Calibration Method, Equipment, Medium and Product for the Relationship between a Two-Axis Turntable and a Collimator

Abstract

The present invention discloses a calibration method, device, medium and product for the relationship between a two-axis turntable and a collimator, relating to the technical field of data processing. The method includes: when the theodolite and the collimator are in the light alignment condition, obtaining first angle data of the rotation of the two-axis turntable and second angle data of the rotation of the theodolite; constructing a coordinate system conversion model according to the first angle data and the second angle data; based on the first angle data, the second angle data and the coordinate system conversion model, determining a plurality of conversion matrices between the two-axis turntable coordinate system, the theodolite coordinate system of the theodolite and the collimator coordinate system; and determining the conversion relationship between the two-axis turntable and the collimator according to the plurality of conversion matrices. The present invention enables the two-axis turntable in the ground inspection simulation system to be accurately aligned and calibrated with the collimator, provides a reliable guarantee for the research and development test of the laser communication terminal, and improves the accuracy and reliability of satellite communication simulation.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular, to a method, device, medium and product for calibrating the relationship between a two-axis turntable and a collimator. Background Art

[0002] In low-earth orbit satellites, communication between satellites is the key to achieving global coverage and efficient data transmission. As an important device for satellite-to-satellite communication, the demand for laser communication terminals will continue to grow with the increase in the number of satellites.

[0003] The ground test simulation system can simulate the working environment of the laser communication terminal on the satellite, and can assist in the research, development, debugging and acceptance of the laser communication terminal on the ground. The traditional ground test simulation system mainly consists of devices such as a two-axis turntable and a collimator. The azimuth angle and elevation angle of the two-axis turntable both have the function of continuous change, and can simulate the two-axis attitude movement of the satellite; the collimator has the function of laser transceiver, and can simulate the communication transceiver of the opposite satellite.

[0004] During the research and development and testing of the laser communication terminal, it is necessary to clarify the relationship of the laser vector of the opposite satellite in the coordinate system of the local satellite. Correspondingly, in the ground test simulation system, it is necessary to clarify the relationship of the light output vector of the collimator in the coordinate system of the two-axis turntable.

[0005] Therefore, the accurate calibration of the relationship between the two-axis turntable and the collimator affects the research and development and testing of the laser communication terminal. With the rapid development of the laser communication terminal, higher requirements are also put forward for the calibration accuracy of the relationship between the two-axis turntable and the collimator. Summary of the Invention

[0006] Aiming at the above technical problems and defects, the purpose of the present invention is to provide a method, device, medium and product for calibrating the relationship between a two-axis turntable and a collimator, which can enable the two-axis turntable in the ground test simulation system to be accurately aligned and calibrated with the collimator, provide a reliable guarantee for the research and development and testing of the laser communication terminal, and improve the accuracy and reliability of satellite communication simulation.

[0007] To achieve the above object, in a first aspect, the present invention provides a method for calibrating the relationship between a two-axis turntable and a collimator, which is applied to the control processing unit of a ground inspection simulation system. The ground inspection simulation system further includes a two-axis turntable, a collimator, and a theodolite. The two-axis turntable includes a pitch rotation assembly and a horizontal azimuth rotation assembly. The theodolite includes a base that can rotate in the horizontal azimuth and a telescope that can pitch and rotate in the vertical direction. The base is connected to the pitch rotation assembly, and the telescope is disposed opposite to the light outlet of the collimator. The method includes: when the theodolite and the collimator are in the light alignment condition, obtaining the first angle data of the rotation of the two-axis turntable and the second angle data of the rotation of the theodolite, where the light alignment condition means that the light spot of the telescope coincides with the light spot of the collimator; in the case of defining the two-axis turntable coordinate system of the two-axis turntable, the theodolite coordinate system of the theodolite, and the collimator coordinate system of the collimator, constructing a coordinate system transformation model according to the first angle data and the second angle data; based on the first angle data, the second angle data, and the coordinate system transformation model, determining a plurality of transformation matrices between the two-axis turntable coordinate system, the theodolite coordinate system of the theodolite, and the collimator coordinate system; and determining the transformation relationship between the two-axis turntable and the collimator according to the plurality of transformation matrices.

[0008] Through the above method, the present invention can improve the accuracy and reliability of the ground inspection simulation system in simulating inter-satellite laser communication. By accurately obtaining the angle data of the two-axis turntable and the theodolite in the light alignment condition and constructing a coordinate system transformation model, the transformation relationship between the two-axis turntable coordinate system and the collimator coordinate system can be accurately calculated. This process not only considers the rotation angles of the two-axis turntable and the theodolite, but also comprehensively considers the spatial relationship between multiple coordinate systems through the coordinate system transformation model, so as to ensure that the two-axis turntable can accurately align with the light beam emitted by the collimator during the simulation of satellite communication. Moreover, by optimizing the algorithm and the true value loss function, the accuracy of the calibration process is further improved, and the influence of human measurement error and environmental noise is reduced. Finally, the efficient and accurate testing of the satellite communication terminal is realized, providing strong support for the research and development and quality assurance of satellite communication technology.

