Simulation method for determining calibration error of inclinometer

Abstract

The invention discloses a simulation method for determining calibration errors of an inclinometer, which comprises the following steps of: firstly, acquiring a simulation measurement value of a three-axis sensor, an error measurement value of the three-axis sensor and a rotary table reference angle matrix R, and further determining a second calibration multiplication coefficient matrix and a second calibration addition coefficient matrix of the three-axis sensor by utilizing a least square method; then, a verification rotation position is randomly constructed, a simulation measurement value for verifying the three-axis acceleration sensor and a calibration value for verifying errors of the three-axis magnetic sensor are obtained, finally, the average value of the azimuth angle relative calibration errors serves as the calibration error value of the azimuth angle of the three-axis magnetic sensor, and simulation of the calibration errors of the inclinometer is achieved. The technical problems that in the prior art, an inclinometry calibration method is too long in error evaluation time and low in efficiency are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of geophysical well logging, and in particular relates to a simulation method for determining an inclinometer calibration error. Background Art

[0002] Coal is a major fossil energy source in my country. Water and gas are the main sources of hazards during coal mining. Drilling to extract water and gas from coal mines is the most effective means of disaster prevention. Inclinometers can accurately measure borehole trajectories, thereby understanding the effectiveness of gas control in mining areas and preventing blind spots in extraction. Inclinometer measurements are affected by multiple factors, among which the calibration method is a major factor affecting the accuracy of borehole trajectory measurements. Currently used inclinometer calibration methods primarily involve multi-position calibration, such as the twelve-position method, the twenty-four-position method, and artificial intelligence methods. Most existing methods evaluate the calibration error by fixing the inclinometer on a high-precision non-magnetic turntable and comparing the error between the measured value and the non-magnetic turntable output. This approach suffers from the following drawbacks: calibration is time-consuming, requiring one to three hours per evaluation. Furthermore, during the method testing phase, the calibration error of different methods, error types, and measurement accuracies must be evaluated, resulting in a large number of tests and a long calibration process, making it difficult to meet the needs of method research. Summary of the Invention

[0003] In view of the defects and shortcomings of the existing technology, the present invention provides a simulation method for determining the calibration error of an inclinometer, so as to solve the technical problems of the existing inclinometer calibration method, such as long error assessment time and low evaluation efficiency.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A simulation method for determining an inclinometer calibration error comprises the following steps:

[0006] Step 1: placing a calibrated inclinometer on a three-axis non-magnetic turntable, wherein the inclinometer is provided with a three-axis magnetic sensor and a three-axis acceleration sensor;

[0007] Step 2: Using a three-axis magnetic sensor to obtain multiple sets of geomagnetic field measurement values in the northeast celestial coordinate system, and using the average value of the multiple sets of geomagnetic field measurement values as the standard geomagnetic field value; using a three-axis acceleration sensor to obtain multiple sets of gravitational acceleration measurement values in the northeast celestial coordinate system, and using the average value of the multiple sets of gravitational acceleration measurement values as the standard gravitational acceleration value;

[0008] Step 3, setting multiple simulated rotation positions of the three-axis non-magnetic turntable, and forming a turntable reference angle matrix with multiple turntable reference angles corresponding to the multiple simulated rotation positions; obtaining a turntable coordinate rotation matrix based on the obtained turntable reference angle matrix and the existing coordinate rotation matrix; multiplying the standard geomagnetic field value obtained in step 2 by the turntable coordinate rotation matrix to obtain multiple three-axis magnetic sensor simulated measurement values; multiplying the standard gravity acceleration value obtained in step 2 by the turntable coordinate rotation matrix to obtain multiple three-axis acceleration sensor simulated measurement values;

[0009] Step 4: Adding Gaussian distributed noise to each obtained three-axis magnetic sensor simulation measurement value to obtain multiple three-axis magnetic sensor noisy measurement values;

[0010] Step 5: Setting a first calibration multiplication coefficient matrix and a first calibration addition coefficient matrix for instrument measurement error calibration; obtaining a plurality of three-axis magnetic sensor error-containing measurement values based on the set first calibration multiplication coefficient matrix, the first calibration addition coefficient matrix, and the plurality of three-axis magnetic sensor noise-containing measurement values obtained in step 4;

