阅读说明：本技术 一种双轴磁强计的多方位椭圆拟合标定方法及系统 (Multi-azimuth ellipse fitting calibration method and system for double-shaft magnetometer ) 是由 安亮亮 董蔺 周胜宏 颜舒琳 魏培平 陈晓智 张龙龙 刘海龙 周航 马英辉 焦志 于 2021-10-19 设计创作，主要内容包括：本发明公开了一种双轴磁强计的多方位椭圆拟合标定方法及系统,将多个方位角的采集数据分别进行椭圆拟合,获得椭圆方程,根据每个椭圆方程的系数计算椭圆的中心点坐标；根据计算出的椭圆的中心点坐标与最优估计值的均方差最小原则,求出最优估计值；将每个方位角的采集数据拟合出的椭圆的中心点坐标减去最优估计值,获得每个方位角的采集数据的随机平移误差；将每个方位角的采集数据去除随机平移误差,得到优化数据；将每个方位角的优化数据分别进行椭圆拟合,获得优化的椭圆方程,计算每个方位角的补偿系数和零偏误差；计算所有方位角的补偿系数的平均值,获得补偿系数；计算所有方位角的零偏误差的平均值,获得零偏误差；本发明提高了标定效果。(The invention discloses a multi-azimuth ellipse fitting calibration method and a multi-azimuth ellipse fitting calibration system for a double-shaft magnetometer, wherein acquired data of a plurality of azimuth angles are subjected to ellipse fitting respectively to obtain ellipse equations, and the coordinates of the center points of the ellipses are calculated according to the coefficient of each ellipse equation; solving the optimal estimation value according to the calculated mean square error minimum principle of the central point coordinate of the ellipse and the optimal estimation value; subtracting the optimal estimated value from the center point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the acquired data of each azimuth angle; removing random translation errors from the collected data of each azimuth angle to obtain optimized data; respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and calculating a compensation coefficient and a zero offset error of each azimuth angle; calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients; calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error; the invention improves the calibration effect.)

1. A multi-azimuth ellipse fitting calibration method of a double-shaft magnetometer is characterized in that: the method comprises the following steps:

(1) establishing a calibration equation of the double-shaft magnetometer;

；

wherein the content of the first and second substances,the real value of the geomagnetism;is the measured value of the biaxial magnetometer;

is zero of a two-axis magnetometerA bias error;is a compensation coefficient;

(2) solving forAnd：

(21) acquiring data acquired by the double-shaft magnetometer at a plurality of azimuth angles;

(22) respectively carrying out ellipse fitting on the acquired data of each azimuth angle to obtain an ellipse equation, and calculating the center point coordinate of each ellipse according to the coefficient of each ellipse equation;

(23) solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse;

(24) subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle;

(25) removing random translation errors from the collected data of each azimuth angle to obtain optimized data;

(26) respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to each obtained optimized ellipse equation;

(27) calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a Calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error。

2. The method for multi-azimuth ellipse fitting calibration of a dual-axis magnetometer of claim 1, wherein: in step (22), the acquired data of each azimuth angle is respectively subjected to ellipse fitting based on a least square method to obtain an ellipse equation.

3. The method for multi-azimuth ellipse fitting calibration of a dual-axis magnetometer of claim 1, wherein: in step (26), the optimized data of each azimuth angle is respectively subjected to ellipse fitting based on a least square method to obtain an optimized ellipse equation.

4. The method for multi-azimuth ellipse fitting calibration of a dual-axis magnetometer of claim 1, wherein: in step (26), the calculating the compensation coefficient and the zero offset error of each azimuth angle according to each obtained optimized ellipse equation specifically includes the following steps:

(26-1) fromThe optimized elliptical equation fitted to the optimized data for each azimuth is:

；

（26-2），，；

；；

(26-3) the firstZero offset error of individual azimuthComprises the following steps:；

(26-4) matrix；

Will be provided withSingular value decomposition is carried out to obtain(ii) a Wherein the content of the first and second substances,is composed of a characteristic value (、) The diagonal matrix is formed by the two groups of the diagonal matrix,is a feature vector matrix;

first, theCompensation coefficient of individual azimuthComprises the following steps:。

5. the utility model provides a diversified ellipse fitting calibration system of biax magnetometer which characterized in that: the method comprises the following steps:

the equation establishing module is used for establishing a calibration equation of the double-shaft magnetometer;