[0009] Combined with some embodiments of the first aspect, in some embodiments, the first angle data includes a plurality of first pitch angles and a plurality of first azimuth angles, and the second angle data includes a plurality of second pitch angles and a plurality of second azimuth angles; the two-axis turntable coordinate system includes the two-axis turntable zero-position coordinate system when both the first pitch angle and the first azimuth angle are 0, and the two-axis turntable instantaneous coordinate system when at least one of the first pitch angle and the first azimuth angle is not 0; the theodolite coordinate system includes the theodolite zero-position coordinate system when both the second pitch angle and the second azimuth angle are 0, and the theodolite instantaneous coordinate system when at least one of the second pitch angle and the second azimuth angle is not 0.

[0010] Adopting the technical solution of the above embodiment, by defining the first angle data and the second angle data in detail, including multiple pitch angles and azimuth angles, it provides a data basis for the precise control of the two-axis turntable and the theodolite. The acquisition of such multi-angle data allows the system to capture more subtle attitude changes, thus achieving more precise alignment when simulating satellite communication. By distinguishing the zero-position coordinate system and the instantaneous coordinate system of the two-axis turntable, as well as the zero-position coordinate system and the instantaneous coordinate system of the theodolite, the adaptability and flexibility of the system to the attitude changes of the equipment are enhanced. This provides richer and more precise input parameters for the subsequent coordinate transformation model, ensuring the accuracy of the calibration process and the reliability of the coordinate transformation.

[0011] Combined with some embodiments of the first aspect, in some embodiments, a coordinate transformation model is constructed according to the first angle data and the second angle data, including: determining a first known transformation matrix between the zero-position coordinate system of the two-axis turntable and the instantaneous coordinate system of the two-axis turntable, and a second known transformation matrix between the zero-position coordinate system of the theodolite and the instantaneous coordinate system of the theodolite; defining the representation of the first unit vector of the x-axis in the collimator coordinate system in the zero-position coordinate system of the two-axis turntable as a first unknown transformation matrix, and the transformation matrix between the instantaneous coordinate system of the two-axis turntable and the zero-position coordinate system of the theodolite as a second unknown transformation matrix; when, under the collimation condition, the second unit vector of the x-axis in the instantaneous coordinate system of the theodolite coincides with the first unknown transformation matrix, determining the mathematical relationship between the second unit vector, the first known transformation matrix, the second known transformation matrix, the first unknown transformation matrix, and the second unknown transformation matrix; constructing a coordinate transformation model according to the first angle data, the second angle data, and the mathematical relationship.

[0012] Adopting the technical solution of the above embodiment, by constructing a coordinate system transformation model, the known transformation matrices between the zero-position coordinate system of the two-axis turntable and the instantaneous coordinate system, between the zero-position coordinate system of the theodolite and the instantaneous coordinate system, and the representation of the first unit vector of the x-axis in the parallel light tube coordinate system in the zero-position coordinate system of the two-axis turntable are clarified. The refinement of this step makes the transformation relationship between coordinate systems clearer, providing a clear framework for subsequent mathematical calculations and calibrations. By defining known and unknown transformation matrices and establishing the mathematical relationship between them under the light alignment condition, it lays a foundation for accurately solving the unknown transformation matrix, thereby improving the accuracy and efficiency of the calibration process. Combining some embodiments of the first aspect, in some embodiments, the mathematical relationship among the second unit vector, the first known transformation matrix, the second known transformation matrix, the first unknown transformation matrix, and the second unknown transformation matrix specifically includes: the third unknown transformation matrix between the zero-position coordinate system of the two-axis turntable and the instantaneous coordinate system of the theodolite is equal to the product of the first known transformation matrix, the second unknown transformation matrix, and the second known transformation matrix; the first unknown transformation matrix is equal to the product of the third unknown transformation matrix and the second unit vector.

[0013] Adopting the technical solution of the above embodiment, the construction process of the coordinate system transformation model is further refined, especially by clarifying the calculation method of the third unknown transformation matrix, that is, the transformation relationship between the zero-position coordinate system of the two-axis turntable and the instantaneous coordinate system of the theodolite. The clarification of this step makes the coordinate transformation from the two-axis turntable to the theodolite more accurate, providing a key intermediate result for finally determining the transformation relationship between the two-axis turntable and the parallel light tube. By relating the solution values of the first unknown transformation matrix and the third unknown transformation matrix, it provides a powerful mathematical tool for realizing accurate coordinate system transformation, thereby ensuring the accuracy of the calibration result.

[0014] Combining some embodiments of the first aspect, in some embodiments, the steps of constructing a coordinate system transformation model according to the first angle data, the second angle data, and the mathematical relationship include: constructing a solution function of the first unknown transformation matrix according to the mathematical relationship between the first unknown transformation matrix, the first known transformation matrix, the second unknown transformation matrix, and the second known transformation matrix; determining the truth value loss function of the truth value matrix corresponding to the first unknown transformation matrix based on the first angle data, the second angle data, and the solution function; determining the coordinate system transformation model based on the truth value loss function.

[0015] Adopting the technical solution of the above embodiment, by constructing a solution function and a truth loss function, an effective numerical method is provided for determining the first unknown transformation matrix. This method allows the system to minimize the difference between the predicted value and the actual measured value through an iterative optimization process, thereby improving the accuracy of the transformation matrix solution. By substituting the first angle data and the second angle data into the solution function, the system can calculate multiple possible solution values, and by averaging and optimizing these solution values, a more reliable transformation matrix can be obtained. This process not only improves the accuracy of calibration but also provides an effective strategy for dealing with measurement errors and noise.

