CN115586347A - Magnetic sensitivity calibration system and method for linear accelerometer - Google Patents
Magnetic sensitivity calibration system and method for linear accelerometer Download PDFInfo
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Abstract
The invention discloses a magnetic sensitivity calibration system and method for a linear accelerometer, and belongs to the technical field of inertia. The invention mainly comprises a test platform, a direct-current strong magnetic field generating device, a magnetic field control device, a gauss meter, a power supply, a voltmeter and an electric control rotary table. The tested linear accelerometer is connected with a rotating shaft of the electric control rotating platform, and the whole rotating platform is placed in the central area of the direct-current strong magnetic field generating device; the gaussmeter is used for measuring the magnetic induction intensity received by the sensor; the direct-current strong magnetic field generating device is connected with the magnetic field control device to adjust the magnetic induction intensity; the accelerometer output is converted into an equivalent voltage signal through operation. According to the invention, the magnetic sensitivity coupling model based on the linear accelerometer is established, the magnetic sensitivity of the linear accelerometer is tested under a magnetic sensitivity calibration system, test data is used as input and output, and a least square method based on limited memory is adopted for parameter identification, so that the accurate calibration of the magnetic sensitivity and each coefficient of the linear accelerometer is realized.
Description
Technical Field
The invention relates to a magnetic sensitivity calibration system and method for a linear accelerometer, and belongs to the technical field of inertia.
Background
Along with the industrial development, the requirement on the accuracy of sensor measurement in the application of aerospace and weaponry industries is higher and higher, and the magnetic field is more and more concerned by people as one of the important factors influencing the accuracy of the sensor. For example, the aviation inertial navigation system is very complex, the working environment is relatively severe, and the sensors for aviation inertial navigation measurement are mainly acceleration sensors. When the sensors work in the environment with magnetic field interference, the output accuracy of the sensors is greatly reduced due to the influence of the magnetic field, and great potential safety hazards exist for the flight of airplanes. It is therefore necessary to accurately calibrate the magnetic sensitivity coefficients in the acceleration sensor model equation.
Firstly, a method of 'static magnetic field and rotating sensor' is adopted, as the sensor is a sensitive device for vibration, when the sensor rotates, useless signals caused by the sensor are often much larger than signals to be measured, so that an amplifier is always in an overload blocking state, the useless signals caused by environmental vibration and wire movement are mixed with the signals to be measured and cannot be separated during the test, the method for testing the magnetic sensitivity of the piezoelectric sensor has low signal-to-noise ratio and is very difficult, and for a plurality of sensors, the method for testing the magnetic sensitivity of the piezoelectric sensor cannot be used for testing at all; secondly, a method of 'sensor static and magnetic field rotation' is adopted, the method only measures the magnetic sensitivity of a certain plane of the sensor, the magnetic sensitivity of each plane of the sensor cannot be detected in all directions, and if the maximum value of the magnetic sensitivity is positioned on other planes, the magnetic sensitivity cannot be measured.
Ninchen sylvester proposed a solenoid coil as a magnetic field generator to find the maximum magnetic sensitivity by rotating the sensor. Because the sensor is a vibrating element, the sensor can mistake the vibration output quantity of the sensor as the output value of the magnetic sensitivity in the measuring process, so that the measuring error is caused, and the system can not ensure that the sensor is in an effective uniform magnetic field. The Zhu adult and the like solve the problem that the magnetic sensitivity of the sensor measures the uniformity of a magnetic field, and the maximum magnetic sensitivity is found by rotating the sensor, but the problem of vibration noise caused by the rotating sensor exists, the magnetic sensitivity of the sensor in a single plane can only be measured, and the magnetic sensitivity values of other planes of the sensor in the space cannot be measured. International standard ISO/5347-19-1993 method for calibration of vibration and shock sensors magnetic sensitivity test a rotary sensor measures its magnetic sensitivity by placing the sensor in a uniform magnetic field, and there is also a problem that the rotary sensor causes vibration noise. The existing measuring methods all have different defects, are easily interfered by other signals in the measuring process, cause larger measuring result errors, and can not meet the requirement of accurate measurement of the magnetic sensitivity of the piezoelectric acceleration sensor.