；

wherein the content of the first and second substances,the real value of the geomagnetism;is the measured value of the biaxial magnetometer;

zero bias error for a dual axis magnetometer;is a compensation coefficient;

a solving module for solvingAndthe method specifically comprises the following steps:

the acquisition unit is used for acquiring the acquired data of the double-shaft magnetometer at a plurality of azimuth angles;

the first fitting calculation unit is used for respectively carrying out ellipse fitting on the acquired data of each azimuth angle to obtain an ellipse equation, and calculating the center point coordinate of each ellipse according to the coefficient of each ellipse equation;

the optimal estimated value solving unit is used for solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse;

the random translation error calculation unit is used for subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle;

the optimized data calculation unit is used for removing random translation errors from the acquired data of each azimuth angle to obtain optimized data;

the second fitting calculation unit is used for respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to the obtained optimized ellipse equation;

a calculating unit for calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a Calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error。

6. The multi-orientation ellipse fitting calibration system of the dual-axis magnetometer of claim 5, wherein: the first fitting calculation unit is specifically configured to perform ellipse fitting based on a least square method on the acquired data of each azimuth angle respectively to obtain an ellipse equation.

7. The multi-orientation ellipse fitting calibration system of the dual-axis magnetometer of claim 5, wherein: the second fitting calculation unit is specifically configured to perform ellipse fitting based on a least square method on the optimized data of each azimuth angle respectively to obtain an optimized ellipse equation.

8. The multi-orientation ellipse fitting calibration system of the dual-axis magnetometer of claim 5, wherein: the second fitting calculation unit is specifically configured to:

(26-1) fromThe optimized elliptical equation fitted to the optimized data for each azimuth is:

；

（26-2），，；

；；

(26-3) the firstZero offset error of individual azimuthComprises the following steps:；

(26-4) matrix；

Will be provided withSingular value decomposition is carried out to obtain(ii) a Wherein the content of the first and second substances,is composed of a characteristic value (、) The diagonal matrix is formed by the two groups of the diagonal matrix,is a feature vector matrix;

first, theCompensation coefficient of individual azimuthComprises the following steps:。

Technical Field

The invention belongs to the technical field of sensor measurement, and particularly relates to a multi-azimuth ellipse fitting calibration method and system for a double-shaft magnetometer.

Background

With the continuous development of carrier intelligence, the roll angle measurement technology has become one of the key technologies for attitude measurement, navigation and control of a rotating carrier. The geomagnetic attitude measurement has the advantages of being passive, autonomous, wide in coverage area, high in reliability, good in stability and the like, and meanwhile, the magnetometer has the characteristics of being low in cost, strong in autonomy, high in sensitivity, small in size, low in power consumption, free of error accumulation along with time and the like, so that the adoption of the magnetometer to measure the roll angle becomes one of important means for measuring the attitude of the rotary carrier. However, since the geomagnetic field is a weak magnetic field, the signal of the magnetometer is very easily affected by the surrounding interference magnetic field, and the ferromagnetic carrier has ferromagnetism because of being placed in the geomagnetic field for a long time, the magnetometer must be effectively calibrated and compensated for errors in order to obtain high-precision geomagnetic information.

At present, the traditional calibration methods of a biaxial magnetometer (biaxial geomagnetic sensor) include multi-sensor fusion, a given reference method, an ellipse fitting method, and the like. The multi-sensor fusion and the given reference method both need the assistance of other sensors or external postures, and the calibration process is relatively complex. The most common calibration method is an ellipse fitting calibration method, which is widely used in engineering due to its simple and easy-to-implement characteristics. However, the traditional ellipse fitting calibration method is based on data acquired at a certain angle and then ellipse coefficient fitting is performed, so that errors caused by too strong randomness of a single-angle experiment are inevitable, and further calibration effect is influenced.

Disclosure of Invention

The invention provides a multi-azimuth ellipse fitting calibration method of a double-shaft magnetometer, and the calibration effect is improved.

In order to solve the technical problems, the invention adopts the following technical scheme:

a multi-azimuth ellipse fitting calibration method of a double-shaft magnetometer comprises the following steps:

(1) establishing a calibration equation of the double-shaft magnetometer;

；

wherein the content of the first and second substances,the real value of the geomagnetism;is the measured value of the biaxial magnetometer;

zero bias error for a dual axis magnetometer;is a compensation coefficient;

(2) solving forAnd：

(21) acquiring data acquired by the double-shaft magnetometer at a plurality of azimuth angles;

(22) respectively carrying out ellipse fitting on the acquired data of each azimuth angle to obtain an ellipse equation, and calculating the center point coordinate of each ellipse according to the coefficient of each ellipse equation;

(23) solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse;

(24) subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle;

(25) removing random translation errors from the collected data of each azimuth angle to obtain optimized data;

(26) respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to each obtained optimized ellipse equation;

(27) calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a Calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error。

Further, in step (22), the acquired data of each azimuth angle is respectively subjected to ellipse fitting based on a least square method to obtain an ellipse equation.