[0016] In combination with some embodiments of the first aspect, in some embodiments, based on the first angle data, the second angle data, and the solution function, determining the truth loss function corresponding to the first unknown transformation matrix includes: substituting the first angle data and the second angle data into the solution function to calculate multiple solution values of the first unknown transformation matrix; calculating the average value of the multiple solution values of the first unknown transformation matrix to obtain an average vector; and determining the truth loss function based on the difference between the multiple solution values of the first unknown transformation matrix and the average vector.

[0017] Adopting the technical solution of the above embodiment, by specifying the determination process of the truth loss function, a systematic method is provided for accurately solving the first unknown transformation matrix. By substituting the first angle data and the second angle data into the solution function, calculating multiple solution values, and determining the truth loss function based on the difference between these solution values and the average vector, a clear mathematical basis is provided for optimizing the transformation matrix. This method not only improves the accuracy of the solution process but also provides an effective strategy for dealing with multiple sets of data, thereby ensuring the reliability and stability of the final calibration result.

[0018] In combination with some embodiments of the first aspect, in some embodiments, the steps of determining the transformation relationship between the two-axis turntable and the collimator according to the multiple transformation matrices include: solving to obtain the solution value of the second unknown transformation matrix according to the truth loss function and the solution value of the first unknown transformation matrix; determining the solution value of the third unknown transformation matrix based on the solution value of the second unknown transformation matrix and the solution function; and determining the Euler angles between the two-axis turntable and the collimator according to the solution value of the third unknown transformation matrix, where the Euler angles are used to represent the transformation relationship between the two-axis turntable and the collimator.

[0019] Adopting the technical solution of the above embodiment, by clarifying the steps to finally determine the conversion relationship between the two-axis turntable and the collimator, a key solution for achieving precise calibration is provided. By solving the solution value of the second unknown conversion matrix, the solution value of the third unknown conversion matrix is determined, and finally, the Euler angles are calculated based on these solution values, providing an intuitive and accurate method for describing the spatial relationship between the two-axis turntable and the collimator. These Euler angles not only reflect the rotation relationship between the two coordinate systems but also provide key parameters for achieving precise equipment alignment and simulation. Through this method, the system can ensure that during the simulation of satellite communication, the two-axis turntable can accurately point to the collimator, thereby improving the accuracy of the simulation and the reliability of communication testing.

[0020] In a second aspect, an embodiment of the present invention provides an electronic device, including: one or more processors and a memory; the memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code includes computer instructions, and the one or more processors call the computer instructions to cause the electronic device to execute the method described in the first aspect or the second aspect, and any possible implementation manner in the first aspect or the second aspect.

[0021] In a third aspect, the present invention provides a computer-readable storage medium, including instructions, when the above instructions run on an electronic device, causing the above electronic device to execute the method described in the first aspect or the second aspect, and any possible implementation manner in the first aspect or the second aspect.

[0022] In a fourth aspect, the present invention provides a computer program product containing instructions, when the above computer program product runs on an electronic device, causing the above electronic device to execute the method described in the first aspect or the second aspect, and any possible implementation manner in the first aspect or the second aspect.

[0023] It can be understood that the electronic device provided in the second aspect, the storage medium provided in the third aspect, and the computer program product provided in the fourth aspect are all used to execute the method provided by the present invention. Therefore, the beneficial effects that can be achieved can refer to the beneficial effects in the corresponding method and will not be elaborated here.

[0024] One or more technical solutions provided by the present invention have at least the following technical effects or advantages:

[0025] 1. Improve calibration accuracy: The present invention improves the calibration accuracy between the two-axis turntable and the collimator. By comprehensively utilizing the multi-angle data of the two-axis turntable and the theodolite and combining with the coordinate system conversion model, multiple conversion matrices can be accurately calculated, thereby ensuring that the conversion relationship between the two-axis turntable coordinate system and the collimator coordinate system can be accurately determined. This high-precision calibration is crucial for simulating satellite-to-satellite communication because it directly affects the accuracy of the communication system alignment.

[0026] 2. Enhance the adaptability and flexibility of the system: The adaptability and flexibility of the ground test simulation system are enhanced. By defining the zero-position coordinate system and the instantaneous coordinate system of the two-axis turntable, as well as the corresponding coordinate systems of the theodolite, the system can adapt to various different measurement postures and position changes. This design enables the system not only to handle calibrations under ideal conditions but also to cope with complex situations that may occur in practical applications, such as small changes in the equipment posture or measurement errors, thus providing reliable calibration results under various working conditions.

[0027] 3. Optimize the measurement data processing and calibration process: The present invention also optimizes the measurement data processing and calibration process, improving the efficiency and convenience of operation. By constructing a solution function and a true value loss function, the system can automatically process and analyze data, reducing the interference of human factors and accelerating the calibration process. This method not only improves the speed of data processing but also enhances the stability and reliability of the calibration results through an iterative optimization algorithm. In addition, by clearly defining each step and mathematical model, this solution provides clear guidance for operators, making the entire calibration process more standardized and systematic. Description of the Drawings

[0028] The drawings here are incorporated into the specification and form a part of this specification, showing embodiments in accordance with the present invention, and are used together with the specification to explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts. In the drawings:

[0029] Figure 1 is a schematic diagram of the architecture of a ground test simulation system according to an embodiment of the present invention;

[0030] Figure 2 is a schematic diagram of the process of a calibration method for the relationship between a two-axis turntable and a collimator according to an embodiment of the present invention;

[0031] Figure 3 is a schematic diagram of the architecture of an electronic device according to an embodiment of the present invention. Detailed Embodiments

[0032] The terms used in the following embodiments of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention, the singular forms "a", "an", "the above", "the", and "this" are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used in the present invention refers to any or all possible combinations including one or more of the listed items.

