On-orbit calibration method and system of vector magnetometer and star sensor coordinate system transfer matrix

Abstract

The invention relates to the technical field of space environment detection, in particular to an on-orbit calibration method and system for a vector magnetometer and star sensor coordinate system transfer matrix. The method comprises the following steps: for each rotation maneuver, drawing a three-dimensional scatter diagram from a magnetometer output magnetic field vector, identifying a stable arc segment, carrying out singular value decomposition on original magnetic field data of the stable arc segment after de-averaging, extracting a vector corresponding to a minimum singular value as a unit direction vector of a rotation axis of the stable arc segment in a magnetometer coordinate system, and extracting a vector corresponding to the minimum singular value as a unit direction vector of the rotation axis of the stable arc segment; combining the vectors of all stable arc segments under the same maneuver; under the same maneuver, selecting a non-zero constant vector as a reference vector in an inertial coordinate system, converting the non-zero constant vector into a star sensor coordinate system by using a star sensor measurement sequence, performing singular value decomposition on the obtained sequence after mean removal, and extracting a vector corresponding to a minimum singular value as a unit direction vector of a rotating shaft in the star sensor coordinate system; and solving a transfer matrix based on the rotation axis unit direction vectors under the two coordinate systems to complete in-orbit calibration.

Description

Technical Field

[0001] This application relates to the field of space environment detection technology, and in particular to an on-orbit calibration method and system for the coordinate system transfer matrix of a vector magnetometer and a star sensor. Background Technology

[0002] In deep space exploration and Earth orbit science missions, vector magnetometers are key payload devices for acquiring vector information about the space magnetic field. They are widely used in planetary magnetic field detection, solar wind-magnetospheric interaction research, and space weather modeling. To reduce the impact of electromagnetic interference from the spacecraft platform itself on the accuracy of magnetic field measurements, vector magnetometers are typically mounted at the end of a boom, away from the main structure. For example, NASA's Voyager spacecraft's magnetometer was mounted on a 13-meter-long deployable boom to effectively isolate it from magnetic interference from the spacecraft itself.

[0003] However, due to space constraints during launch, these extension rods are typically stored in a folded or compressed state, unfolding to their working position via mechanical mechanisms after entering orbit. The extension process is affected by factors such as material deformation, thermal stress, microgravity, and non-ideal motion of the drive mechanism, which may cause a significant deviation between the actual orientation of the magnetometer mounting platform and its design nominal attitude. Furthermore, the extension rod may deform during long-term on-orbit operation, leading to attitude drift of the magnetometer. Therefore, the installation error of the magnetometer frame (MAG) relative to the spacecraft frame or star tracker frame (STR) cannot be fully determined during ground calibration and requires on-orbit alignment calibration.

[0004] To achieve precise alignment between the coordinate systems of the magnetometer and the star sensor, it is necessary to obtain the three-dimensional attitude transfer matrix (i.e., rotation matrix) between them. This matrix transforms the magnetic field vector from the magnetometer coordinate system to the star sensor coordinate system. Currently, the main international methods for on-orbit calibration are as follows: 1. Optical prism method (e.g., the US MAGSAT mission): A reflecting prism or corner reflector is installed on the magnetometer mounting platform. The spacecraft emits a laser or infrared beam to illuminate the reflecting device, and the spatial orientation of the magnetometer is estimated by receiving the direction of the reflected light. This method has a clear principle and high accuracy, but it has obvious limitations: it requires an additional beam transmission and reception system, increasing system complexity and power consumption.

[0005] 2. Artificial magnetic field method (e.g., the Japanese SELENE / Kaguya mission): Two orthogonally arranged calibration coils are installed on the spacecraft body, and an alternating current of a specific frequency and waveform is passed through them to generate a controllable artificial magnetic field signal. A magnetometer located at the top of the extension rod detects the amplitude and phase response of this alternating magnetic field. Combined with the known coil position and current parameters, the spatial orientation of the magnetometer relative to the coil system is deduced. This method can complete calibration without attitude maneuvering, but it also has a problem: it requires the design of a dedicated coil and its driving circuit, increasing the risks of mass, power consumption, and electromagnetic compatibility; and the artificial magnetic field may interfere with other scientific payloads (such as electric field meters and plasma detectors); in addition, the accuracy of magnetic field modeling is highly dependent on the precise information of the coil geometry parameters, and any assembly error or on-orbit deformation will directly introduce calibration deviation.