Still further, in step (26), the optimized data of each azimuth angle is respectively subjected to ellipse fitting based on a least square method to obtain an optimized ellipse equation.

Further, in step (26), the calculating the compensation coefficient and the zero offset error for each azimuth angle according to each obtained optimized ellipse equation specifically includes the following steps:

(26-1) fromThe optimized elliptical equation fitted to the optimized data for each azimuth is:

；

（26-2），，；

；；

(26-3) the firstZero offset error of individual azimuthComprises the following steps:；

(26-4) matrix；

Will be provided withSingular value decomposition is carried out to obtain(ii) a Wherein the content of the first and second substances,is composed of a characteristic value (、) The diagonal matrix is formed by the two groups of the diagonal matrix,is a feature vector matrix;

compensation coefficient of first azimuthComprises the following steps:。

a multi-azimuth ellipse fitting calibration system of a dual-axis magnetometer comprises:

the equation establishing module is used for establishing a calibration equation of the double-shaft magnetometer;

；

wherein the content of the first and second substances,the real value of the geomagnetism;is the measured value of the biaxial magnetometer;

zero bias error for a dual axis magnetometer;is a compensation coefficient;

a solving module for solvingAndthe method specifically comprises the following steps:

the acquisition unit is used for acquiring the acquired data of the double-shaft magnetometer at a plurality of azimuth angles;

the first fitting calculation unit is used for respectively carrying out ellipse fitting on the acquired data of each azimuth angle to obtain an ellipse equation, and calculating the center point coordinate of each ellipse according to the coefficient of each ellipse equation;

the optimal estimated value solving unit is used for solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse;

the random translation error calculation unit is used for subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle;

the optimized data calculation unit is used for removing random translation errors from the acquired data of each azimuth angle to obtain optimized data;

the second fitting calculation unit is used for respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to the obtained optimized ellipse equation;

a calculating unit for calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a Calculating zeros in all azimuthsAverage value of bias error to obtain zero bias error。

Further, the first fitting calculation unit is specifically configured to perform ellipse fitting based on a least square method on the acquired data of each azimuth angle, respectively, to obtain an ellipse equation.

Still further, the second fitting calculation unit is specifically configured to perform ellipse fitting based on a least square method on the optimized data of each azimuth angle, respectively, to obtain an optimized ellipse equation.

Further, the second fitting calculation unit is specifically configured to:

(26-1) fitting the optimized elliptical equation from the optimized data for the first azimuth as:

；

（26-2），，；

；；

(26-3) zero offset error of first azimuth angleComprises the following steps:；

(26-4) matrix；

Will be provided withSingular value decomposition is carried out to obtain(ii) a Wherein the content of the first and second substances,is composed of a characteristic value (、) The diagonal matrix is formed by the two groups of the diagonal matrix,is a feature vector matrix;

compensation coefficient of first azimuthComprises the following steps: .

Compared with the prior art, the invention has the advantages and positive effects that: the multi-azimuth ellipse fitting calibration method and system of the double-shaft magnetometer obtain the acquired data of the double-shaft magnetometer at a plurality of azimuth angles, respectively perform ellipse fitting on the acquired data of each azimuth angle to obtain an ellipse equation, and calculate the center point coordinate of each ellipse according to the coefficient of each ellipse equation; solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse; subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle; removing random translation errors from the collected data of each azimuth angle to obtain optimized data; respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to each obtained optimized ellipse equation; calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients; calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error; the multi-azimuth ellipse fitting calibration method of the double-shaft magnetometer eliminates random errors and improves the calibration effect.

Other features and advantages of the present invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.

Drawings

FIG. 1 is a schematic view of the installation of a two-axis magnetometer;

FIG. 2 is a flow chart of one embodiment of a multi-orientation ellipse fitting calibration method of the dual-axis magnetometer proposed by the present invention;

FIG. 3 is raw acquisition data;

FIG. 4 is a diagram illustrating the effect of a conventional calibration method;

FIG. 5 is a result of ellipse center estimation and center translation processing of acquired measurement data;

FIG. 6 is a calibration result of the calibration method of the present invention;

FIG. 7 is a schematic structural diagram of an embodiment of a multi-orientation ellipse fitting calibration system of the dual-axis magnetometer provided by the present invention.