[0033] Hereinafter, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0034] It should also be noted that, unless otherwise clearly specified and defined, in the embodiments of the present invention, terms such as "arranged" and "connected" should be understood in a broad sense. For example, "connected" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, and can be the communication inside two components; it can be a wired communication connection or a wireless communication connection. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. The embodiments of the present invention will be specifically described below.

[0035] An embodiment of the present invention provides a ground inspection simulation system, as Figure 1 shown, including a control processing unit 101, a two-axis turntable 102, a theodolite 103, and a collimator 104. The two-axis turntable 102 includes a pitch rotation assembly and a horizontal azimuth rotation assembly. The theodolite 103 includes a base that can rotate in the horizontal azimuth and a telescope that can pitch and rotate in the vertical direction. The base is connected to the pitch rotation assembly, and the telescope is disposed opposite to the light outlet of the collimator 104.

[0036] The two-axis turntable 102 is used to simulate the attitude changes of a satellite in space through the pitch rotation assembly and the horizontal azimuth rotation assembly. This high-precision simulation is crucial for testing the orientation and communication equipment of the satellite.

[0037] The collimator 104 serves to simulate the laser communication signal of the opposite satellite. It can generate a highly collimated light beam to simulate the laser signal used in actual satellite-to-satellite communication, ensuring the authenticity of the test environment.

[0038] The theodolite 103 is an instrument for precisely measuring angles. It includes a base that can rotate horizontally and a telescope that can pitch and rotate vertically. In the ground inspection simulation system, the theodolite 103 is used to precisely align with the light beam emitted by the collimator 104 to achieve precise calibration.

[0039] The control processing unit 101 is the brain of the ground inspection simulation system, responsible for coordinating and controlling the operations of the two-axis turntable 102, the collimator 104, and the theodolite 103. It receives data from each component, executes the calibration algorithm, and outputs the final calibration result to ensure the precise operation of the entire system.

[0040] An embodiment of the present invention provides a method for calibrating the relationship between a two-axis turntable and a collimator, which is applied to the ground inspection simulation system provided in the above embodiment and is executed by the control processing unit. This embodiment can improve the accuracy and reliability of the ground inspection simulation system when simulating inter-satellite laser communication. By precisely obtaining the angular data of the two-axis turntable and the theodolite under the light alignment condition and constructing a coordinate system transformation model, the transformation relationship between the two-axis turntable coordinate system and the collimator coordinate system can be accurately calculated. This process not only considers the rotation angles of the two-axis turntable and the theodolite but also comprehensively considers the spatial relationship between multiple coordinate systems through the coordinate system transformation model, thereby ensuring that the two-axis turntable can accurately align with the light beam emitted by the collimator during the simulation of satellite communication. Moreover, by optimizing the algorithm and the true value loss function, the accuracy of the calibration process is further improved, reducing the influence of human measurement errors and environmental noise. Finally, the efficient and precise testing of the satellite communication terminal is realized, providing strong support for the research and development and quality assurance of satellite communication technology.

[0041] The following will specifically describe the method of this embodiment in conjunction with Figure 2 and specifically includes the following steps:

[0042] Step 201, when the theodolite and the collimator are in the light alignment condition, obtain the first angular data of the rotation of the two-axis turntable and the second angular data of the rotation of the theodolite.

[0043] Among them, the light alignment condition means that the light spot of the telescope coincides with the light spot of the collimator.

[0044] In the ground inspection simulation system, the light alignment condition is a key step, which ensures the precise alignment between the telescope of the theodolite and the collimator. When the theodolite and the collimator are in the light alignment condition, it means that the light spot of the theodolite telescope coincides precisely with the light spot of the light outlet of the collimator.

[0045] In the ground inspection simulation system, to complete the process of light alignment, it is first necessary to ensure the correct configuration of the two-axis turntable and the theodolite so that the telescope of the theodolite is aligned with the light outlet of the collimator.

[0046] The specific operation begins with setting the collimator to the emission mode to generate a highly collimated beam. Then, the position of the two-axis turntable is adjusted so that its pitch rotation assembly and horizontal azimuth rotation assembly reach predetermined angles, which are pre-calculated or determined through experiments to simulate a specific attitude of the satellite.

[0047] Then, operate the theodolite so that its base rotates horizontally and the telescope rotates vertically until the center of the field of view of the telescope coincides exactly with the light spot emitted from the light outlet of the collimator, achieving light alignment.

[0048] At this position, record the current angle data of the two-axis turntable and the theodolite. These data are the first angle data and the second angle data under the light alignment condition. These data reflect the precise attitudes of the two-axis turntable and the theodolite in the light alignment state, providing key input parameters for the subsequent establishment and calibration of the coordinate system conversion model.

[0049] Through precise light alignment operations, it can be ensured that during the simulation of satellite communication, the two-axis turntable can accurately simulate the attitude changes of the satellite, while the theodolite can precisely track and align with the analog signals emitted by the collimator, thus achieving high-precision satellite communication simulation tests.