[0006] Both of the aforementioned methods rely on additional hardware support (prisms, light sources, coils, etc.), which not only increases system cost and integration complexity but also limits their application in resource-constrained small probes or deep space missions. Therefore, there is an urgent need for a coordinate system alignment and calibration method for magnetometers and star sensors that requires no additional hardware and possesses high accuracy and robustness. Ideally, existing spacecraft attitude control systems and navigation sensor resources should be fully utilized. By designing a reasonable on-orbit maneuvering strategy and combining magnetic field and attitude observation data, efficient and reliable coordinate system transfer matrix estimation can be achieved. Summary of the Invention

[0007] The purpose of this application is to overcome the aforementioned deficiencies of the prior art, thereby providing an on-orbit calibration method and system for the coordinate system transfer matrix between a vector magnetometer and a star sensor in deep space exploration missions. This application is particularly applicable to spacecraft platforms where the magnetometer is mounted on an extended structure (such as a strut), enabling autonomous calibration of a high-precision attitude transfer matrix between the magnetometer's body coordinate system and the star sensor's coordinate system without relying on ground observations or additional hardware devices.

[0008] To solve the above-mentioned technical problems, the technical solution of this application provides an on-orbit calibration method for the coordinate system transfer matrix of a vector magnetometer and a star sensor, including: Step 1: For each rotational maneuver, plot the magnetic field vector sequence output by the magnetometer into a 3D scatter plot in the magnetometer coordinate system and identify stable arc segments. After removing the mean from the original magnetic field data set corresponding to each stable arc segment, perform singular value decomposition to extract the vector corresponding to the smallest singular value as the unit direction vector of the rotation axis corresponding to that stable arc segment in the magnetometer coordinate system. Combine the unit direction vectors of the rotation axis corresponding to all stable arc segments under the same rotational maneuver to obtain the unit direction vector of the rotation axis under that rotational maneuver in the magnetometer coordinate system. Step 2: For each rotational maneuver, select any non-zero constant vector in the inertial coordinate system as the reference vector in the inertial coordinate system; use the star sensor measurement sequence to transform the reference vector in the inertial coordinate system to the star sensor coordinate system to obtain the reference vector sequence in the star sensor coordinate system; after removing the mean value from the reference vector sequence in the star sensor coordinate system, perform singular value decomposition and extract the vector corresponding to the minimum singular value as the unit direction vector of the rotation axis in the star sensor coordinate system under this rotational maneuver; Step 3: Solve the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system based on the unit direction vector of the rotation axis in the magnetometer coordinate system and the unit direction vector of the rotation axis in the star sensor coordinate system, thereby completing the on-orbit calibration.

[0009] As an improvement to the above method, the method is based on the following assumptions: during the time window in which the spacecraft performs a rotational maneuver, the space background magnetic field is approximately constant in the inertial coordinate system; during the duration of the calibration operation, the magnitude and direction of the magnetic field vector remain essentially unchanged; in the magnetometer coordinate system that rotates with the spacecraft, the projection of the magnetic field vector will form a circular trajectory or an arc trajectory, wherein the normal direction of the plane containing the circular trajectory or arc trajectory is the direction of the rotation axis.

[0010] As an improvement to the above method, step 1 specifically includes: performing the following operations for each rotational motion: Step 1.1: Plot the magnetic field vector sequence output by the magnetometer into a three-dimensional scatter plot in the magnetometer coordinate system; identify M relatively stable continuous data arc segments, the m-th arc segment containing Data points, Each data point is obtained from the original magnetic field data set. In this representation, the superscript m indicates the arc segment ordinal number, m = 1, 2, 3, ..., M; i indicates the data point ordinal number. Step 1.2: Analyze the original magnetic field data set for the m-th segment. The mean-removed magnetic field data set is obtained through mean-removed processing. The set of magnetic field data after removing the mean Arranged into Obtain the magnetic field data matrix for this arc segment in dimensional matrix form. ; Step 1.3: Analyze the magnetic field data matrix. Perform singular value decomposition and take the vector corresponding to the smallest singular value as the unit direction vector of the rotation axis corresponding to the stable arc segment in the magnetometer coordinate system. ; Step 1.4: Take a weighted average of the unit direction vectors of the rotation axes corresponding to all stable arc segments under the same rotational maneuver in the magnetometer coordinate system to obtain the unit direction vector of the rotation axis corresponding to the k-th rotational maneuver in the magnetometer coordinate system. : ; in, Let be the total number of valid arc segments identified in the k-th rotational maneuver. For weights.

[0011] As an improvement to the above method, step 2 specifically includes: performing the following operations for each rotational motion: Step 2.1: Arbitrarily select a non-zero constant vector in the inertial coordinate system as the reference vector in the inertial coordinate system. Among them, the reference vector in the inertial coordinate system Not parallel to the axis of rotation; Step 2.2: For each time point Using a star sensor measurement sequence, the reference vector in the inertial coordinate system is... Transform to the star sensor coordinate system to obtain the reference vector in the star sensor coordinate system. ; Step 2.3: Reference vector sequence in star-sensitive coordinate system A circular or arc-shaped trajectory is formed in the star sensor coordinate system, and a reference vector sequence in the star sensor coordinate system is obtained. After mean-free processing, singular value decomposition is performed, and the vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis in the star sensor coordinate system corresponding to the k-th rotational maneuver. .