Detailed Description

Aiming at the problems of large error and poor effect of the conventional calibration method, the invention provides a multi-azimuth ellipse fitting calibration method and system of a double-shaft magnetometer, and the calibration effect is improved. In order to make the objects, technical solutions and advantages of the present invention more clearly understood, the following describes in detail a multi-orientation ellipse fitting calibration method and system of a two-axis magnetometer, with reference to the accompanying drawings and embodiments.

The invention provides a multi-azimuth ellipse fitting calibration method based on MSE (mean Squared error) center translation. Firstly, an error source of a double-shaft orthogonal magnetometer is analyzed, an error model is established according to an error influence effect, a traditional ellipse calibration principle based on a least square method is introduced, and then a multi-azimuth ellipse fitting calibration method based on MSE center translation is provided from the practical engineering application. The main principle is as follows: the method comprises the steps of collecting experimental data of multiple azimuths within a range of 360 degrees, adopting an MSE (mean square error) method to estimate the random error between the optimal ellipse center and measured data aiming at the collected data of the multiple azimuths, eliminating the random error of the measured data by adopting a center translation method, and then carrying out multidirectional ellipse fitting calibration based on a least square method. Finally, a field calibration experiment proves that the method has better calibration effect.

Firstly, error source analysis and error model establishment of the double-axis magnetometer.

Because the magnetometer has errors such as process manufacturing and the like, and the measurement target is magnetic due to long-time placement in the earth magnetic field, the measurement error of the whole system can be caused finally. Therefore, calibration compensation of the output of the magnetometer is required before the measurement is taken.

The double-axis magnetometer being mounted on a rotary carrierShaft andthe axes are perpendicular to the longitudinal axis of the carrier (i.e. the central axis of the carrier, the axis of rotation) and to each other, and the installation is schematically shown in fig. 1.

(1) And (5) analyzing an error source.

The error sources for the entire dual-axis magnetometer can be summarized in three aspects:

(a) self-error of the magnetometer components. The self-error of the magnetometer component refers to the process error and the installation error generated in the manufacturing and installation process of the magnetometer, and can be divided into sensitivity error, non-orthogonal error and zero error. The sensitivity error refers to an error caused by the sensitivity of each sensitive axis of the magnetometer and material problems, and can be represented by a diagonal matrix; the non-orthogonal error refers to an error caused by the fact that sensitive axes of the magnetometer cannot be orthogonal, and can be represented by a coupling term of a matrix; the zero error is an error in which the output of the magnetometer is not zero when the external magnetic strength is zero, and can be represented by a one-dimensional matrix.

(b) The influence error of the external environment mainly refers to the influence error of the ferromagnetic carrier on the magnetometer. Since the carrier is ferromagnetic material, the output of the magnetometer deviates from the true value of the geomagnetic intensity. Such effects can be classified into hard magnetic and soft magnetic effects depending on the material causing the error. In describing the error model, such errors can be summarized as sensitivity errors, non-quadrature errors, and zero errors, along with the self-errors of the magnetometer components.

(c) The temperature drift error mainly refers to drift error caused by temperature change after the magnetometer is powered on. Because the production material of the magnetometer is influenced by the temperature, the output voltage of the magnetometer changes along with the temperature change, and the output of the magnetometer drifts along with the temperature change. Compared with other errors, the temperature drift error is smaller, and the temperature change can be ignored when not much.

(2) Error model

According to the influence effect of the errors, three types of errors can be summarized: sensitivity error, coupling effect error, and zero offset error. Aiming at an error source and an installation model of the double-shaft magnetometer, an error calibration model is established:

（1）

or

（2）

Wherein the content of the first and second substances,

，for geomagnetism in a two-axis magnetometerA shaft,The true value of the axial direction;

，being a two-axis magnetometerA shaft,An axis measured value;

，being a two-axis magnetometerA shaft,Zero axis offset error;

sensitivity error and coupling error of the biaxial magnetometer.

Second, ellipse fitting calibration principle based on least square method

The calibration equation of the biaxial magnetometer can be obtained from the formula (1) as follows:

（3）

wherein the content of the first and second substances,

，for geomagnetism in a two-axis magnetometerA shaft,The true value of the axial direction;

，being a two-axis magnetometerA shaft,An axis measured value;

，being a two-axis magnetometerA shaft,Zero axis offset error;

and is a compensation coefficient for the sensitivity error and the coupling error of the biaxial magnetometer.