[0050] In some embodiments, the light alignment operation can be performed in the following manner:

[0051] First, connect a red visible laser at the beam analyzer of the collimator. After the laser is beam-expanded by the collimator, it is transformed into a parallel beam and emitted from the light outlet. At this time, place a corner cube prism at the light outlet so that the emitted parallel beam is reflected back to the collimator at the same angle and forms a point light source after re-convergence. Through the beam analyzer and its host computer, the centroid position of this reflected light spot A can be measured and recorded as the coordinates (x1, y1).

[0052] Subsequently, aim the theodolite telescope at the collimator, turn on the red visible laser, adjust the two-axis turntable to a specific attitude, and record the pitch angle and azimuth angle of the two-axis turntable at this time through the host computer of the two-axis turntable, denoted as Then, adjust the horizontal and vertical angles of the theodolite so that the laser emitted by the telescope can enter the collimator and re-converge to form a laser light spot on the target surface of the beam analyzer. Through careful adjustment, make the centroid of this laser light spot coincide with the centroid of the light spot A recorded in step one, thus completing one light alignment.

[0053] Finally, record the vertical angle (pitch angle) and horizontal angle (azimuth angle) of the theodolite at this time. This angle is denoted as

[0054] In this way, an accurate optical alignment operation is completed, providing the necessary initial data and attitude information for subsequent calibration work.

[0055] Step 202, in the case where the two-axis turntable coordinate system of the two-axis turntable, the theodolite coordinate system of the theodolite, and the collimator coordinate system of the collimator are defined, a coordinate system transformation model is constructed according to the first angle data and the second angle data.

[0056] Among them, the coordinate system transformation model can describe the spatial pose relationship between the two-axis turntable coordinate system, the theodolite coordinate system, and the collimator coordinate system. As Figure 1 shown, the X-axis, Y-axis, Z-axis, and origin O of the two-axis turntable coordinate system Tun are denoted as X Tun , Y Tun , Z Tun and O Tun respectively; the X-axis, Y-axis, Z-axis, and origin O of the theodolite coordinate system Theo are denoted as X Theo , Y Theo , Z Theo and O Theo respectively; the X-axis, Y-axis, Z-axis, and origin O of the collimator coordinate system Coll are denoted as X Coll , Y Coll , Z Coll and O Coll respectively.

[0057] First, define the origin, axial direction, and relative positions of these three coordinate systems. The two-axis turntable coordinate system is based on the pitch and azimuth rotation axes of the two-axis turntable, the theodolite coordinate system is based on the vertical and horizontal rotation axes of the theodolite, and the origin of the collimator coordinate system is located at the center of the light outlet of the collimator, and its axial direction is consistent with the light propagation direction of the collimator.

[0058] After defining these coordinate systems, using the first angle data and the second angle data collected from the two-axis turntable and the theodolite, the control processing unit can construct a mathematical model to describe the conversion relationship between these coordinate systems. The first angle data includes the pitch angle and azimuth angle of the two-axis turntable in various postures, and these angles reflect the current spatial orientation of the turntable. The second angle data includes the vertical and horizontal angles of the theodolite, and these angles determine the pointing direction of the theodolite telescope.

[0059] Through these angle data, the control processing unit can calculate the transformation matrix from the two-axis turntable coordinate system to the theodolite coordinate system, the transformation matrix from the theodolite coordinate system to the collimator coordinate system, and the transformation matrix from the collimator coordinate system to the two-axis turntable coordinate system. These matrices are realized through the product of rotation matrices. The rotation matrix is defined according to Euler angles and can transform points in one coordinate system to another coordinate system. In actual operation, the construction and calculation of these matrices involve trigonometric functions and vector algebra.

[0060] Finally, the coordinate system conversion model enables the control processing unit to calculate the corresponding position and orientation in the collimator coordinate system based on the measured angle data of the two-axis turntable and the theodolite.

[0061] In some embodiments, the first angle data includes a plurality of first pitch angles and a plurality of first azimuth angles, and the second angle data includes a plurality of second pitch angles and a plurality of second azimuth angles.

[0062] Exemplarily, the first pitch angle and the first azimuth angle can be denoted as The second pitch angle and the first azimuth angle can be denoted as

[0063] The two-axis turntable coordinate system includes the two-axis turntable zero-position coordinate system when both the first pitch angle and the first azimuth angle are 0, and the two-axis turntable instantaneous coordinate system when at least one of the first pitch angle and the first azimuth angle is not 0.

[0064] Exemplarily, the two-axis turntable zero-position coordinate system can be denoted as Tun-Zero. The two-axis turntable zero-position coordinate system defines the initial spatial orientation of the two-axis turntable when no rotation is performed, that is, when both the pitch angle and the azimuth angle are 0. In this state, the origin of the coordinate system is set at the intersection of the pitch rotation axis and the azimuth rotation axis of the two-axis turntable, and this point is the center of the rotational movement of the two-axis turntable. According to the right-hand rule, with the thumb pointing in the positive x-axis direction, the index finger pointing in the positive y-axis direction, and the middle finger pointing in the positive z-axis direction, the x-axis, y-axis, and z-axis of the two-axis turntable zero-position coordinate system are determined by the right-hand rule: the y-axis is along the pitch rotation axis direction of the two-axis turntable, and the z-axis is along the azimuth rotation axis direction, and the x-axis is determined by the right-hand rule. Regardless of how the two-axis turntable rotates, the two-axis turntable zero-position coordinate system always remains unchanged, providing a reference for the movement of the turntable, such that the attitude of the turntable at any moment can be described by the angular changes relative to this zero-position coordinate system.

