Satellite under-configured condition magnetometer on-orbit fast calibration method

Abstract

The application relates to a magnetometer on-orbit fast calibration method under a satellite under-configuration condition and belongs to the technical field of satellite attitude control. The method is characterized in that a magnetometer measurement error model is constructed, the difference between a magnetometer measurement modulus and a geomagnetic field modulus is utilized, and a least square algorithm is adopted to realize fast estimation of a magnetometer constant drift. The method mainly solves the problem that a traditional magnetometer on-orbit calibration method needs to rely on external sensor data or satellite attitude information. By establishing a magnetic measurement error model containing only a measurement constant drift term, constructing an estimation function by utilizing the difference between the geomagnetic field modulus and the magnetometer measurement modulus, and through power reduction processing and least square estimation, the fast calibration of the magnetometer constant drift can be completed without the aid of satellite attitude determination sensors, the measurement error is reduced from above 5000 nT to within 200 nT after calibration, and the magnetic damping and magnetic attitude determination measurement accuracy requirements are met.

Description

Technical Field

[0001] This invention relates to the field of satellite attitude control technology, specifically to a method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions. Background Technology

[0002] In recent years, with the large-scale development of satellites, in order to reduce costs, attitude control thrusters have been gradually phased out and replaced by magnetic torque generators to control the generation of magnetic moments to eliminate the angular velocity during satellite-launch separation. The magnetic torque generator requires the satellite's three-axis magnetic field as a control input, and an onboard magnetometer is used to measure the strength of the satellite's three-axis magnetic field.

[0003] Onboard magnetometer measurements are affected by residual magnetism, induced magnetism, and installation errors within the satellite, necessitating calibration to improve accuracy. Calibration methods can be divided into ground calibration and on-orbit calibration. Ground calibration requires the use of zero-magnetic equipment to generate a specified magnetic field in space, which is costly and complex. On-orbit calibration relies on onboard attitude sensors and GNSS to determine satellite attitude and positioning, using a geomagnetic model to determine the geomagnetic field projection onto the satellite's three axes. However, when the separation angular velocity is too high, the satellite may be unable to achieve attitude determination. Since the magnetometer is primarily used to measure rate damping after separation, it requires rapid attitude determination after orbital insertion, thus lacking practical engineering applications.

[0004] Currently, on-orbit calibration of magnetometers requires satellite positioning and attitude determination information. If the separation between the satellite and the launch vehicle is significant after orbit insertion, attitude determination becomes impossible, and thus calibration becomes impossible.

[0005] The main challenge in calibrating a magnetometer under insufficient configuration conditions lies in completing the rapid calibration of the magnetometer when satellite attitude information is missing and the theoretical three-axis geomagnetic field strength of the satellite cannot be obtained. Summary of the Invention

[0006] The problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for rapid on-orbit calibration of magnetometers under satellite under-configuration conditions. This method does not require satellite attitude information and can be calibrated quickly after entering orbit. After calibration, it can be used immediately for magnetic field measurement of magnetic torque damper.

[0007] The technical solution of this invention is: a method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions, the method comprising the following steps: S1. Construct a magnetometer measurement error model, the expression of which is: Mx = Bx + Mx0 My = By + My0 Mz = Bz + Mz0 Where Mx0, My0, and Mz0 are the constant drifts of the magnetometer on the X, Y, and Z axes, Mx, My, and Mz are the measured values ​​of the magnetometer on the X, Y, and Z axes, used to measure the magnetic field strength on the X, Y, and Z axes of the satellite reference coordinate system, and Bx, By, and Bz are the projections of the geomagnetic field on the X, Y, and Z axes of the satellite reference coordinate system. S2. Based on the magnetometer measurement error model, the square difference between the geomagnetic field modulus and the magnetometer measurement modulus is derived to obtain the magnetometer constant drift estimation equation. The magnetometer constant drift estimation equation is the relationship between the magnetometer constant drift and the square of the geomagnetic field modulus and the magnetometer measurement modulus. S3. Obtain the squares of the magnitudes of the X-axis, Y-axis, and Z-axis measurements of the magnetometer and the corresponding projections of the geomagnetic field onto the X-axis, Y-axis, and Z-axis of the satellite body coordinate system at multiple times, substitute them into the magnetometer constant drift estimation equation, and construct the magnetometer constant drift estimation equation set. S4. Solve the estimation equations for the constant drift of the magnetometer to obtain the constant drifts Mx0, My0, and Mz0 of the X-axis, Y-axis, and Z-axis of the magnetometer. Substitute these values ​​into the measurement error model of the magnetometer to complete the on-orbit calibration of the magnetometer.