Is thatThe inverse of the matrix of (a) is,sensitivity error and coupling error of the double-shaft magnetometer, and compensation coefficient of the error.

The process of calibration is solving andthe most effective method in engineering is a least square fitting method based on an ellipse, which is mainly divided into two steps: 1. carrying out ellipse fitting on the acquired magnetometer measurement data and solving an ellipse fitting coefficient; 2. performing ellipse calibration, rounding, solving and。

(1) ellipse fitting of geomagnetic measurement data

From equation (3) we can derive:

（4）

note the book

（5）

Considering any fixed position, the earth magnetic field vector can be regarded as a constant vector when rotating around the longitudinal axis of the carrier, and the magnetic field intensity is a constant, soIs constant, then equation (5) is an elliptical trajectory equation (in the form of a matrix of ellipses), which means thatThe measurement is limited to an elliptical trajectory, and by using this characteristic, the error correction parameters of the two-axis magnetometer can be estimated. The output data can be rotated around the longitudinal axis of the carrier by using a magnetometerThe coefficient of equation (5) is obtained by fitting an ellipse by the least square methodAnd。

the elliptical trajectory equation can be expressed as

（6）

Defining elliptic coefficients

The hypothesis magnetometer outputs a set of geomagnetic vector data，，Defining a measurement data matrix for the length of the geomagnetic vector data

Then can obtain

（7）

The least squares fitting problem of equation (7), i.e.Minimization problem, i.e.

（8）

From the knowledge of the least squares method, it can be known

（9）

Thus, the ellipse fitting coefficient of the geomagnetic measurement data is obtained。

(2) Error compensation coefficient calculation

After the fitting coefficient of the elliptical trajectory is obtained, the error compensation coefficient can be calculated.

The ellipse equation (6) can be rewritten as the following form:

（10）

wherein the content of the first and second substances,，，。

the formula (10) is further derived as

（11）

Wherein can be obtained

（12）

（13）

The left and right of the equal sign of the formula (5) are respectively divided byThen, the reaction is compared with the formula (11), whereby the compound

（14）

（15）

Will matrixSingular value decomposition is carried out to obtain

（16）

Wherein the content of the first and second substances,is composed of a characteristic value (、) The diagonal matrix is formed by the two groups of the diagonal matrix,is a feature vector matrix. Suppose that

，

Then

（17）

Due to the fact thatTherefore, there are

（18）

The compensation coefficient of the magnetometer is determinedAnd。

three, MSE method

In the experimental process, due to the randomness factor, the test measurement data acquired each time are interfered by random quantity, and the results are not completely consistent. Therefore, in order to ensure that accurate calibration parameters are obtained as much as possible, multi-azimuth data acquisition is required, ellipse fitting is performed on a plurality of groups of acquired measurement data respectively, the optimal central point of an ideal ellipse is estimated, and then calibration compensation is performed. In the invention, the MSE method is adopted to carry out ellipse center estimation on the measured data.

The MSE (mean square error) method is a common method for measuring the average error in engineering, is simple, convenient and quick, and the smaller the MSE value is, the better the accuracy of test data described by a prediction model is. The value of MSE is expressed as

（19）

In the formula (I), the compound is shown in the specification,in order to measure the data of the object,are estimated values.

The first embodiment,

The multi-azimuth ellipse fitting calibration method of the biaxial magnetometer of the embodiment mainly comprises the following steps, which are shown in fig. 2.

Step S1: and establishing a calibration equation of the double-shaft magnetometer.

；

Wherein the content of the first and second substances,

the real value of the geomagnetism;

is the measured value of the biaxial magnetometer;

zero bias error for a dual axis magnetometer;

compensation coefficients for sensitivity error and coupling error of the two-axis magnetometer.

Step S2: solving forAnd (c).

The calibration process is to solve the coefficientsAndthe process specifically comprises the following steps:

step S21: acquiring data acquired by a dual-axis magnetometer at multiple azimuth angles, comprisingThe shaft collects data andthe shaft collects data.

Of dual-axis magnetometers at first azimuthThe axis collects data as；

Of dual-axis magnetometers at first azimuthThe axis collects data as；

；Is the number of azimuth angles selected.

、Is a vector, is a data set.

Step S22: and respectively carrying out ellipse fitting on the acquired data of each azimuth angle to obtain an ellipse equation, and calculating the center point coordinate of each ellipse according to the coefficient of each ellipse equation.

In this embodiment, the ellipse fitting based on the least square method is performed on the collected data of each azimuth angle, so that a high-precision ellipse equation can be fitted, and the fitting speed is high.