[0065] The two-axis turntable instantaneous coordinate system can be denoted as Tun-Ins. The two-axis turntable instantaneous coordinate system is a dynamically changing coordinate system that is updated in real time based on the two-axis turntable zero-position coordinate system with any rotation of the pitch angle and the azimuth angle of the two-axis turntable. When the two-axis turntable performs a rotation operation, whether it is a small adjustment or a large rotation, the instantaneous coordinate system will accurately reflect the current attitude change. The origin of the two-axis turntable instantaneous coordinate system is the same as that of the zero-position system, located at the intersection of the pitch axis and the azimuth axis. However, different from this, the directions of the x-axis, y-axis, and z-axis of the two-axis turntable instantaneous coordinate system will change with the pitch and azimuth rotations of the two-axis turntable, always consistent with the current attitude of the two-axis turntable. This design enables the instantaneous coordinate system to capture and describe the spatial orientation of the turntable in real time, providing an important reference framework for accurately controlling and monitoring the movement of the turntable.

[0066] The theodolite coordinate system includes the theodolite zero coordinate system when both the second pitch angle and the second azimuth angle are 0, and the theodolite instantaneous coordinate system when at least one of the second pitch angle and the second azimuth angle is not 0.

[0067] Exemplarily, the theodolite zero coordinate system can be denoted as Theo-Zero. The theodolite zero coordinate system is a reference coordinate system used to describe the initial coordinate state of the theodolite when it has not undergone any rotation. In the theodolite zero coordinate system, when the pitch angle and the azimuth angle of the theodolite are both set to zero degrees, the coordinate system remains fixed and does not change with the subsequent rotation of the theodolite. The origin of the theodolite zero coordinate system is set at the intersection of the vertical rotation axis (pitch rotation axis) and the horizontal rotation axis (azimuth rotation axis) of the theodolite. The x-axis of the theodolite zero coordinate system is determined according to the right-hand rule, the y-axis is along the pitch rotation axis direction of the theodolite, and the z-axis is along the azimuth rotation axis direction. Such a coordinate system setting provides a stable reference for the theodolite, enabling accurate determination of the spatial relationship in any other attitude starting from this zero state when performing angle measurement and positioning.

[0068] The theodolite instantaneous coordinate system can be denoted as Theo-Ins, which is a dynamic coordinate system. The theodolite instantaneous coordinate system starts from the theodolite zero coordinate system and updates its direction in real time with the vertical and horizontal rotations of the theodolite. When the theodolite performs an observation or positioning operation, its vertical axis (pitch axis) and horizontal axis (azimuth axis) will rotate to specific angles as needed. This rotation causes a change in the observation direction of the theodolite, and the instantaneous coordinate system accurately reflects this change. Specifically, the origin of the theodolite instantaneous coordinate system remains at the rotation center of the theodolite, but the coordinate axes (x-axis, y-axis, z-axis) will rotate according to the adjustment of the vertical angle and the horizontal angle to ensure consistency with the current observation direction of the theodolite at all times. Such a coordinate system provides a dynamic reference framework for precise measurement and real-time tracking, enabling the theodolite to flexibly align with different targets while maintaining the accuracy and consistency of measurement data.

[0069] The collimator coordinate system can be denoted as Coll, which is a fixed coordinate system. Similar to the two-axis turntable zero coordinate system, the collimator coordinate system does not change with any mechanical movement and provides a stable reference for the system. In the collimator coordinate system, the origin is set at the center of the light exit port of the collimator, which is the starting point for beam emission and propagation. The x-axis is along the direction of the incident light inside the collimator, defining the direction of light propagation, and the y-axis and z-axis are determined according to the right-hand rule, where the y-axis is perpendicular to the x-axis and the z-axis, and the z-axis points vertically downward. Such a coordinate system setting enables the collimator system to clearly describe the spatial propagation characteristics of the light beam and the relative position relationship between the light beam and other devices (such as the two-axis turntable and the theodolite), which is crucial for accurately simulating and testing the optical system.

[0070] In some embodiments, step 202 may include the following steps:

[0071] S21. Determine a first known transformation matrix between the two-axis turntable zero-position coordinate system and the two-axis turntable instantaneous coordinate system, and a second known transformation matrix between the theodolite zero-position coordinate system and the theodolite instantaneous coordinate system.

[0072] Among them, the first known transformation matrix can be denoted as The second known transformation matrix can be denoted as

[0073] Specifically, the first known transformation matrix is the transformation matrix from the zero-position coordinate system of the two-axis turntable to its instantaneous coordinate system, which reflects the transformation of the turntable from its initial position (pitch angle and azimuth angle are zero) to an arbitrary attitude. The second known transformation matrix is the transformation matrix from the theodolite zero-position coordinate system to the theodolite instantaneous coordinate system, which describes the transformation of the theodolite from its standard position (vertical and horizontal angles are zero) to the current measurement position.

[0074] These first known transformation matrix and second known transformation matrix are known because they are based on the design parameters of the two-axis turntable and the theodolite, and can be obtained through direct measurement or calculation.