[0012] As an improvement to the above method, the star sensor measurement sequence includes the quaternions measured by the star sensor. .

[0013] As an improvement to the above method, step 3 specifically includes: determining the unit direction vector of the rotation axis corresponding to the same rotational maneuver in the magnetometer coordinate system. The unit direction vector of the rotation axis in the star sensor coordinate system To form vector pairs, obtain Group vector pairs , among which, among which, Let k be the total number of rotational maneuvers, and k be the ordinal number of the rotational maneuvers; based on the obtained... The transfer matrix between the magnetometer coordinate system and the star sensor coordinate system is calculated using the TRIAD algorithm or singular value decomposition algorithm. The on-orbit calibration has been completed.

[0014] As an improvement to the above method, when Furthermore, when the data standard deviation is less than 0.5nT, the TRIAD algorithm is used to construct an orthogonal basis and calculate the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. ; when If the data standard deviation is greater than or equal to 0.5nT, use the singular value decomposition algorithm or the QUEST algorithm to calculate the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. .

[0015] To achieve another objective of the present invention, the present invention also provides an on-orbit calibration system for the coordinate system transfer matrix of a vector magnetometer and a star sensor, used to implement the above-mentioned on-orbit calibration method for the coordinate system transfer matrix of a vector magnetometer and a star sensor, comprising: The unit direction vector acquisition module of the magnetometer coordinate system is used to plot the magnetic field vector sequence output by the magnetometer into a three-dimensional scatter plot in the magnetometer coordinate system for each rotational maneuver, identify stable arc segments, and perform singular value decomposition on the original magnetic field data set corresponding to each stable arc segment after demeaning. The vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis corresponding to that stable arc segment in the magnetometer coordinate system. It is also used to merge the unit direction vectors of the rotation axis corresponding to all stable arc segments under the same rotational maneuver to obtain the unit direction vector of the rotation axis under that rotational maneuver in the magnetometer coordinate system. The unit direction vector acquisition module of the star sensor coordinate system, for each rotational maneuver, selects a non-zero constant vector in the inertial coordinate system as the reference vector in the inertial coordinate system; uses the star sensor measurement sequence to transform the reference vector in the inertial coordinate system to the star sensor coordinate system, and obtains the reference vector sequence in the star sensor coordinate system; after the reference vector sequence in the star sensor coordinate system is demeaned, singular value decomposition is performed, and the vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis in the star sensor coordinate system under that rotational maneuver; The calibration module is used to solve the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system based on the unit direction vector of the rotation axis in the magnetometer coordinate system and the unit direction vector of the rotation axis in the star sensor coordinate system, thereby completing the on-orbit calibration.

[0016] The on-orbit calibration method and system for the coordinate system transfer matrix of the vector magnetometer and star sensor provided in this application have the following significant advantages compared with the prior art: 1. No additional hardware required: Unlike MAGSAT's prism method or SELENE's coil method, this application only relies on the spacecraft's existing attitude control system and sensors, significantly reducing system complexity and cost.

[0017] 2. Strong resistance to zero bias: The magnetometer’s zero bias is automatically eliminated through the mean removal operation, avoiding the dependence on precise zero bias calibration in traditional methods.

[0018] 3. Supports limited angle rotation: It does not require a full 360° rotation, making it suitable for deep space missions with limited fuel or communication windows.

[0019] 4. Supports segmented processing: Allows extraction of multiple stable arc segments from a single rotational maneuver, improving data utilization efficiency and calibration robustness.

[0020] 5. Repeatable: It can run periodically in orbit to monitor long-term deformation of the strut structure or installation attitude drift. Attached Figure Description

[0021] Figure 1(a) is a schematic diagram of the spacecraft about the first rotation axis; Figure 1(b) is a schematic diagram of the spacecraft rotating around the second axis. Figure 2(a) is a schematic diagram of the trajectory of the change of the magnetic field vector in the magnetometer coordinate system when the spacecraft rotates around the first rotation axis; Figure 2(b) is a schematic diagram of the trajectory of the change of the magnetic field vector in the magnetometer coordinate system when the spacecraft rotates around the second rotation axis; Figure 3 The flowchart shows the on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor provided by the present invention. Detailed Implementation

[0022] The technical solutions provided in this application are further illustrated below with reference to the embodiments.