[0011] Step 6: Using a multi-position calibration method, according to the error-containing measurement values of the three-axis magnetic sensor and the turntable reference angle matrix, a least square method is used to determine a second calibration multiplication coefficient matrix and a second calibration addition coefficient matrix;

[0012] Step 7. Randomly set multiple verification rotation positions of the three-axis non-magnetic turntable within [0°, 360°], and form a turntable verification reference angle matrix with multiple turntable reference angles corresponding to the multiple verification rotation positions; obtain the turntable verification coordinate rotation matrix based on the turntable verification reference angle matrix and the existing coordinate rotation matrix; multiply the standard geomagnetic field value obtained in step 2 by the turntable verification coordinate rotation matrix to obtain multiple simulated measurement values for three-axis magnetic sensor verification; multiply the standard gravity acceleration value obtained in step 2 by the turntable verification coordinate rotation matrix to obtain multiple simulated measurement values for three-axis acceleration sensor verification;

[0013] Step 8: Repeat the operations of steps 4 and 5 to obtain multiple error measurement values for verification of the three-axis magnetic sensor;

[0014] Step 9: Determine multiple error-free verification calibration values for the three-axis magnetic sensor verification based on the multiple simulated measurement values for verification of the three-axis magnetic sensor obtained in step 7, and the second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix obtained in step 6; determine multiple error-containing verification calibration values for the three-axis magnetic sensor based on the multiple error measurement values for verification of the three-axis magnetic sensor obtained in step 8, and the second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix obtained in step 6;

[0015] Step 10: Based on the multiple three-axis magnetic sensor verification simulation measurement values and the multiple three-axis acceleration sensor verification simulation measurement values obtained in step 7, a plurality of error-free azimuths are obtained using an azimuth angle calculation formula; based on the multiple three-axis acceleration sensor verification simulation measurement values obtained in step 7 and the multiple three-axis magnetic sensor error verification calibration values obtained in step 9, a plurality of error-containing azimuths are obtained using an azimuth angle calculation formula;

[0016] Step 11: Determine the azimuth relative calibration error based on the error-free azimuth and the error-containing azimuth;

[0017] Step 12: Repeat steps 7 to 11 for a set number of operations to obtain multiple azimuth relative calibration errors, and then obtain an average value of the azimuth relative calibration errors as the azimuth calibration error value of the three-axis magnetic sensor.

[0018] The present invention also has the following technical features:

[0019] Specifically, the error-containing measurement value of the three-axis magnetic sensor in step 5 is determined by the following formula:

[0020]

[0021] Where,

[0022] HK j is the jth error-containing measurement value of the three-axis magnetic sensor;

[0023] Ke is the multiplication coefficient matrix;

[0024] HDnoise j is the jth noisy measurement value;

[0025] b is the additive coefficient matrix;

[0026] T stands for transpose.

[0027] Furthermore, the second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix described in step 6 are determined by the following formula:

[0028] [C m , C b ]=(HKI T ·HKI) -1 (HKI T ·R)

[0029] Where,

[0030] C m is the second calibration multiplication coefficient matrix;

[0031] C b is the second calibration coefficient matrix;

[0032] HK is the error-containing measurement value of the three-axis magnetic sensor;

[0033] I is a column vector whose elements are all 1;

[0034] R is the turntable reference angle matrix.

[0035] Furthermore, the calibration value for error verification of the three-axis magnetic sensor described in step 9 is determined by the following formula:

[0036] HDtc=C m ·HDt T +C b T

[0037] Where,

[0038] HDtc is the error measurement value used for verification of the three-axis magnetic sensor;

[0039] C m is the second calibration multiplication coefficient matrix;

[0040] C b is the second calibration coefficient matrix;

[0041] HDt is the simulated measurement value used for verification of the three-axis magnetic sensor;

[0042] T stands for transpose.

[0043] Furthermore, the number of operations set in step 12 is 5000 to 10000.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] (1) The method of the present invention can accurately determine the influence of the inclinometer error on the calibration result by changing the error parameter, and further can measure the influence of the error on the calibration method. This solves the problem that when measuring the calibration error using the actual measurement method, multiple errors will affect the measurement result, and the influence of a certain error cannot be determined.