[0008] Preferably, the magnetometer constant drift estimation equation is:

[0009] Preferably, the estimation equations for the constant drift of the magnetometer are as follows:

[0010] In the formula, , , These are the X, Y, and Z axis measurements of the magnetometer in the i-th measurement. , , Let be the projection of the geomagnetic field at the time of the i-th magnetometer measurement onto the X-axis, Y-axis, and Z-axis of the satellite body coordinate system; , The number of measurements taken by the magnetometer.

[0011] Preferably, the number of magnetometer measurements The value range is 20 to 100.

[0012] Preferably, the method for solving the estimation equations for the constant drift of the magnetometer is as follows: By subtracting the pairwise equations for the magnetometer constant drift, the quadratic term Mx0 of the estimated magnetometer constant drift is eliminated. 2 My0 2 Mz0 2 Construct a first-order error estimation equation; By solving the first-order error estimation equation using the least squares method, the constant drift values ​​Mx0, My0, and Mz0 of the magnetometer's X, Y, and Z axes are obtained.

[0013] Preferably, the squares of the magnitudes of the projections of the geomagnetic field onto the X, Y, and Z axes of the satellite's body coordinate system are obtained based on the geomagnetic field model mounted on the satellite and the satellite position information measured by GNSS.

[0014] Preferably, the geomagnetic field model bound on the satellite is a function of the satellite's position.

[0015] Preferably, the measurement interval of the triaxial magnetic field strength of the magnetometer is greater than or equal to 1 second and less than 100 seconds.

[0016] The advantages of this invention compared to the prior art are: (1) This invention reduces the power of the error equations by subtracting the error equations from the two measurements, constructs a set of first-order error model equations, and then estimates the constant drift of the magnetometer using the least squares method. Compared with existing algorithms in on-orbit magnetometer calibration, this invention significantly simplifies the calibration calculation process while meeting the estimation accuracy requirements, and achieves rapid on-orbit calibration.

[0017] (2) The error model constructed in this invention only includes the satellite's three-axis magnetic field magnitude, which is the same as the Earth's magnetic field magnitude. Therefore, by obtaining the magnetic field magnitude using only the satellite's current position and the Earth's magnetic field model, this invention can complete the magnetometer calibration. Compared with existing on-orbit calibration methods, it is not necessary to obtain the satellite's current three-axis magnetic field strength through attitude information; on-orbit calibration can be achieved using only the satellite's position information.

[0018] (3) Using this method, there is no need to carry out ground calibration of the magnetometer, which optimizes the satellite development process and reduces the development cost. Attached Figure Description

[0019] Figure 1 This is a flowchart of the on-orbit rapid calibration method for magnetometers under satellite under-configuration conditions according to an embodiment of the present invention; Figure 2 This is a comparison chart of the magnetometer measurement modulus error before and after calibration in an embodiment of the present invention. Detailed Implementation

[0020] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. These embodiments are for illustrative purposes only and do not constitute a limitation.

[0021] 1. Implementation Environment In this embodiment, a satellite is separated from its launch vehicle after entering orbit. Under under-configuration conditions, i.e., GNSS completes positioning but the satellite has not completed attitude determination, the magnetometer is calibrated only using on-board positioning information and geomagnetic field model.

[0022] 2. Process Description like Figure 1 As shown, this invention proposes a rapid on-orbit calibration method for magnetometers under satellite under-configuration conditions. This method utilizes only satellite position information to quickly complete the on-orbit calibration of the magnetometer in a short time. The method includes steps S1-S4: S1. Construct a magnetometer measurement error model; the magnetometer measurement error model only includes the measurement constant drift term; The main sources of measurement error for onboard magnetometers include: residual magnetism within the satellite, additional magnetic fields generated by magnetizing materials, magnetic fields induced by onboard electrical equipment and cables, and installation errors of the magnetometer relative to the overall satellite reference coordinate system. Its measurement error model can be expressed by the following formula:

[0023] Where x, y, and z are the installation offset angles of the magnetometer's body coordinate system relative to the satellite reference coordinate system in the roll, pitch, and yaw directions; K1, K2, and K3 are the magnetization coefficients at the magnetometer's installation position in the satellite reference coordinate system; Mx, My, and Mz are the measured values ​​of the magnetometer along the X, Y, and Z axes; and Mbx, Mby, and Mbz are the magnetic field strengths along the X, Y, and Z axes of the satellite reference coordinate system. During standard calibration, the multiplication of two matrices is combined into:

[0024] During calibration, Cbm and magnetometer constant drift are determined. Based on the analysis of multiple ground calibration results and on-orbit data, the deviation of Cbm has little impact on the measurement results; the main influencing factor is the magnetometer constant drift. Therefore, the on-orbit calibration model can be simplified to include only the measurement constant drift term. The expression for the magnetometer measurement error model is as follows: Mx = Bx + Mx0 My = By + My0 Mz = Bz + Mz0 Where: Mx0, My0, and Mz0 are the constant drifts of the magnetometer on the X, Y, and Z axes; Mx, My, and Mz are the measured values ​​of the magnetometer on the X, Y, and Z axes; and Bx, By, and Bz are the projections of the geomagnetic field onto the X, Y, and Z axes of the satellite reference coordinate system. S2. Based on the magnetometer measurement error model, the square difference between the geomagnetic field modulus and the magnetometer measurement modulus is derived to obtain the magnetometer constant drift estimation equation. The magnetometer constant drift estimation equation is the relationship between the magnetometer constant drift and the square of the geomagnetic field modulus and the magnetometer measurement modulus. The constant drift estimation equation for the magnetometer is as follows:

[0025] S2. Obtain the squares of the magnitudes of the X-axis, Y-axis, and Z-axis measurements of the magnetometer and the corresponding projections of the geomagnetic field onto the X-axis, Y-axis, and Z-axis of the satellite body coordinate system at multiple times, substitute them into the magnetometer constant drift estimation equation, and construct the magnetometer constant drift estimation equation set. The estimation equations for the constant drift of the magnetometer are as follows:

[0026] In the formula, , , These are the X, Y, and Z axis measurements of the magnetometer in the i-th measurement. , , Let be the projection of the geomagnetic field at the time of the i-th magnetometer measurement onto the X-axis, Y-axis, and Z-axis of the satellite body coordinate system; , The number of measurements taken by the magnetometer.

[0027] Bxi, Byi, and Bzi represent the i-th geomagnetic field projection onto the satellite's three axes. These are unmeasurable terms, but in practice, the current geomagnetic field modulus can be obtained using satellite position information and a geomagnetic field model. This modulus is related to the satellite's three-axis magnetic field strength modulus Bxi. 2 +Byi 2 +Bzi 2 same; Number of magnetometer measurements The value ranges from 20 to 100. In this embodiment, 20 triaxial measurements by the magnetometer and the triaxial projection of the geomagnetic field onto the satellite are obtained.

[0028] Because the satellite orbits the Earth after launch, its position relative to the Earth and its magnetic field change in real time. Maintaining a certain measurement interval ensures that the equations obtained from each measurement are independent. The measurement interval can be between 1 and 100 seconds; for rapid calibration, a measurement interval of 1 second is selected in this embodiment. S4. Solve the estimation equations for the constant drift of the magnetometer to obtain the constant drifts Mx0, My0, and Mz0 of the X-axis, Y-axis, and Z-axis of the magnetometer. Substitute these values ​​into the measurement error model of the magnetometer to complete the on-orbit calibration of the magnetometer.

[0029] The method for solving the estimation equations for the constant drift of the magnetometer is as follows: By subtracting the pairwise equations for the magnetometer constant drift, the quadratic term Mx0 of the estimated magnetometer constant drift is eliminated. 2 My0 2 Mz0 2 Construct a first-order error estimation equation; By solving the first-order error estimation equation using the least squares method, the constant drift values ​​Mx0, My0, and Mz0 of the magnetometer's X, Y, and Z axes are obtained.

[0030] The squares of the magnitudes of the projections of the geomagnetic field onto the X, Y, and Z axes of the satellite's coordinate system are obtained based on the geomagnetic field model mounted on the satellite and the satellite position information measured by GNSS, without the need for attitude information from the onboard attitude sensor.

[0031] The geomagnetic field model mounted on the satellite adopts the International Reference Magnetic Field Model (IGRF) published by the International Association for Geomagnetism and Upper Atmosphere Physics (IAGA). This model represents the magnetic field strength V above the Earth's surface using a gradient:

[0032] In the formula, R is the average radius of the Earth; r is the distance from the Earth's center; λ is the longitude; θ is the latitude; and g nm and h nm These are the Gaussian coefficients provided by the model based on observed data; P nm It is an nth-order m-th degree Legendre function. This model is a function of the satellite's position. After obtaining the satellite's geocentric distance r, longitude λ, and latitude θ, the magnitude and direction of the geomagnetic vector at the current position can be obtained.