In summary, based on the preliminary study of the calibration of the magnetic sensitivity of the vibration sensor, the invention aims at the problems of model errors, identification precision and the like in the calibration of the magnetic sensitivity of the linear accelerometer by taking the technical requirement of realizing the calibration of the magnetic sensitivity of the linear accelerometer of weapons such as electromagnetic guns and the like in a strong magnetic field environment as a background, and mainly develops a deep study around the identification of the magnetic sensitivity coupling model and the magnetic sensitivity parameters of the linear accelerometer, thereby solving the technical problems of related engineering.
Disclosure of Invention
The invention mainly aims to provide a magnetic sensitivity calibration system and a method for a linear accelerometer, which are used for accurately calibrating the magnetic sensitivity and various coefficients of the linear accelerometer by establishing a magnetic sensitivity coupling model based on the linear accelerometer, testing the magnetic sensitivity of the linear accelerometer under the magnetic sensitivity calibration system, taking the obtained test data as input and output and adopting a least square method based on limited memory to carry out parameter identification.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a magnetic sensitivity calibration system for a linear accelerometer, which mainly comprises a test platform, a magnetic field generating device, a magnetic field control device, a gauss meter (magnetic field measuring instrument), a power supply, a voltmeter and an electric control rotary table. The tested line accelerometer is connected with a rotating shaft of the electric control rotating platform, and the whole rotating platform is placed in the central area of the magnetic field generating device; the gaussmeter is used for measuring the magnetic induction intensity of the sensor; the magnetic field generating device is connected with the magnetic field control device to adjust the magnetic induction intensity; the output of the accelerometer of the tested line is converted into an equivalent voltage signal through an operational amplifier and an AD/DA (analog-to-digital) and is acquired by a digital multimeter to obtain an effective real voltage value.
Helmholtz coils are used as magnetic field generating devices and are composed of a pair of identical circular conductor coils. In order to realize the magnetic sensitivity calibration of the linear accelerometer, the magnetic sensitivity distribution of a magnetic field space is analyzed according to the Biot-Saval law, a magnetic sensitivity coupling model based on the linear accelerometer is established, the magnetic sensitivity of the linear accelerometer is tested under a magnetic sensitivity calibration system, the obtained test data is used as input and output, and the least square method based on limited memory is adopted for parameter identification, so that the accurate calibration of the magnetic sensitivity and each coefficient of the linear accelerometer is realized.
The invention also discloses a magnetic sensitivity calibration method for the linear accelerometer, which is realized based on the magnetic sensitivity calibration system for the linear accelerometer, and comprises the following steps:
(1) Horizontally mounting the accelerometer of the line to be tested on a test platform;
(2) Setting a range of the magnetic field intensity to be tested; setting magnetic field intensity intervals; controlling a magnetic field generating device to generate a magnetic field according to the magnetic field intensity interval;
(3) The digital voltmeter performs measurement recording in real time;
(4) Repeating the step (2) until the magnetic field intensity is tested to the maximum, and obtaining a group of measurement data of the test plane;
(5) Rotating the angle of the accelerometer of the measured line;
(6) Repeating the steps (1) to (5) to obtain a new set of measurement data of the test plane;
(7) The angle of the measured linear accelerometer is continuously and uniformly changed, and the linear accelerometer is measured in a plane one by one until the linear accelerometer rotates 360 degrees. And taking the test data as input and output data of the line accelerometer.
(8) And (4) combining the input and output data obtained in the step (7), performing parameter identification by adopting a least square method based on limited memory, and realizing accurate calibration of the magnetic sensitivity and each coefficient of the linear accelerometer.
And further, establishing a magnetic sensitivity coupling model of the linear accelerometer according to the standard model of the linear accelerometer.
First, according to IEEE 836-2009 and IEEE 1293-1998, a linear accelerometer model is selected as shown in equation (1).
Where Y is the linear accelerometer output, K 0 Zero offset, K, of linear accelerometer i Is the linear accelerometer scale factor, K ii Is a second order nonlinear coefficient, K iii Is a third order nonlinear coefficient, K io ，K ip Is the cross-coupling coefficient, K oo ，K pp Is a second order cross-coupled nonlinear coefficient, ε is the measurement noise, A i ,A o ,A p Is the component of the input acceleration on the linear accelerometers IA, OA, PA, in units of gravitational acceleration, g.