[0046] (2) The method of the present invention can determine the inclinometer calibration error in a very short time (a few seconds) after inputting the relevant parameters. Compared with the existing inclinometer calibration method that takes 1-2 hours to complete the actual measurement of 120 positions, the method of the present invention can greatly shorten the evaluation time and improve the inclinometer calibration efficiency. DETAILED DESCRIPTION

[0047] In the calibration system of the present invention, the movement of the three-axis non-magnetic turntable is manually controlled to achieve the position change of the inclinometer on the three-axis non-magnetic turntable. After the inclinometer moves to a rotational position, the three-axis magnetic sensor and the three-axis acceleration sensor collect data. After the collection and storage are completed, the three-axis non-magnetic turntable moves to the next rotational position for data collection.

[0048] The inventive concept of the present invention is: using pure theoretical values, first simulating theoretical measurement values without errors, adding errors to the theoretical measurement values of the instrument, using the data with added errors to simulate the calibration results, obtaining calibration coefficients, and then using random measurement data to verify the error elimination effect of the calibration coefficients and the effectiveness of the verification method.

[0049] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by any person skilled in the art are within the scope of protection of the present invention.

[0050] Example 1

[0051] In accordance with the above technical solution, this embodiment discloses a simulation method for determining an inclinometer calibration error, comprising the following steps:

[0052] Step 1: placing a calibrated inclinometer on a three-axis non-magnetic turntable, wherein the inclinometer is provided with a three-axis magnetic sensor and a three-axis acceleration sensor;

[0053] Step 2: Using a three-axis magnetic sensor to obtain multiple sets of geomagnetic field measurement values in the northeast celestial coordinate system, and using the average value of the multiple sets of geomagnetic field measurement values as the standard geomagnetic field value; using a three-axis acceleration sensor to obtain multiple sets of gravitational acceleration measurement values in the northeast celestial coordinate system, and using the average value of the multiple sets of gravitational acceleration measurement values as the standard gravitational acceleration value;

[0054] Step 3. Set 12 simulated rotation positions of the three-axis non-magnetic turntable. Each simulated rotation position corresponds to three turntable reference angles (inclination, tool face angle, and azimuth). The turntable reference angles for the 12 simulated rotation positions are shown in the following table:

[0055] inclination Tool face Azimuth inclination Tool face Azimuth 0 0 0 0 90 180 0 0 180 0 90 0 0 180 180 90 90 0 0 180 0 90 270 0 0 270 0 -90 90 0 0 270 180 -90 270 0

[0056] The turntable reference angle matrix R is composed of the turntable reference angles corresponding to the set 12 simulated rotation positions. The matrix dimension is n rows and 3 columns. n varies according to the selected multi-position calibration method. For example, n=12, 24, 120, 276, 322, etc. can be selected. In this embodiment, n=12.

[0057] In the borehole trajectory measurement, the borehole inclinometer is used to realize the inclination angle θ and tool face angle of different measuring points. The three basic parameters of the borehole inclinometer are measured: azimuth Ψ. Azimuth Ψ is the angle between the magnetic north direction and the projection of the y-axis on the horizontal plane in a counterclockwise direction; inclination θ is the angle between the drilling axis Y and the horizontal plane; and tool face angle φ is the angle from the high side of the borehole to the Z-axis within the borehole cross section. The three basic parameters of the borehole inclinometer can be obtained through a series of rotations of the drill tool coordinate system relative to the geographic coordinate system. Each rotation is equivalent to a coordinate transformation and can be represented by the corresponding transformation matrix. Therefore, the standard form of the three rotations is as follows:

[0058]

[0059] Therefore, according to the turntable reference angle matrix R and the known universal coordinate rotation matrix, the turntable coordinate rotation matrix RRotate can be obtained; the standard geomagnetic field value and the standard gravity acceleration value are rotated to the corresponding turntable reference angle to obtain multiple three-axis magnetic sensor simulation measurement values and multiple three-axis acceleration sensor simulation measurement values, that is, the standard geomagnetic field value is multiplied by the turntable coordinate rotation matrix to obtain multiple three-axis magnetic sensor simulation measurement values; the standard gravity acceleration value is multiplied by the turntable coordinate rotation matrix to obtain multiple three-axis acceleration sensor simulation measurement values, and the three-axis magnetic sensor simulation measurement values and the three-axis acceleration sensor simulation measurement values are all theoretical measurement values that do not contain errors;

[0060] Step 4: Add Gaussian distributed noise to each of the three-axis magnetic sensor analog measurement values and each of the three-axis acceleration sensor analog measurement values obtained in step 3 to obtain 12 three-axis magnetic sensor noisy measurement values and 12 three-axis acceleration sensor noisy measurement values;

[0061] Step 5: In this embodiment, the first calibration multiplication coefficient matrix and the first calibration addition coefficient matrix for instrument measurement error calibration are obtained by a conventional multi-position calibration method. Specifically, the first calibration multiplication coefficient matrix and the first calibration addition coefficient matrix are as follows:

[0062]

[0063] Among them, Ke is the first calibration multiplication coefficient matrix, and b is the first calibration addition coefficient matrix.