[0033] 3. Effect Verification like Figure 2 As shown, before calibration, the difference between the three-axis magnetic field strength measurement modulus of the magnetometer and the Earth's magnetic field modulus was 5000 nT. After calibration, after deducting constant drift, the difference between the magnetometer modulus and the Earth's magnetic field modulus was reduced to less than 200 nT, which meets the requirements of the magnetic torque damper for the measurement accuracy of the magnetometer.

[0034] In summary, this invention provides a rapid on-orbit calibration method for magnetometers under under-configuration conditions. It eliminates the need for onboard attitude sensors to obtain attitude information, requiring only onboard positioning information to complete rapid calibration of the magnetometer after orbit insertion. This enables on-orbit engineering applications, frees users from the constraints of ground-based calibration, optimizes the satellite development process, and reduces development costs.

[0035] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions, characterized in that, Includes the following steps: S1. Construct a magnetometer measurement error model, the expression of which is: Mx = Bx + Mx0 My = By + My0 Mz = Bz + Mz0 Where Mx0, My0, and Mz0 are the constant drifts of the magnetometer on the X, Y, and Z axes, Mx, My, and Mz are the measured values ​​of the magnetometer on the X, Y, and Z axes, used to measure the magnetic field strength on the X, Y, and Z axes of the satellite reference coordinate system, and Bx, By, and Bz are the projections of the geomagnetic field on the X, Y, and Z axes of the satellite reference coordinate system. S2. Based on the magnetometer measurement error model, the square difference between the geomagnetic field modulus and the magnetometer measurement modulus is derived to obtain the magnetometer constant drift estimation equation. The magnetometer constant drift estimation equation is the relationship between the magnetometer constant drift and the square of the geomagnetic field modulus and the magnetometer measurement modulus. S3. Obtain the squares of the magnitudes of the X-axis, Y-axis, and Z-axis measurements of the magnetometer and the corresponding projections of the geomagnetic field onto the X-axis, Y-axis, and Z-axis of the satellite body coordinate system at multiple times, substitute them into the magnetometer constant drift estimation equation, and construct the magnetometer constant drift estimation equation set. S4. Solve the estimation equations for the constant drift of the magnetometer to obtain the constant drifts Mx0, My0, and Mz0 of the magnetometer's X-axis, Y-axis, and Z-axis. Substitute these values ​​into the magnetometer's measurement error model to complete the on-orbit calibration of the magnetometer.

2. The method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions according to claim 1, characterized in that, The constant drift estimation equation for the magnetometer is as follows: 。 3. The method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions according to claim 2, characterized in that, The estimation equations for the constant drift of the magnetometer are as follows: In the formula, , , These are the X, Y, and Z axis measurements of the magnetometer in the i-th measurement. , , Let be the projection of the geomagnetic field at the time of the i-th magnetometer measurement onto the X-axis, Y-axis, and Z-axis of the satellite body coordinate system; , The number of measurements taken by the magnetometer.

4. The method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions according to claim 3, characterized in that, Number of magnetometer measurements The value range is 20 to 100.

5. The method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions according to claim 3, characterized in that, The method for solving the estimation equations for the constant drift of the magnetometer is as follows: By subtracting the pairwise equations for the magnetometer constant drift, the quadratic term Mx0 of the estimated magnetometer constant drift is eliminated. 2 My0 2 Mz0 2 Construct a first-order error estimation equation; By solving the first-order error estimation equation using the least squares method, the constant drift values ​​Mx0, My0, and Mz0 of the magnetometer's X, Y, and Z axes are obtained.

6. The method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions according to claim 3, characterized in that, The squares of the magnitudes of the projections of the geomagnetic field onto the X, Y, and Z axes of the satellite's coordinate system are obtained based on the geomagnetic field model mounted on the satellite and the satellite position information measured by GNSS.

7. The method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions according to claim 3, characterized in that, The geomagnetic field model mounted on the satellite is a function of the satellite's position.

8. The method for rapid on-orbit calibration of a magnetometer under satellite under-configuration conditions according to claim 1, characterized in that, The measurement interval of the triaxial magnetic field strength of the magnetometer is greater than or equal to 1 second and less than 100 seconds.

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