[0075] Exemplarily, the two-axis turntable zero-position coordinate system Tun-Zero is converted to the two-axis turntable instantaneous coordinate system Tun-Ins through ZY internal rotation, and the conversion relationship between the two can be represented by the following mathematical formula:

[0076]

[0077] Among them, ψ and θ respectively represent the azimuth angle and pitch angle of the two-axis turntable zero-position coordinate system Tun-Zero rotating to the two-axis turntable instantaneous coordinate system Tun-Ins. This azimuth angle and pitch angle can be measured and obtained by the upper computer of the two-axis turntable. Therefore, the first known transformation matrix is a known matrix.

[0078] The theodolite zero-position coordinate system Theo-Zero is converted to the theodolite instantaneous coordinate system Theo-Ins through ZY internal rotation, and the conversion relationship between the two can be expressed as:

[0079]

[0080] Among them, ψ and θ respectively represent the azimuth angle and pitch angle of the theodolite zero-position coordinate system Theo-Zero rotating to the theodolite instantaneous coordinate system Theo-Ins. This azimuth angle and pitch angle can be measured and obtained by the upper computer of the theodolite. Therefore, the second known transformation matrix is a known matrix.

[0081] S22. Define the representation of the first unit vector of the x-axis in the collimator coordinate system in the two-axis turntable zero-position coordinate system as the first unknown transformation matrix, and the transformation matrix between the two-axis turntable instantaneous coordinate system and the theodolite zero-position coordinate system as the second unknown transformation matrix.

[0082] Among them, the first unknown transformation matrix can be denoted as W TUN-Zero , and the second unknown transformation matrix can be denoted as

[0083] Specifically, the control processing unit defines the representation of the first unit vector of the x-axis in the collimator coordinate system in the two-axis turntable zero-position coordinate system, which constitutes the first unknown transformation matrix. At the same time, the control processing unit also defines the transformation matrix between the two-axis turntable instantaneous coordinate system and the theodolite zero-position coordinate system, which is the second unknown transformation matrix.

[0084] These two matrices are unknown because they involve the relative position and orientation between the two-axis turntable and the collimator during the actual measurement process and need to be determined through subsequent data processing and calculations.

[0085] Exemplarily, the two-axis turntable zero-position coordinate system Tun-Zero is transformed to the collimator coordinate system Coll through an internal rotation of ZYX, and the transformation relationship between them can be expressed as:

[0086]

[0087]

[0088] Among them, ψ, θ, and φ respectively represent the azimuth angle, pitch angle, and roll angle when the two-axis turntable zero-position coordinate system Tun-Zero is rotated to the collimator coordinate system Coll.

[0089] The first unit vector W Coll =(1 0 0) T , and its representation in the two-axis turntable zero-position coordinate system Tun-Zero is the first unknown transformation matrix The first unknown transformation matrix is constant and is an unknown vector to be solved.

[0090] The two-axis turntable instantaneous coordinate system Tun-Ins is transformed to the theodolite zero-position coordinate system Theo-Zero through an internal rotation of ZYX, and the transformation relationship between them can be expressed as:

[0091]

[0092] Among them, ψ, θ, and φ respectively represent the azimuth angle, pitch angle, and roll angle when the two-axis turntable instantaneous coordinate system Tun-Ins is rotated to the theodolite zero-position coordinate system Theo-Zero.

[0093] Second unknown transformation matrix Represents the installation matrix of the theodolite on the pitch rotation assembly of the two-dimensional turntable, which is unknown but constant.

[0094] S23. Under the collimation condition, when the second unit vector of the x-axis in the theodolite instantaneous coordinate system coincides with the first unknown transformation matrix, determine the mathematical relationship among the second unit vector, the first known transformation matrix, the second known transformation matrix, the first unknown transformation matrix, and the second unknown transformation matrix.

[0095] Among them, the second unit vector can be denoted as W Theo-Ins .

[0096] Under the collimation condition, that is, when the collimation point of the theodolite telescope coincides with the collimation point of the collimator, the control processing unit determines the relationship between the second unit vector of the x-axis in the theodolite instantaneous coordinate system and the first unknown transformation matrix. At this time, the second unit vector just coincides with the first unknown transformation matrix, and the control processing unit uses this condition to establish the mathematical relationship among the second unit vector, the first known transformation matrix, the second known transformation matrix, the first unknown transformation matrix, and the second unknown transformation matrix.

[0097] In some embodiments, the mathematical relationship among the second unit vector, the first known transformation matrix, the second known transformation matrix, the first unknown transformation matrix, and the second unknown transformation matrix may include:

[0098] The third unknown transformation matrix between the zero-position coordinate system of the two-axis turntable and the theodolite instantaneous coordinate system Is equal to the product of the first known transformation matrix, the second unknown transformation matrix, and the second known transformation matrix; the first unknown transformation matrix is equal to the product of the third unknown transformation matrix and the second unit vector.

[0099] Specifically, the third unknown transformation matrix can be denoted as

[0100] In this embodiment, the process of transforming the zero-position coordinate system Tun-Zero of the two-axis turntable to the theodolite instantaneous coordinate system Theo-Ins is as follows: First, the zero-position coordinate system Tun-Zero of the two-axis turntable is transformed to the instantaneous coordinate system Tun-Ins of the two-axis turntable, then the instantaneous coordinate system Tun-Ins of the two-axis turntable is transformed to the zero-position coordinate system Theo-Zero of the theodolite, and finally the zero-position coordinate system Theo-Zero of the theodolite is transformed to the theodolite instantaneous coordinate system Theo-Ins.