[0064] Based on the first calibration multiplication coefficient matrix, the first calibration addition coefficient matrix, and the 12 three-axis magnetic sensor noise-containing measurement values obtained in step 4, the following formula is used to obtain the 12 three-axis magnetic sensor error-containing measurement values;

[0065]

[0066] Where,

[0067] HK j is the jth error-containing measurement value of the three-axis magnetic sensor;

[0068] Ke is the first calibration multiplication coefficient matrix;

[0069] HDnoise j is the jth noisy measurement value of the three-axis magnetic sensor;

[0070] b is the first calibration coefficient matrix;

[0071] T stands for transpose.

[0072] The error-containing measurement value of the three-axis magnetic sensor is the three-axis magnetic sensor simulation data that includes the non-orthogonality error, installation error, soft magnetic error, hard magnetic error, sensitivity error, and measurement error of the simulated instrument.

[0073] Step 6: Calibrate the 12 three-axis magnetic sensor error-containing measurement values obtained in step 5: Use a multi-position calibration method to determine a second calibration multiplication coefficient matrix and a second calibration addition coefficient matrix of the three-axis magnetic sensor based on the 12 three-axis magnetic sensor error-containing measurement values obtained in step 5 and the turntable reference angle matrix R determined in step 3 using a least squares method;

[0074] Specifically, the second calibration coefficient is determined by the following formula:

[0075] [C m , C b ]=(HKI T ·HKI) -1 (HKI T ·R)

[0076] in,

[0077] HK is the error-containing measurement value of the three-axis magnetic sensor;

[0078] I is a column vector whose elements are all 1;

[0079] R is the turntable reference angle matrix;

[0080] C m is the second calibration multiplication coefficient matrix;

[0081] C b is the second calibration coefficient matrix.

[0082] HKI is a matrix composed of HK and I. HK is an n*3 matrix, I is an n*1 matrix, and the resulting HKI is an n*4 matrix.

[0083] Step 7: To evaluate the accuracy and reliability of the calibration coefficient matrix in the entire space, randomly set M verification rotation positions of the three-axis non-magnetic turntable in [0°, 360°], and use the turntable verification angles corresponding to the M verification rotation positions to form the turntable verification angle matrix R t , the matrix dimension is 1 row and 3 columns, according to the turntable reference angle matrix R t and the existing coordinate rotation matrix to obtain the turntable coordinate verification rotation matrix; multiply the standard geomagnetic field value obtained in step 2 by the turntable coordinate verification rotation matrix to obtain M simulated measurement values for three-axis magnetic sensor verification; multiply the standard gravity acceleration value obtained in step 2 by the turntable coordinate verification rotation matrix to obtain M simulated measurement values for three-axis acceleration sensor verification;

[0084] Step 8: Repeat steps 4 and 5 to obtain M error measurement values for verification of the three-axis magnetic sensor.

[0085] Step 9: Determine error-free verification calibration values for the M three-axis magnetic sensors based on the M three-axis magnetic sensor verification simulation measurement values obtained in step 7, and the second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix obtained in step 6. Determine error-containing verification calibration values for the M three-axis magnetic sensors based on the M three-axis magnetic sensor verification error measurement values obtained in step 8, and the second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix obtained in step 6.

[0086] Specifically, the calibration value for the three-axis magnetic sensor error verification is determined by the following formula:

[0087] HDtc=C m ·HDt T +C b T

[0088] Where,

[0089] HDtc is the error measurement value used for verification of the three-axis magnetic sensor;

[0090] C m is the second calibration multiplication coefficient matrix;

[0091] C b is the second calibration coefficient matrix;

[0092] HDt is the simulated measurement value used for verification of the three-axis magnetic sensor;

[0093] T stands for transpose.