[0023] Example 1 The purpose of this embodiment is to provide an on-orbit calibration method for the coordinate system transfer matrix of a vector magnetometer and star sensor used in deep space exploration missions. This method requires no additional equipment, can be performed on-orbit, is resistant to zero-bias interference, and is suitable for weak magnetic field environments. Specifically, this embodiment aims to solve the following technical problems: 1. How to achieve high-precision alignment between the coordinate system of the rod-type magnetometer and the star sensor without relying on additional hardware such as prisms, lasers, or calibration coils; 2. How to reduce the dependence of the calibration process on the prior information of the magnetometer's zero bias and improve the robustness of the calibration results; 3. How to effectively extract the rotation axis direction and complete the calibration under the condition of non-perfect periodic change of background magnetic field through attitude maneuvering with limited angles; 4. How to support repeated execution in orbit to monitor long-term deformation of the extension rod structure or installation attitude drift.

[0024] By solving the above problems, vector magnetic field measurement data in deep space exploration missions can be accurately converted to inertial coordinate systems or orbital systems, meeting the scientific exploration requirements for high-precision and high-reliability coordinate alignment.

[0025] The on-orbit calibration method for aligning the magnetometer and star sensor coordinate systems provided in this embodiment is applicable to deep space exploration missions in geosynchronous orbit or further interplanetary space and in weak magnetic field environments (generally less than 1000 nT). In such environments, the background magnetic field strength is weak, and the influence of non-ideal factors (such as orthogonality error and sensitivity coefficient deviation) of vector magnetometers (such as fluxgate magnetometers) is relatively small, while zero bias becomes one of the main systematic errors affecting magnetic field measurements.

[0026] This method involves controlling the spacecraft to perform finite-angle rotational maneuvers (as shown in Figure 1(a) and Figure 1(b)). Combining measurement data from a vector magnetometer and a star sensor, and utilizing the trajectory characteristics of the approximately constant background magnetic field vector in the vector magnetometer coordinate system during rotation (as shown in Figure 2(a) and Figure 2(b)), the rotation axis direction for each maneuver is extracted. Based on multiple sets of non-collinear direction vector pairs, the three-dimensional attitude transfer matrix between the magnetometer coordinate system and the star sensor coordinate system is solved. This method requires no additional hardware support and features high precision, strong robustness, and good engineering feasibility.

[0027] This method is based on the following physical assumptions: Within the time window during which the spacecraft performs a rotational maneuver, the space background magnetic field remains approximately constant in the inertial coordinate system, i.e., the following condition is satisfied: ; in, Let t represent the vector of the background magnetic field in the inertial coordinate system, and t represent time. This condition indicates that the amplitude and direction of the magnetic field vector remain essentially unchanged during the duration of the calibration operation. Therefore, in the magnetometer coordinate system rotating with the spacecraft, the projection of this magnetic field vector will form a circular or arc trajectory (as shown in Figure 2(a) and Figure 2(b)), and the normal direction of the plane containing it is the direction of the rotation axis.

[0028] To meet this assumption, the timing of the maneuver must be planned in advance based on space environment parameters such as solar activity index, geomagnetic disturbance level, and orbital position. For example, in geosynchronous orbit, calibration operations can be carried out during quiet periods when the local magnetic time is nighttime and the global geomagnetic activity index Kp is less than 3.

[0029] It is worth noting that this method does not require the spacecraft to complete a full 360° rotation. Even a rotation of only 90° or even smaller is sufficient for effective calibration as long as a sufficient number of data points are collected and the magnetic field remains stable. Furthermore, since the actual space magnetic field may experience periodic fluctuations, the magnetic field may remain stable for only a few time periods during a complete rotation (as shown in Figure 2(b)). To address this, this method supports processing multiple "stable arcs" within a single rotation maneuver separately, improving data utilization and calibration reliability.

[0030] The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor provided in this embodiment is as follows: Figure 3 As shown, it includes: Step 1: Extract the representation of the rotation axis in the magnetometer coordinate system based on the magnetic field data: For each rotational maneuver, perform the following operations: Step 1.1: Draw the magnetic field trajectory and identify stable arc segments: The magnetic field vector sequence output by the magnetometer is plotted as a three-dimensional scatter plot in the magnetometer coordinate system. Under the condition that the background magnetic field is constant and not parallel to the rotation axis, these points should be distributed on a circular trajectory or arc trajectory in a certain plane (as shown in Figure 2(a) and Figure 2(b)).

[0031] However, due to the possibility of short-term disturbances in the actual space magnetic field (as shown in Figure 2(b)), M relatively stable continuous data arc segments can be identified manually or automatically. The m-th (m=1,2,3,…,M) arc segment contains Data points, Each data point is obtained from the original magnetic field data set. The superscript m represents the arc segment ordinal number, and i represents the data point ordinal number, which is the i-th data point belonging to the m-th arc segment.

