platform interference magnetic field in the magnetic field data are as follows: Set the magnetic field data of the nth sampling point of the vector magnetic field sensor for: In the formula, is the measured geomagnetic field vector at the nth sampling point, is the measured geomagnetic field vector at the first sampling point, R(n) represents the transformation matrix between the coordinate system of the vector magnetic field sensor at the nth (n≥1) sampling point and the coordinate system of the vector magnetic field sensor at the first sampling point, and satisfies is the inductive interference magnetic field caused by the soft iron material in the drone at the nth sampling point, is the induced interference magnetic field caused by the soft iron material in the drone at the first sampling point, and satisfies A is the coefficient matrix of the interference magnetic field caused by soft iron, which is a symmetric matrix; is the constant interference magnetic field generated by the drone at the nth sampling point, is the constant interference magnetic field generated by the drone at the first sampling point, and is set satisfy The platform interference magnetic field is much smaller than the geomagnetic field. The modulus of the magnetic field signal measured by the vector magnetic field is approximately the geomagnetic field modulus superimposed on the projection of the platform interference magnetic field in the geomagnetic field direction. The modulus of the magnetic field signal at the nth sampling point satisfies: In the formula, ‖‖ represents the L2 norm, is the unit vector of the geomagnetic field vector at the nth sampling point; combined with equations (1) and (2), the platform interference magnetic field extracted by the high-pass filter is obtained as follows:

5. The aeromagnetic compensation method of a vector magnetic field sensor based on a small signal model according to claim 1, characterized in that: In step 5, the specific steps of determining the compensation parameters using the least squares method are: Obtain the N sampling point data obtained from the compensation flight, and then form a series of linear equations according to formula (6): PXc=Bn(7) Where, X c is the compensation parameter, X c =[α xx α xy α xz α yy α yz α zz b x b y b z ] T ,definition p1, p2, ... and p N Respectively represent the vectors at the 1st, 2nd, ... and Nth sampling points, and define …and They respectively represent the signals of the magnetic field measured at the (n=1, 2, …, N)th sampling point after high-pass filtering; Then P and B h Calculate the compensation parameter X of the system c for: X c =(P T P) -1 P T B h (8) Where P T is the transpose of P.

6. The aeromagnetic compensation method of a vector magnetic field sensor based on a small signal model according to claim 5, characterized in that: In step 6, the specific steps of applying the compensation parameters to the aeromagnetic compensation of the vector magnetic field sensor are: Determine the compensation parameter X according to formula (8): c After that, the compensation magnetic field signal is obtained for:

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