[0094] Step 10: Based on the M three-axis magnetic sensor verification simulation measurement values and the M three-axis acceleration sensor verification simulation measurement values obtained in step 7, use the azimuth angle calculation formula to obtain M error-free azimuth angles DAZ; based on the M three-axis acceleration sensor verification simulation measurement values obtained in step 7 and the M three-axis magnetic sensor error verification calibration values obtained in step 9, use the azimuth angle calculation formula to obtain M error-containing azimuth angles DAZn;

[0095] Specifically, the calculation formula for the error-free azimuth angle DAZ is as follows:

[0096]

[0097] in,

[0098]

[0099] Where,

[0100] Among them, Gx, Gr, and Gz are the simulated measurement values verified by the three-axis magnetic sensor, and Bx, B, and Bz are the simulated measurement values verified by the three-axis magnetic sensor.

[0101] Similarly, the azimuth angle DAZn including the error can be obtained by substituting the simulated measurement value of the three-axis acceleration sensor and the calibration value of the three-axis magnetic sensor for error verification into the above-mentioned azimuth angle calculation formula.

[0102] Step 11: Determine the relative calibration errors of the M azimuths based on the M error-free azimuths and the M error-containing azimuths using the following formula:

[0103] r=(DAZn-DAZ) / DAZ*100%

[0104] Where r is the relative calibration error of azimuth, DAZ is the error-free azimuth, and DAZn is the error-containing azimuth.

[0105] Step 12: Repeat steps 7 to 11 for a total of 10,000 times to obtain multiple azimuth relative calibration errors, obtain 10,000 azimuth relative calibration errors, and calculate the average value of the 10,000 azimuth relative calibration errors as the azimuth calibration error value of the three-axis magnetic sensor.

[0106] In this example, when using a non-magnetic turntable to test calibration error, first prepare the inclinometer, a computer equipped with the test program, a data cable, and a power cord. The inclinometer is secured to the three-axis non-magnetic turntable with a dedicated fixture and secured securely. The power cord is connected to the inclinometer, the serial port is connected to the computer, and the pre-installed recording software is launched. The instrument is then allowed to warm up for 5 minutes. After warming up, each test point (rotational position) requires rotating the three-axis non-magnetic turntable to the corresponding reference angle, and then testing and calculating the error. The final calculated azimuth calibration error of the three-axis magnetic sensor in this example was 0.596°, and the calculation took only approximately 0.083 seconds (an average of 8.8 microseconds per point).

[0107] In the prior art, it takes about 1 to 3 hours to calibrate and test the calibration error of 100 points using a non-magnetic turntable (an average of 36 to 108 seconds per point). It can be seen that the method of the present invention can effectively shorten the calibration time.