[0032] Step 1.2: For each arc segment, take the mean and construct a data matrix: For the m-th segment of the original magnetic field data set The mean-reduction process (i.e., subtracting the average value of the original magnetic field data for that arc segment) yields the mean-reduced magnetic field data set. ; This operation can effectively eliminate the influence of constant interference terms such as magnetometer bias and residual magnetism of spacecraft platforms. This is one of the important advantages of this invention compared with other calibration methods: high-precision coordinate system alignment can be achieved without prior precise calibration or compensation of magnetometer bias.

[0033] The set of magnetic field data after removing the mean Arranged into Obtain the magnetic field data matrix for this arc segment in dimensional matrix form. .

[0034] Step 1.3: Extract the rotation axis direction using Singular Value Decomposition (SVD): magnetic field data matrix Perform singular value decomposition (SVD): ; in, This indicates that the singular value decomposition yields the left singular matrix. Σ represents the right singular matrix obtained after singular value decomposition, and Σ represents the diagonal matrix obtained after singular value decomposition. is the transpose symbol; both the left and right singular matrices are orthogonal matrices.

[0035] Pick The vector corresponding to the smallest singular value, i.e., the unit direction vector of the rotation axis corresponding to that arc segment in the magnetometer coordinate system: .

[0036] Step 1.4: Merge the rotation axis estimation results of multiple arc segments under the same rotational maneuver: If extracted in a single rotational motion For each effective arc segment, a weighted average is taken of all estimated direction vectors to obtain the unit direction vector of the rotation axis in the magnetometer coordinate system corresponding to the k-th rotational maneuver. : ; in, Let be the total number of valid arc segments identified in the k-th rotation. As shown in Figure 2(b), in the rotation, if two valid arc segments with relatively stable data are identified, then... =2, weight It can be set according to indicators such as signal-to-noise ratio and data length.

[0037] Output: The unit direction vector of the rotation axis corresponding to the k-th rotational maneuver in the magnetometer coordinate system. .

[0038] Step 2: Extract the representation of the rotation axis in the star sensor coordinate system based on the attitude data: For each rotational maneuver, acquire the star sensor measurement sequence. Typically in the form of quaternions The form represents the rotation from the inertial coordinate system (ECI) to the star sensor coordinate system. The following steps are used to obtain the representation of the unit vector of the rotation axis of the sequential rotational maneuver in the star sensor coordinate system: Step 2.1: Select the reference vector for the inertial coordinate system: In the inertial coordinate system, arbitrarily choose a non-zero constant vector as the reference vector. ,for example Note that this vector can be chosen arbitrarily, but it cannot be parallel to the axis of rotation; otherwise, a valid trajectory cannot be formed.

[0039] Step 2.2: Transform the inertial coordinate system reference vector to the star sensor coordinate system: For each moment Quaternions measured using a star sensor The reference vector in the inertial coordinate system Transform to the star sensor coordinate system to obtain the reference vector in the star sensor coordinate system. ; Step 2.3: Extract the rotation axis direction in the star sensor coordinate system Reference vector sequence in star-sensitive coordinate system In the star sensor coordinate system, a circular or arc-shaped trajectory will also be formed. Repeat the Singular Value Decomposition (SVD) process in step 1 for this sequence: Take the mean -> construct the data matrix -> singular value decomposition -> take the vector corresponding to the minimum singular value.

[0040] Obtain the unit direction vector of the rotation axis corresponding to the k-th rotational maneuver in the star sensor coordinate system. .

[0041] Step 3: Solve for the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. : Assuming a total of Each independent rotational motion (each around a different axis, and the axes of rotation are not collinear in space; an angle greater than 30 degrees is recommended) yields... Group vector pairs Each pair of vectors represents the same physical rotation axis in both the magnetometer coordinate system and the star sensor coordinate system, where, Let represent the total number of rotational maneuvers, and k be the ordinal number of the rotational maneuvers.

[0042] The goal is to solve for the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system, such that:

[0043] in, It is a general mathematical symbol representing all k; This problem is solved using a classic attitude calculation algorithm: when Furthermore, when the measurement noise is low, such as when the data standard deviation is less than 0.5nT, the TRIAD algorithm is used to construct an orthogonal basis and directly calculate the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. .

[0044] when When measurement noise is significant, such as when the data standard deviation is greater than or equal to 0.5nT, use the Singular Value Decomposition (SVD) algorithm or the QUEST (Quaternion Estimator Algorithm) algorithm to solve for the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. .

[0045] The final output is the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. .