Through the sections of formula (6) to formula (9), the ellipse equation fitted by the acquired data of each azimuth angle is obtained, that is, n ellipse equations are obtained in total.

From the firstData collected at each azimuth angle: (，) The fitted elliptic equation is:

（20）

the coordinate of the center point of the fitted ellipse is (，) The coordinate calculation formula of the central point of the ellipse is as follows:

（21）

、is as followsFitting of acquired data at individual azimuthsCenter point of the ellipseThe axis coordinate,Axis coordinates.

Step S23: and solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse.

Since the azimuth angle of the carrier is changed to perform the rolling operation each time the data is acquired, the acquired data will contain random offset(，) Therefore, the coordinates of the central point of the ellipse fitted by the acquired data are selected as an optimization object of the MSE method.

The coordinate of the central point of the ideal ellipse after optimization is assumed to be (，) Then the system of equations can be constructed with reference to equation (19):

（22）

order to、Minimum, finding the coordinates of the center point of the ideal ellipseOptimum estimated value of (a)，) And completing the optimized estimation of all the ellipse center coordinates.

Wherein the content of the first and second substances,、is the mean square error;

、is as followsCenter point of ellipse fitted by acquired data of each azimuth angleThe axis coordinate,Axis coordinates;

、is the center point of an ellipseThe axis coordinate,Optimal estimation of axis coordinatesThe value is obtained.

Step S24: and subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle.

(ii) estimating the optimum estimated value of the coordinates of the center point of the ellipse，) The error of the center point of the ellipse fitted by the acquired data for each azimuth can then be calculated.

（23）

Wherein the content of the first and second substances,、is composed ofCenter point of ellipse fitted by acquired data of each azimuth angleThe error of the shaft,Axis error.

It can be known from the general expression (6) of the analysis ellipse and the calculation formula (22) of the center point of the ellipse that the center point coordinate of the ellipse is calculated by the ellipse parameter fitted by the measured data, that is, the ellipse data and the center point coordinate of the ellipse are in one-to-one correspondence. Thus, the coordinate error of the center point of the ellipse is the random translation error of the ellipse, i.e. the error of the ellipse

（24）

Wherein the content of the first and second substances,、is as followsAnd (4) random translation error of the ellipse fitted by the acquired data of each azimuth angle.

After the random translation error in the measured data is removed, ellipse fitting and calibration can be performed.

Step S25: and removing random translation errors from the acquired data of each azimuth angle to obtain optimized data.

（25）

Is as followsData collected at each azimuthThe optimization data of (2);

is as followsData collected at each azimuthThe optimization data of (1).

Step S26: and respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to each obtained optimized ellipse equation.

In this embodiment, the ellipse fitting based on the least square method is performed on the optimized data of each azimuth angle, so that an optimized ellipse equation with high precision can be fitted, and the fitting speed is high.

Is as followsCompensation coefficients for each azimuth angle; is as followsZero offset error for each azimuth angle.

In this step, the compensation coefficient and the zero offset error of each azimuth angle are calculated according to each obtained optimized elliptical equation, which specifically includes the following steps:

step S26-1: from the firstAzimuthal optimization data: (，) The fitted optimized ellipse equation is:

（26）

are the coefficients of an elliptic equation.

And fitting the optimized elliptical equation by the optimized data of each azimuth angle, substituting the coefficient of each optimized elliptical equation into formulas (10) to (18), and calculating the compensation coefficient and the zero offset error of each azimuth angle.

Therefore, with reference to equations (10) to (18), the following calculation is performed:

step S26-2: from the firstThe optimized elliptical equation fitted to the optimized data for each azimuth is rewritten as follows:

； （27）

wherein, the step of,;

byFurther derived is:

； （28）

wherein, can be obtained;

； （29）

； （30）

； （31）

； （32）

(26-3) thus, the firstThe zero offset error for each azimuth is: ,.

(26-4) singular value decomposition of the matrix to obtain

（33）

The matrix is a diagonal matrix composed of eigenvalues (,) and is an eigenvector matrix. Suppose that

，

Then

（34）

Due to the fact thatTherefore, there are

（35）

Thus, firstThe compensation coefficients for each azimuth are:。

in the step, the optimized data of each azimuth angle is respectively subjected to ellipse fitting calibration based on a least square method to obtain a compensation coefficient and a zero offset error of the magnetometer at each azimuth angle.

Through S26-1-S26-4, the compensation coefficient and the zero offset error of each azimuth angle are calculated, and the method is simple and fast.