However, the above linear accelerometer model does not consider the influence of the magnetic field on the output of the linear accelerometer, which may cause the accuracy of the calibration result to decrease when there is magnetic field interference. Therefore, the method is improved on the original linear accelerometer model to establish a coupling model of the linear accelerometer
Wherein, K m Coefficient of magnetic sensitivity of linear accelerometer, K mm Is the second order nonlinear coefficient of the linear accelerometer magnetic sensitivity, K im ,K om ,K pm Is the cross-coupling coefficient of magnetic sensitivity to other axis inputs, A m Is the magnetic field strength, in units of T.
Therefore, the magnetic sensitivity coupling model of the linear accelerometer is adopted to introduce the coupling terms of the magnetic sensitivity coefficient and other coefficients, so that the influence of a magnetic field on the output of the linear accelerometer can be fully reflected, and the calibration precision of the linear accelerometer is improved.
And further, based on the data obtained by testing as input and output data, performing parameter identification on the data by adopting a limited memory least square method, and realizing the magnetic sensitivity calibration of the linear accelerometer.
When the traditional least square method is used for estimating parameters, a data saturation phenomenon easily occurs. In order to overcome the difficulty and prevent estimation divergence, the invention adopts a least square method based on limited memory to carry out parameter identification on a magnetic sensitivity coupling model of the linear accelerometer.
The limited memory least square method is that when parameter estimation is carried out, the obtained observation data are always the latest observation data of a limited group, and each time a group of latest observation data is added, a group of oldest observation data are discarded. Therefore, the magnetic sensitivity coupling model of the linear accelerometer is subjected to parameter estimation based on the limited memory least square method, so that the data saturation phenomenon caused by increase of test data can be effectively eliminated, and the estimation precision of the magnetic sensitivity coupling model is improved.
Has the beneficial effects that:
1. the invention discloses a magnetic sensitivity calibration system and method for a linear accelerometer, which are used for analyzing the magnetic sensitivity distribution of a magnetic field space according to the Biot-Saval law, establishing the magnetic sensitivity calibration system of the linear accelerometer and providing a corresponding calibration scheme to realize the omnibearing magnetic sensitivity measurement of the linear accelerometer space.
2. According to the magnetic sensitivity calibration system and method for the linear accelerometer, coupling terms of a magnetic sensitivity coefficient and other coefficients are introduced into a constructed magnetic sensitivity coupling model based on the linear accelerometer, so that the physical characteristics of the linear accelerometer in a magnetic environment are accurately reflected, the problem of reduced calibration precision caused by the fact that a traditional linear accelerometer model is not in accordance with an actual model can be solved, and the magnetic sensitivity and various coefficients of the linear accelerometer are accurately calibrated.
3. According to the magnetic sensitivity calibration system and method for the linear accelerometer, disclosed by the invention, the magnetic sensitivity of the linear accelerometer is tested under the magnetic sensitivity calibration system, the obtained test data is used as input and output, and a least square method based on limited memory is adopted for parameter identification, so that the data saturation phenomenon accompanying increase of the test data can be effectively eliminated, and the calibration precision is improved.
Drawings
FIG. 1 is a Helmholtz coil uniform magnetic field distribution plot;
FIG. 2 is a diagram of a linear accelerometer magnetic sensitivity test system;
FIG. 3 is a graph of a line accelerometer magnetic field test;
FIG. 4 is a diagram of a process for identifying magnetic sensitivity parameters of a linear accelerometer.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
the present embodiment provides a magnetic sensitivity calibration system for a linear accelerometer and a magnetic sensitivity calibration method for a linear accelerometer, which are used to implement the magnetic sensitivity calibration method for a linear accelerometer.
In the embodiment, the magnetic sensitivity coupling model based on the linear accelerometer is established, the magnetic sensitivity of the linear accelerometer is tested under the magnetic sensitivity calibration system, the obtained test data is used as input and output, and the least square method based on limited memory is adopted for parameter identification, so that the accurate calibration of the magnetic sensitivity and each coefficient of the linear accelerometer is realized.
The embodiment discloses a magnetic sensitivity calibration method for a linear accelerometer, which comprises the following specific implementation steps:
step one, analyzing the magnetic sensitivity distribution of a magnetic field space, and establishing a linear accelerometer magnetic sensitivity calibration system.