[0046] The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor provided in this embodiment has the following significant advantages compared with the prior art: 1. No additional hardware support required, reducing system complexity and mission cost. This method does not rely on additional devices such as prisms, lasers, or calibration coils. Calibration can be completed using only the spacecraft's existing attitude control system, star sensor, and vector magnetometer. Compared to MAGSAT's optical reflection method and SELENE's artificial magnetic field excitation method, it avoids the quality, power consumption, electromagnetic compatibility, and reliability issues associated with dedicated equipment, making it particularly suitable for resource-constrained small probes or deep space missions. 2. It possesses inherent immunity to magnetometer bias, enhancing calibration robustness. During data processing, by averaging the magnetic field sequence, it automatically eliminates the influence of constant interference terms such as the magnetometer's own bias and the residual magnetism of the spacecraft platform. Therefore, high-precision coordinate system alignment can be achieved without prior ground bias calibration or on-orbit bias estimation, significantly reducing reliance on prior knowledge of the calibration state. 3. Supports limited-angle rotation and segmented data processing, with strong adaptability. This method does not require the spacecraft to complete a full 360° rotation. Even with a rotation of only 90° or even smaller, as long as a sufficient number of data points are collected and the background magnetic field is stable, the rotation axis direction can still be effectively extracted. Furthermore, it supports identifying and processing multiple magnetically stable arc segments from a single rotational maneuver, improving data utilization and calibration success rate in complex space environments. 4. It possesses good engineering feasibility and repeatability. The required maneuvers are conventional attitude control actions, which can be smoothly executed by reaction wheels or thrusters. The core algorithm utilizes mature numerical methods such as SVD, TRIAD, and QUEST. This method can be periodically repeated to monitor long-term on-orbit deformation or installation attitude drift of the extension rod structure, achieving dynamic calibration.

[0047] The following example, using a typical geostationary meteorological satellite mission, details the specific implementation process of this invention. This embodiment uses this satellite as an example, which carries a three-axis fluxgate magnetometer mounted at the end of an 8-meter-long deployable boom, and is also equipped with a high-precision star sensor for attitude determination.

[0048] Implementation Background and Preparation Mission phase: The satellite has entered geosynchronous orbit, and the extension rod has been fully deployed; Space environment: The current background magnetic field strength is approximately 100 nT, the Kp index is 2, and the solar wind speed and magnetic field are stable, indicating a stable magnetic field window; Calibration objective: Determine the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. ; Planned maneuvers: Two rotational maneuvers are planned, each around two approximately perpendicular axes of the spacecraft's coordinate system. Each rotational maneuver is approximately 360°, with an angular velocity set at 0.5° / s. Data sampling frequency: The magnetometer sampling frequency is 10Hz, and the star sensor sampling frequency is 1Hz.

[0049] The implementation steps are as follows: Step 1: First rotational motion (around preset axis 1) Ground commands or autonomous programs trigger the attitude control system, causing the probe to slowly rotate 360° around a preset axis 1. Simultaneous recording of triaxial magnetic field data output by the magnetometer Attitude quaternion output by the star sensor ; Data feedback: drawing In the three-dimensional trajectory in the magnetometer coordinate system, two segments (points 200–800 and 2100–3500) were found to be clearly circular arcs (as shown in Figure 2(b)), which were identified as two arc segments with stable magnetic fields. Perform SVD processing independently for each arc segment data: Mean removal → Data matrix construction → SVD decomposition → Extraction of minimum singular vectors, resulting in two direction estimates: the unit direction vector of the rotation axis corresponding to the first arc segment in the magnetometer coordinate system. The unit direction vector of the rotation axis corresponding to the second arc segment in the magnetometer coordinate system ; Weighted average (assuming equal weights) is used to obtain the unit direction vector of the rotation axis corresponding to the first rotational maneuver in the magnetometer coordinate system. : ; ; Using attitude quaternions The reference vector in the inertial coordinate system Transform to the star sensor coordinate system to obtain the reference vector in the star sensor coordinate system. Repeat the Singular Value Decomposition (SVD) process to obtain the unit direction vector of the rotation axis corresponding to the first rotational maneuver in the star sensor coordinate system. .

[0050] Step 2: Second rotational motion (around preset axis 2) After the spacecraft regains triaxial stability, it will perform a second maneuver, rotating 360° around the preset axis 2. Repeat the above data acquisition and processing steps to obtain the second set of direction vector pairs. ;in, To obtain the unit direction vector of the rotation axis corresponding to the second rotational maneuver in the magnetometer coordinate system, This is the unit direction vector of the rotation axis corresponding to the second rotational maneuver in the star sensor coordinate system.

[0051] The angle between the directions of the two rotational axes in the inertial coordinate system is approximately 86°, which satisfies the noncollinearity requirement.