Step S27: calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a And calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error.

（36）

In this step, the final compensation coefficient is calculated by averagingAnd zero offset error.

In the multi-azimuth ellipse fitting calibration method of the double-axis magnetometer, ellipse fitting is performed on acquired data of each azimuth angle to obtain an ellipse equation, and a center point coordinate of each ellipse is calculated according to a coefficient of each ellipse equation; according to the calculated central point coordinates of the ellipse and the central point coordinates of the ellipse, the optimal estimation is carried outSolving the optimal estimated value of the coordinate of the central point of the ellipse according to the principle of minimum mean square error of the value; subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle; removing random translation errors from the collected data of each azimuth angle to obtain optimized data; respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to each obtained optimized ellipse equation; calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a Calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error; the multi-azimuth ellipse fitting calibration method of the double-shaft magnetometer eliminates random errors and improves the calibration effect.

Field verification experiment:

the verification experiment is carried out in a wide open field in a certain outdoor area, and the geomagnetic environment nearby is good and free of interference. A measuring assembly is constructed by adopting a double-shaft magnetometer and then is fixed on a non-magnetic turntable to keep horizontal.

The eight azimuth angles of the biaxial magnetometer are respectively 0 degrees, 45 degrees, 90 degrees, 135 degrees, 180 degrees, 225 degrees, 270 degrees and 315 degrees by taking the north direction of the geomagnetism as zero degrees and the east direction as positive. And at each azimuth position, rotating around the longitudinal axis of the carrier, setting the sampling frequency of a computer to be 100Hz, and continuously recording the output signal of the double-shaft magnetometer, wherein the output signal is a digital signal and the unit is AD points.

After the experiment, the data were read, one of the rotation cycles was selected, and discrete measurement data were collected, as shown in fig. 3. It can be seen from the figure that the central points of the ellipses formed by the original collected data are relatively dispersed, which indicates that different random drifts occur in the ellipse fitted by the collected data as a whole due to different random errors of each azimuth position during the experiment.

The calibration effect of the traditional method is as follows:

firstly, a traditional ellipse fitting method based on a least square method is adopted for calibration, ellipse fitting calibration is respectively carried out on collected data of each azimuth angle, then an averaging method is adopted for solving a unified compensation coefficient and a zero offset error, and the final calibration effect is shown in an attached figure 4. As can be seen from fig. 4, although the conventional ellipse fitting calibration method achieves the effect of drawing a circle, due to the influence of the random error of each azimuth position, the calibrated circles are not concentric, the circle center is greatly dispersed, the maximum difference is about 1400 AD points, the random error is not eliminated, the random error still exists, and the calibration effect is not ideal.

The multi-azimuth ellipse fitting calibration effect based on MSE center translation of the embodiment:

according to the MSE center shifting method proposed in this embodiment, the acquired measurement data is processed by ellipse center estimation, center shifting, and the like, and the processing result is shown in fig. 5.

After MSE center translation is adopted, the ellipse center points fitted by all azimuth angle measurement data are gathered near the optimal ellipse center point. Then, ellipse fitting calibration based on least square method and compensation coefficient solving by mean value method are carried outAndfinally compensate the calibration result (will)Andthe effect applied to the measurement data) is shown in fig. 6. As can be seen from fig. 6, the multi-azimuth ellipse fitting calibration method based on MSE center translation can make the calibrated circles substantially concentric, the dispersion of the circle centers is small, the maximum difference is about 25 AD points, the random error of each azimuth position is substantially eliminated, and the calibration effect is far better than that of the conventional method.

The method for measuring the roll angle of the rotating carrier by adopting the biaxial magnetometer is an important means widely used in the current engineering, but the traditional ellipse fitting calibration method is based on single azimuth data acquisition, is simpler, is influenced by random factors to generate larger errors, and further influences the calibration effect. The multi-azimuth ellipse fitting method based on MSE center translation provided by the embodiment focuses on practical engineering application, and can optimize measurement data acquired at multiple azimuth angles, eliminate random translation errors and then perform multi-azimuth ellipse fitting calibration. In the embodiment, through perfect practical experiments, the calibration effect of the method can reach a higher level, the output information of the dual-axis magnetometer can be effectively corrected, and technical support is provided for roll angle measurement, navigation guidance and control of the rotating carrier. The invention has complete independent intellectual property rights, novel method and advanced level.