In order to realize the magnetic sensitivity calibration of the linear accelerometer, the magnetic sensitivity distribution of the magnetic field space needs to be analyzed firstly. In the test system, a helmholtz coil is used as a magnetic field generator (magnetic field generating device) of the system, and the magnetic field generator is composed of a pair of identical circular conductor coils, as shown in fig. 1. And (4) analyzing the magnetic sensitivity distribution in the magnetic field space according to the Biao-Saval law, and establishing a magnetic sensitivity coupling model based on a linear accelerometer.
The system for calibrating the magnetic sensitivity of the linear accelerometer mainly comprises a test platform, a magnetic field generating device, a magnetic field controller, a gauss meter (magnetic field measuring instrument), a power supply, a voltmeter, an electric control rotating platform and the like, as shown in figure 2. The linear accelerometer is connected with a rotating shaft of the electric control rotating platform, the whole rotating platform is placed in the central area of the magnetic field generating device, the gaussmeter is placed near the linear accelerometer to measure the magnetic induction intensity of the sensor, the magnetic field generating device is connected with the magnetic field control system to adjust the magnetic induction intensity, the output of the linear accelerometer is converted into equivalent voltage signals through the operational amplifier and the AD/DA, and effective real voltage values are acquired through the digital multimeter.
When the magnetic field generator works, current generated by an excitation power supply flows through a Helmholtz coil of the magnetic field generating device. The magnetic field generating device is activated to generate a magnetic field having a uniformity of 10 at the location of the linear accelerometer mounting -3 Δ H/H, the uniform magnetic field area is a spherical test magnetic field with the radius of 30 mm. And the current intensity is adjusted to change the magnetic field intensity, so that the test of the linear accelerometer under different magnetic field intensities is completed. And controlling a motor driver to drive the horizontal electric control platform to rotate, so as to drive the linear accelerometer to rotate in the spherical magnetic field, and repeating the process to complete the space omnibearing magnetic sensitivity test of the linear accelerometer.
Step two, based on the linear accelerometer magnetic sensitivity calibration system established in the step one, the linear accelerometer magnetic sensitivity is tested under the magnetic sensitivity calibration system, and the obtained test data is used as input and output, and the specific calibration steps are as follows:
(1) Horizontally mounting the accelerometer of the line to be tested on a test platform;
(2) Setting the range of the magnetic field intensity: 0GS to 4000GS; setting the magnetic field intensity interval to be 100GS; controlling a magnetic field generating device to generate a magnetic field according to the magnetic field intensity interval;
(3) The digital voltmeter performs measurement recording in real time;
(4) Repeating the step (2) until the magnetic field intensity is tested to the maximum, and obtaining a group of measurement data of the test plane;
(5) Rotating the angle of the accelerometer of the measured line;
(6) Repeating the steps to obtain a group of new measurement data of the test plane;
(7) The angle of the measured linear accelerometer is continuously and uniformly changed, and the linear accelerometer is measured in a plane one by one until the linear accelerometer rotates 360 degrees. And taking the test data as input and output data of the line accelerometer.
(8) And (6) combining the input and output data obtained in the step (7) to realize the magnetic sensitivity test of the linear accelerometer.
And step three, establishing a magnetic sensitivity coupling model of the linear accelerometer according to the standard model of the linear accelerometer.
First, we select a linear accelerometer model as shown in equation (3) according to IEEE 836-2009 and IEEE 1293-1998.
Where Y is the linear accelerometer output, K 0 Zero offset, K, of linear accelerometer i Is the linear accelerometer scale factor, K ii Is a second order nonlinear coefficient, K iii Is a third order nonlinear coefficient, K io ，K ip Is the cross-coupling coefficient, K oo ，K pp Is a second order cross-coupled nonlinear coefficient, ε is the measurement noise, A i ,A o ,A p Is the component of the input acceleration on the linear accelerometers IA, OA, PA, in units of gravitational acceleration, g.