[0108] The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, all equivalent changes made to the contents described in the claims of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A simulation method for determining the calibration error of an inclinometer, characterized in that: The following steps are involved: Step 1: placing a calibrated inclinometer on a three-axis non-magnetic turntable, wherein the inclinometer is provided with a three-axis magnetic sensor and a three-axis acceleration sensor; Step 2: Using a three-axis magnetic sensor to obtain multiple sets of geomagnetic field measurement values in the northeast celestial coordinate system, and using the average value of the multiple sets of geomagnetic field measurement values as the standard geomagnetic field value; using a three-axis acceleration sensor to obtain multiple sets of gravitational acceleration measurement values in the northeast celestial coordinate system, and using the average value of the multiple sets of gravitational acceleration measurement values as the standard gravitational acceleration value; Step 3, setting multiple simulated rotation positions of the three-axis non-magnetic turntable, and forming a turntable reference angle matrix with multiple turntable reference angles corresponding to the multiple simulated rotation positions; obtaining a turntable coordinate rotation matrix based on the obtained turntable reference angle matrix and the existing coordinate rotation matrix; multiplying the standard geomagnetic field value obtained in step 2 by the turntable coordinate rotation matrix to obtain multiple three-axis magnetic sensor simulated measurement values; multiplying the standard gravity acceleration value obtained in step 2 by the turntable coordinate rotation matrix to obtain multiple three-axis acceleration sensor simulated measurement values; Step 4: Adding Gaussian distributed noise to each obtained three-axis magnetic sensor simulation measurement value to obtain multiple three-axis magnetic sensor noisy measurement values; Step 5: Setting a first calibration multiplication coefficient matrix and a first calibration addition coefficient matrix for instrument measurement error calibration; obtaining a plurality of three-axis magnetic sensor error-containing measurement values based on the set first calibration multiplication coefficient matrix, the first calibration addition coefficient matrix, and the plurality of three-axis magnetic sensor noise-containing measurement values obtained in step 4; Step 6: Using a multi-position calibration method, according to the error-containing measurement values of the three-axis magnetic sensor and the turntable reference angle matrix, a least squares method is used to determine a second calibration multiplication coefficient matrix and a second calibration addition coefficient matrix of the three-axis magnetic sensor; Step 7. Randomly set multiple verification rotation positions of the three-axis non-magnetic turntable within [0°, 360°], and form a turntable verification reference angle matrix with multiple turntable reference angles corresponding to the multiple verification rotation positions; obtain the turntable verification coordinate rotation matrix based on the turntable verification reference angle matrix and the existing coordinate rotation matrix; multiply the standard geomagnetic field value obtained in step 2 by the turntable verification coordinate rotation matrix to obtain multiple simulated measurement values for three-axis magnetic sensor verification; multiply the standard gravity acceleration value obtained in step 2 by the turntable verification coordinate rotation matrix to obtain multiple simulated measurement values for three-axis acceleration sensor verification; Step 8: Repeat the operations of steps 4 and 5 to obtain multiple error measurement values for verification of the three-axis magnetic sensor; Step 9: Determine multiple error-free verification calibration values for the three-axis magnetic sensor verification based on the multiple simulated measurement values for verification of the three-axis magnetic sensor obtained in step 7, and the second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix obtained in step 6; determine multiple error-containing verification calibration values for the three-axis magnetic sensor based on the multiple error measurement values for verification of the three-axis magnetic sensor obtained in step 8, and the second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix obtained in step 6; Step 10: Using the azimuth angle calculation formula based on the multiple three-axis magnetic sensor verification simulation measurement values and the multiple three-axis acceleration sensor verification simulation measurement values obtained in step 7, a plurality of error-free azimuth angles are obtained; using the azimuth angle calculation formula based on the multiple three-axis acceleration sensor verification simulation measurement values obtained in step 7 and the multiple three-axis magnetic sensor error verification calibration values obtained in step 9, a plurality of error-containing azimuth angles are obtained; Step 11: determining a plurality of azimuth relative calibration errors based on a plurality of error-free azimuths and a plurality of error-containing azimuths; Step 12: Repeat steps 7 to 11 for a set number of operations to obtain multiple azimuth relative calibration errors, and then obtain an average value of the azimuth relative calibration errors as the azimuth calibration error value of the three-axis magnetic sensor.

2. The simulation method for determining the calibration error of an inclinometer according to claim 1, wherein: The error-containing measurement value of the three-axis magnetic sensor described in step 5 is determined by the following formula: Where, HK j is the jth error-containing measurement value of the three-axis magnetic sensor; Ke is the first calibration multiplication coefficient matrix; HDnoise j is the jth noisy measurement value of the three-axis magnetic sensor; b is the first calibration coefficient matrix; T stands for transpose.

3. The simulation method for determining the calibration error of an inclinometer according to claim 1, wherein: The second calibration multiplication coefficient matrix and the second calibration addition coefficient matrix described in step 6 are determined by the following formula: [C m , C b = (HKI T ·HKI) -1 (HKI T ·R) where, C m is the second calibration multiplication coefficient matrix; C b is the second calibration coefficient matrix; HK is the error-containing measurement value of the three-axis magnetic sensor; I is a column vector whose elements are all 1; R is the turntable reference angle matrix.

4. The simulation method for determining the calibration error of an inclinometer according to claim 1, wherein: The calibration value for error verification of the three-axis magnetic sensor described in step 9 is determined by the following formula: HDtc=C m ·HDt T +C b T Where, HDtc is the error measurement value used for verification of the three-axis magnetic sensor; C m is the second calibration multiplication coefficient matrix; C b is the second calibration coefficient matrix; HDt is the simulated measurement value used for verification of the three-axis magnetic sensor; T stands for transpose.

5. The simulation method for determining the calibration error of an inclinometer according to claim 1, wherein: The number of calculations set in step 12 is 5,000 to 10,000.

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