[0052] Step 3: Solve for the transfer matrix Input the two sets of direction vectors into the TRIAD algorithm: Construct an orthogonal basis for the reference frame using the rotation axis vectors in the star sensor coordinate system: , in, The construction process is as follows: Let The unit direction vector of the rotation axis corresponding to the second rotational maneuver in the star sensor coordinate system Coincidentally, let the unit direction vector of the rotation axis corresponding to the first rotational maneuver in the star sensor coordinate system be 0. The unit direction vector of the rotation axis corresponding to the second rotational maneuver in the star sensor coordinate system The unit vector in the cross product direction is ,make and It forms a right-handed system.

[0053] Construct the corresponding basis using the rotation axis vector in the magnetometer coordinate system: , in, The construction process is as follows: Let The unit direction vector of the rotation axis corresponding to the second rotational maneuver in the magnetometer coordinate system Let the unit direction vector of the rotation axis corresponding to the first rotational maneuver in the magnetometer coordinate system coincide. The unit direction vector of the rotation axis corresponding to the second rotational maneuver in the magnetometer coordinate system The unit vector in the cross product direction is ,make and It forms a right-handed system.

[0054] Calculate the transfer matrix: .

[0055] Example 2 This embodiment provides an on-orbit calibration system for the coordinate system transfer matrix of a vector magnetometer and a star sensor, used to implement the on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor described in Embodiment 1, including: The unit direction vector acquisition module of the magnetometer coordinate system is used to plot the magnetic field vector sequence output by the magnetometer into a three-dimensional scatter plot in the magnetometer coordinate system for each rotational maneuver, identify stable arc segments, and perform singular value decomposition on the original magnetic field data set corresponding to each stable arc segment after demeaning. The vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis corresponding to that stable arc segment in the magnetometer coordinate system. It is also used to merge the unit direction vectors of the rotation axis corresponding to all stable arc segments under the same rotational maneuver to obtain the unit direction vector of the rotation axis under that rotational maneuver in the magnetometer coordinate system. The unit direction vector acquisition module of the star sensor coordinate system, for each rotational maneuver, selects a non-zero constant vector in the inertial coordinate system as the reference vector in the inertial coordinate system; uses the star sensor measurement sequence to transform the reference vector in the inertial coordinate system to the star sensor coordinate system, and obtains the reference vector sequence in the star sensor coordinate system; after the reference vector sequence in the star sensor coordinate system is demeaned, singular value decomposition is performed, and the vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis in the star sensor coordinate system under that rotational maneuver; The calibration module is used to solve the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system based on the unit direction vector of the rotation axis in the magnetometer coordinate system and the unit direction vector of the rotation axis in the star sensor coordinate system, thereby completing the on-orbit calibration.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An on-orbit calibration method for the coordinate system transfer matrix of a vector magnetometer and a star sensor, characterized in that, include: Step 1: For each rotational maneuver, plot the magnetic field vector sequence output by the magnetometer into a 3D scatter plot in the magnetometer coordinate system and identify stable arc segments. After removing the mean from the original magnetic field data set corresponding to each stable arc segment, perform singular value decomposition to extract the vector corresponding to the smallest singular value as the unit direction vector of the rotation axis corresponding to that stable arc segment in the magnetometer coordinate system. Combine the unit direction vectors of the rotation axis corresponding to all stable arc segments under the same rotational maneuver to obtain the unit direction vector of the rotation axis under that rotational maneuver in the magnetometer coordinate system. Step 2: For each rotational maneuver, select any non-zero constant vector in the inertial coordinate system as the reference vector in the inertial coordinate system; use the star sensor measurement sequence to transform the reference vector in the inertial coordinate system to the star sensor coordinate system to obtain the reference vector sequence in the star sensor coordinate system; after removing the mean value from the reference vector sequence in the star sensor coordinate system, perform singular value decomposition and extract the vector corresponding to the minimum singular value as the unit direction vector of the rotation axis in the star sensor coordinate system under this rotational maneuver; Step 3: Solve the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system based on the unit direction vector of the rotation axis in the magnetometer coordinate system and the unit direction vector of the rotation axis in the star sensor coordinate system, thereby completing the on-orbit calibration.

2. The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor according to claim 1, characterized in that, The method is based on the following assumptions: during the time window in which the spacecraft performs rotational maneuvers, the space background magnetic field is approximately constant in the inertial coordinate system; during the duration of the calibration operation, the magnitude and direction of the magnetic field vector remain essentially unchanged; in the magnetometer coordinate system that rotates with the spacecraft, the projection of the magnetic field vector will form a circular trajectory or an arc trajectory, wherein the normal direction of the plane containing the circular trajectory or arc trajectory is the direction of the rotation axis.