However, the above-mentioned linear accelerometer model does not consider the influence of the magnetic field on the output of the linear accelerometer, which may result in the reduction of the accuracy of the calibration result when there is magnetic field interference. Therefore, the method is improved on the original linear accelerometer model to establish a coupling model of the linear accelerometer
Wherein, K m Linear accelerometer magnetorSensitivity coefficient, K mm Is the second order nonlinear coefficient of the linear accelerometer magnetic sensitivity, K im ,K om ,K pm Is the cross-coupling coefficient of magnetic sensitivity to other axis inputs, A m Is the magnetic field strength, in units of T.
Therefore, the magnetic sensitivity coupling model of the linear accelerometer can fully reflect the influence of the magnetic field on the output of the linear accelerometer, so that the calibration accuracy of the linear accelerometer is improved.
And step four, based on the data obtained by the test as input and output data, performing parameter identification on the data by adopting a limited memory least square method, and realizing the magnetic sensitivity calibration of the linear accelerometer.
When the traditional least square method is used for estimating parameters, a data saturation phenomenon easily occurs. In order to overcome this difficulty and prevent estimation divergence, the present embodiment employs a least squares method based on limited memory to perform parameter identification on the magnetic sensitivity coupling model of the linear accelerometer.
The limited memory least square method is that when parameter estimation is carried out, the obtained observation data are always the latest observation data of a limited group, and each time a group of latest observation data is added, a group of oldest observation data are discarded immediately. Therefore, the parameter estimation is carried out on the magnetic sensitivity coupling model of the linear accelerometer based on the limited memory least square method, so that the data saturation phenomenon caused by increase of test data can be effectively eliminated, and the accuracy of model estimation is improved.
The recursion formula based on the limited memory least squares method is as follows: first, a parameter vector is defined
Information vector
Then (4) is expressed as the following equation:
y＝ψ T θ (5)
where y is the output of the line accelerometer.
Let N represent current data and N represent initial data, define Y (N) = [ Y (N) Y: (N) ((N))n+1) … y(N)] T ，Ψ(N)＝[ψ(n) ψ(n+1) … ψ(N)] T ,P(N)＝[Ψ T (N)Ψ(N)] -1 Then formula (5) can be rewritten as
Y(N)＝Ψ(N)θ (6)
When a new set of data Y (N + 1), u (N) is obtained
Y(N+1)＝Ψ(N+1)θ (7)
From the least squares recursion equation:
L(N+1)＝P(N+1)ψ(N+1) (9)
wherein
For the current time estimate of the parameter theta,
is an estimate of the parameter theta at the next time.
Remove a set of earliest data from Ψ (N + 1), Y (N + 1)
The recursive expression defining the memory least squares can be expressed as:
the method is used for carrying out parameter identification on the test data of the linear accelerometer, the identification result is shown in table 1, and the identification process is shown in fig. 4.
TABLE 1 identification of linear accelerometers in high magnetic fields
| Serial number | Identifying parameters | The result of the recognition |
| 1 | K 0 | 25.6620 |
| 2 | K i | 25.6620 |
| 3 | K ii | 25.6620 |
| 4 | K iii | 25.6620 |
| 5 | K m | -0.0078 |
| 6 | K mm | 1.02856*10 -6 |
| 7 | K im | -0.0078 |
And carrying out a new accelerometer magnetic sensitivity test, using the obtained input and output as verification data, calibrating the linear accelerometer magnetic sensitivity coefficient, and finding that the relative estimation error of each coefficient is less than 0.1%. Therefore, the effectiveness of the magnetic sensitivity calibration system and method for the linear accelerometer disclosed by the embodiment is verified.
The above detailed description is further intended to illustrate the objects, technical solutions and advantages of the present invention, and it should be understood that the above detailed description is only an example of the present invention and should not be used to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A magnetic sensitivity calibration system for a linear accelerometer, characterized by: the device mainly comprises a test platform, a magnetic field generating device, a magnetic field control device, a gaussmeter, a power supply, a voltmeter and an electric control rotating platform; the tested line accelerometer is connected with a rotating shaft of the electric control rotating platform, and the whole rotating platform is placed in the central area of the magnetic field generating device; the gaussmeter is used for measuring the magnetic induction intensity of the sensor; the magnetic field generating device is connected with the magnetic field control device to adjust the magnetic induction intensity; the output of the accelerometer of the tested line is converted into an equivalent voltage signal through an operational amplifier and an AD/DA (analog-to-digital) and is acquired by a digital multimeter to obtain an effective real voltage value.