The multi-azimuth ellipse fitting calibration method of the embodiment mainly comprises the steps of error source analysis and error model establishment of a double-axis magnetometer, an ellipse fitting calibration principle based on a least square method, ellipse center estimation based on MSE, an experimental data processing method based on center translation, a multi-azimuth ellipse fitting calibration method based on a least square method and the like. Meanwhile, the multi-azimuth ellipse fitting calibration method of the double-shaft magnetometer of the embodiment is verified by field experiments and compared with the traditional method, and the calibration effect of the method is proved to be better.

The multi-azimuth ellipse fitting calibration method of the double-shaft magnetometer has complete independent intellectual property and is novel, the method belongs to an advanced level, the output of the double-shaft magnetometer can be effectively calibrated by the multi-azimuth ellipse fitting calibration method based on MSE center translation, the stability and the reliability are higher than those of the traditional method, and technical support is provided for calibration and measurement of the double-shaft magnetometer.

Example II,

Based on the design of the multi-azimuth ellipse fitting calibration method of the dual-axis magnetometer of the first embodiment, the embodiment provides a multi-azimuth ellipse fitting calibration system of a dual-axis magnetometer, which comprises an equation establishing module and a solving module, and is shown in fig. 7.

(1) The equation establishing module is used for establishing a calibration equation of the double-shaft magnetometer;

；

wherein the content of the first and second substances,the real value of the geomagnetism;is the measured value of the biaxial magnetometer;

zero bias error for a dual axis magnetometer;is a compensation coefficient;

(2) a solving module for solvingAndthe solving module specifically comprises the following units:

(21) the acquisition unit is used for acquiring the acquired data of the double-shaft magnetometer at a plurality of azimuth angles;

(22) the first fitting calculation unit is used for respectively carrying out ellipse fitting on the acquired data of each azimuth angle to obtain an ellipse equation, and calculating the center point coordinate of each ellipse according to the coefficient of each ellipse equation;

(23) the optimal estimated value solving unit is used for solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse;

(24) the random translation error calculation unit is used for subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle;

(25) the optimized data calculation unit is used for removing random translation errors from the acquired data of each azimuth angle to obtain optimized data;

(26) the second fitting calculation unit is used for respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to the obtained optimized ellipse equation;

(27) a calculating unit for calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a Calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error。

And the first fitting calculation unit (22) is specifically used for respectively carrying out ellipse fitting based on a least square method on the acquired data of each azimuth angle to obtain an ellipse equation.

And the second fitting calculation unit (26) is specifically used for respectively carrying out ellipse fitting based on a least square method on the optimized data of each azimuth angle to obtain an optimized ellipse equation.

A second fitting calculation unit (26), in particular for:

(26-1) fromThe optimized elliptical equation fitted to the optimized data for each azimuth is:

；

（26-2），，；

；；

(26-3) the firstZero offset error of individual azimuthComprises the following steps:；

(26-4) a matrix;

singular value decomposition is carried out to obtain the singular value decomposition; wherein, the diagonal matrix is formed by eigenvalues (,) and is an eigenvector matrix;

first, theCompensation coefficient of individual azimuthComprises the following steps:。

the working process of the multi-azimuth ellipse fitting calibration system of the dual-axis magnetometer is described in detail in the multi-azimuth ellipse fitting calibration method of the dual-axis magnetometer, and is not described herein again.

In the multi-azimuth ellipse fitting calibration system of the double-axis magnetometer, ellipse fitting is performed on acquired data of each azimuth angle to obtain an ellipse equation, and a center point coordinate of each ellipse is calculated according to a coefficient of each ellipse equation; solving the optimal estimated value of the coordinate of the central point of the ellipse according to the minimum mean square error principle of the calculated coordinate of the central point of the ellipse and the optimal estimated value of the coordinate of the central point of the ellipse; subtracting the optimal estimated value of the central point coordinate of the ellipse from the central point coordinate of the ellipse fitted by the acquired data of each azimuth angle to obtain the random translation error of the ellipse fitted by the acquired data of each azimuth angle; removing random translation errors from the collected data of each azimuth angle to obtain optimized data;respectively carrying out ellipse fitting on the optimized data of each azimuth angle to obtain an optimized ellipse equation, and then calculating a compensation coefficient and a zero offset error of each azimuth angle according to each obtained optimized ellipse equation; calculating the average value of the compensation coefficients of all the azimuth angles to obtain the compensation coefficients(ii) a Calculating the average value of the zero offset errors of all the azimuth angles to obtain the zero offset error(ii) a The multi-azimuth ellipse fitting calibration system of the double-shaft magnetometer eliminates random errors and improves the calibration effect.

It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.