3. The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor according to claim 1, characterized in that, Step 1 specifically includes performing the following operations for each rotational motion: Step 1.1: Plot the magnetic field vector sequence output by the magnetometer into a three-dimensional scatter plot in the magnetometer coordinate system; identify M relatively stable continuous data arc segments, the m-th arc segment containing Data points, Each data point is obtained from the original magnetic field data set. In this representation, the superscript m indicates the arc segment ordinal number, m = 1, 2, 3, ..., M; i indicates the data point ordinal number. Step 1.2: Analyze the original magnetic field data set for the m-th segment. The mean-removed magnetic field data set is obtained through mean-removed processing. The set of magnetic field data after removing the mean Arranged into Obtain the magnetic field data matrix for this arc segment in dimensional matrix form. ; Step 1.3: Analyze the magnetic field data matrix. Perform singular value decomposition and take the vector corresponding to the smallest singular value as the unit direction vector of the rotation axis corresponding to the stable arc segment in the magnetometer coordinate system. ; Step 1.4: Take a weighted average of the unit direction vectors of the rotation axes corresponding to all stable arc segments under the same rotational maneuver in the magnetometer coordinate system to obtain the unit direction vector of the rotation axis corresponding to the k-th rotational maneuver in the magnetometer coordinate system. : ； in, Let be the total number of valid arc segments identified in the k-th rotational maneuver. As weight.

4. The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor according to claim 3, characterized in that, Step 2 specifically includes performing the following operations for each rotational motion: Step 2.1: Arbitrarily select a non-zero constant vector in the inertial coordinate system as the reference vector in the inertial coordinate system. Among them, the reference vector in the inertial coordinate system Not parallel to the axis of rotation; Step 2.2: For each time point Using a star sensor measurement sequence, the reference vector in the inertial coordinate system is... Transform to the star sensor coordinate system to obtain the reference vector in the star sensor coordinate system. ; Step 2.3: Reference vector sequence in star-sensitive coordinate system A circular or arc-shaped trajectory is formed in the star sensor coordinate system, and a reference vector sequence in the star sensor coordinate system is obtained. After mean-free processing, singular value decomposition is performed, and the vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis in the star sensor coordinate system corresponding to the k-th rotational maneuver. .

5. The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor according to claim 4, characterized in that, The star sensor measurement sequence includes the quaternions measured by the star sensor. .

6. The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor according to claim 4, characterized in that, Step 3 specifically includes: determining the unit direction vector of the rotation axis corresponding to the same rotational maneuver in the magnetometer coordinate system. The unit direction vector of the rotation axis in the star sensor coordinate system To form vector pairs, obtain Group vector pairs , among which, among which, Let k be the total number of rotational maneuvers, and k be the ordinal number of the rotational maneuvers; based on the obtained... The transfer matrix between the magnetometer coordinate system and the star sensor coordinate system is calculated using the TRIAD algorithm or singular value decomposition algorithm. The on-orbit calibration has been completed.

7. The on-orbit calibration method for the coordinate system transfer matrix of the vector magnetometer and star sensor according to claim 6, characterized in that, when Furthermore, when the data standard deviation is less than 0.5nT, the TRIAD algorithm is used to construct an orthogonal basis and calculate the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. ; when If the data standard deviation is greater than or equal to 0.5nT, use the singular value decomposition algorithm or the QUEST algorithm to calculate the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system. .

8. An on-orbit calibration system for the coordinate system transfer matrix of a vector magnetometer and a star sensor, used to implement the on-orbit calibration method for the coordinate system transfer matrix of a vector magnetometer and a star sensor as described in any one of claims 1-7, characterized in that, include: The unit direction vector acquisition module of the magnetometer coordinate system is used to plot the magnetic field vector sequence output by the magnetometer into a three-dimensional scatter plot in the magnetometer coordinate system for each rotational maneuver, identify stable arc segments, and perform singular value decomposition on the original magnetic field data set corresponding to each stable arc segment after demeaning. The vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis corresponding to that stable arc segment in the magnetometer coordinate system. It is also used to merge the unit direction vectors of the rotation axis corresponding to all stable arc segments under the same rotational maneuver to obtain the unit direction vector of the rotation axis under that rotational maneuver in the magnetometer coordinate system. The unit direction vector acquisition module of the star sensor coordinate system, for each rotational maneuver, selects a non-zero constant vector in the inertial coordinate system as the reference vector in the inertial coordinate system; uses the star sensor measurement sequence to transform the reference vector in the inertial coordinate system to the star sensor coordinate system, and obtains the reference vector sequence in the star sensor coordinate system; after the reference vector sequence in the star sensor coordinate system is demeaned, singular value decomposition is performed, and the vector corresponding to the minimum singular value is extracted as the unit direction vector of the rotation axis in the star sensor coordinate system under that rotational maneuver; The calibration module is used to solve the transfer matrix between the magnetometer coordinate system and the star sensor coordinate system based on the unit direction vector of the rotation axis in the magnetometer coordinate system and the unit direction vector of the rotation axis in the star sensor coordinate system, thereby completing the on-orbit calibration.

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