2. A magnetic sensitivity calibration system for a linear accelerometer according to claim 1, wherein: helmholtz coils are used as a magnetic field generating device and consist of a pair of identical circular conductor coils; in order to realize the magnetic sensitivity calibration of the linear accelerometer, the magnetic sensitivity distribution of a magnetic field space is analyzed according to the Biot-Saval law, a magnetic sensitivity coupling model based on the linear accelerometer is established, the magnetic sensitivity of the linear accelerometer is tested under a magnetic sensitivity calibration system, the obtained test data is used as input and output, and the least square method based on limited memory is adopted for parameter identification, so that the accurate calibration of the magnetic sensitivity and each coefficient of the linear accelerometer is realized.
3. A magnetic sensitivity calibration method for a linear accelerometer, which is implemented based on a magnetic sensitivity calibration system for a linear accelerometer according to claim 1 or 2, and is characterized in that: comprises the following steps of (a) carrying out,
(1) Horizontally mounting the accelerometer of the line to be tested on a test platform;
(2) Setting a range of the magnetic field intensity to be tested; setting magnetic field intensity intervals; controlling a magnetic field generating device to generate magnetic fields at intervals of magnetic field intensity;
(3) The digital voltmeter performs measurement recording in real time;
(4) Repeating the step (2) until the magnetic field intensity is tested to the maximum, and obtaining a group of measurement data of the test plane;
(5) Rotating the angle of the accelerometer of the measured line;
(6) Repeating the steps (1) to (5) to obtain a group of new measurement data of the test plane;
(7) Continuously and uniformly changing the angle of the measured linear accelerometer, and carrying out plane measurement one by one until the linear accelerometer rotates 360 degrees; taking the test data as input and output data of the line accelerometer;
(8) And (4) combining the input and output data obtained in the step (7), and performing parameter identification by adopting a least square method based on limited memory to realize accurate calibration of the magnetic sensitivity and each coefficient of the linear accelerometer.
4. A method of calibrating magnetic sensitivity for a linear accelerometer according to claim 3, wherein: establishing a magnetic sensitivity coupling model of the linear accelerometer according to the standard model of the linear accelerometer;
first, according to IEEE 836-2009 and IEEE 1293-1998, a linear accelerometer model is selected as shown in equation (1);
where Y is the linear accelerometer output, K 0 Zero offset, K, of linear accelerometer i Is the linear accelerometer scale factor, K ii Is a second order nonlinear coefficient, K iii Is a third order nonlinear coefficient, K io ，K ip Is the cross-coupling coefficient, K oo ，K pp Is a second order cross-coupled nonlinear coefficient, ε is the measurement noise, A i ,A o ,A p Is the component of the input acceleration on the linear accelerometers IA, OA, PA, in units of gravitational acceleration, g;
however, the linear accelerometer model does not consider the influence of a magnetic field on the output of the linear accelerometer, and the accuracy of a calibration result is reduced when the magnetic field interferes; therefore, the method is improved on the original linear accelerometer model to establish a coupling model of the linear accelerometer
Wherein, K m Coefficient of magnetic sensitivity of linear accelerometer, K mm Is the second order nonlinear coefficient of the linear accelerometer magnetic sensitivity, K im ,K om ,K pm Is the cross-coupling coefficient of magnetic sensitivity to other axis inputs, A m Is the magnetic field strength, in units T;
therefore, the magnetic sensitivity coupling model of the linear accelerometer is adopted to introduce the coupling terms of the magnetic sensitivity coefficient and other coefficients, so that the influence of a magnetic field on the output of the linear accelerometer can be fully reflected, and the calibration precision of the linear accelerometer is improved.
5. A method of calibrating magnetic sensitivity for a linear accelerometer according to claim 4, wherein: the limited memory least square method is that when parameter estimation is carried out, the obtained observation data are always the latest observation data of a limited group, and each time one group of latest observation data is added, one group of oldest observation data are discarded immediately; therefore, the magnetic sensitivity coupling model of the linear accelerometer is subjected to parameter estimation based on the limited memory least square method, so that the data saturation phenomenon caused by increase of test data can be effectively eliminated, and the estimation precision of the magnetic sensitivity coupling model is improved.
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