[0101] This process can be expressed as:

[0102]

[0103] That is, the third unknown transformation matrix is equal to the product of the first known transformation matrix and the second unknown transformation matrix and the second known transformation matrix .

[0104] When aligning the light, the second unit vector is represented as W Theo-Ins =(1 0 0) T , which coincides with the first unknown transformation matrix W TUN-Zero , then there is:

[0105]

[0106] wherein, W TUN-Zero and are unknowns, but are constant quantities during the n - time data acquisition process; and W Theo-Ins are known quantities.

[0107] S24. Construct a coordinate system transformation model according to the first angle data, the second angle data and the above - mentioned mathematical relationship.

[0108] Specifically, the control processing unit uses the first angle data and the second angle data, combines with the mathematical relationship established in step S23, and constructs the final coordinate system transformation model. This coordinate system transformation model can describe and calculate the spatial relationship between the two - axis turntable coordinate system and the collimator coordinate system under any given measurement attitude, so as to achieve accurate calibration and alignment. Through this coordinate system transformation model, the control processing unit can accurately guide the operations of the two - axis turntable and the collimator to ensure their accurate alignment during the simulated satellite communication process.

[0109] In some embodiments, this step may specifically include:

[0110] S241. Construct a solution function for the first unknown transformation matrix according to the mathematical relationship between the first unknown transformation matrix, the first known transformation matrix, the second unknown transformation matrix and the second known transformation matrix.

[0111] wherein, this solution function can be used to solve the first unknown transformation matrix W TUN-Zero , that is, the representation of the first unit vector of the x - axis in the collimator coordinate system in the two - axis turntable zero - position coordinate system.

[0112] To construct this solution function, the control processing unit analyzes the first unknown transformation matrix W TUN-Zero and the first known transformation matrix the second unknown transformation matrix and the second known transformation matrix The mathematical relationships among them describe the transformations between the two-axis turntable, the theodolite coordinate system, and the collimator.

[0113] Specifically, the solving function may include:

[0114]

[0115] The second unit vector is denoted as W Theo-Ins is known.

[0116] S242. Based on the first angle data, the second angle data, and the solving function, determine the true value loss function of the true value matrix corresponding to the first unknown transformation matrix.

[0117] The control processing unit uses the first angle data and the second angle data, combined with the above solving function, to determine the true value loss function of the true value matrix corresponding to the first unknown transformation matrix. The true value loss function is a function that evaluates the difference between the model prediction and the actual observed data, usually in the form of the sum of squared errors. The control processing unit quantifies the deviation between the first unknown transformation matrix predicted by the solving function and the actual measurement data through this loss function, thereby evaluating the accuracy and reliability of the solving function. This true value loss function will be used to guide the subsequent numerical optimization process to find the value of the first unknown transformation matrix that best matches the actual measurement data.

[0118] In some embodiments, this step may specifically include:

[0119] S2421. Substitute the first angle data and the second angle data into the solving function to calculate multiple solution values of the first unknown transformation matrix.

[0120] The control processing unit is responsible for substituting the collected first angle data and second angle data into the previously constructed solving function. This solving function is designed to calculate the solution value of the first unknown transformation matrix, that is, to determine the representation of the first unit vector of the x-axis in the collimator coordinate system in the zero-position coordinate system of the two-axis turntable. By applying the actually measured angle data to the function, the control processing unit can calculate multiple possible solution values, which represent the possible states of the unknown transformation matrix under different measurement conditions. This step is the basis of the numerical solution process and provides the original data for subsequent analysis and optimization.

[0121] Specifically, the solving function includes:

[0122]

[0123] Based on the formula in the above solving function, define the expression on the right side of the equation as:

[0124]

[0125] In this expression, there is only one unknown quantity That is, the second unknown transformation matrix.

[0126] First, take any known matrix C as Substitute it into the expression f(right). Then substitute the (pitch, azimuth) angles of the two-axis turntable for collecting n pairs of light-spot points and the (vertical, horizontal) angles of the theodolite into the expression f(right). Then, for n groups of measurement data, n Ws can be calculated TUN-Zero , where W TUN-Zero is defined as the solution value of the first unknown transformation matrix.

[0127] S2422. Calculate the average value of multiple solution values of the first unknown transformation matrix to obtain an average vector.

[0128] The control processing unit calculates the average value of multiple solution values of the first unknown transformation matrix obtained in step S2421. Specifically, the control processing unit aggregates all the solution values and calculates their arithmetic mean to obtain an average vector representing the average state. This average vector is a measure of the central tendency of all possible solution values, and it helps the control processing unit evaluate and optimize the solution process because it provides a reference point for measuring the consistency and accuracy of each solution value.

[0129] Specifically, the above calculation obtains n Ws TUN-Zero , take their average value to obtain an average vector

[0130] S2423. Based on the differences between multiple solution values of the first unknown transformation matrix and the above average vector, determine the true value loss function.

[0131] Among them, the true value loss function is a function that measures the differences between each solution value and the average vector, usually expressed in the form of the sum of squares of these differences. The control processing unit constructs the loss function by calculating the deviation between each solution value and the average vector and accumulating these deviations. This loss function is used to evaluate the degree of agreement between the prediction results of the solution function and the actual measurement data, and it is a key part of the optimization process because it guides the control processing unit to minimize the error by adjusting the solution parameters, so as to find the optimal solution of the first unknown transformation matrix that best conforms to the actual measurement data.

[0132] Specifically, if the above matrix C is the corresponding value matrix, the difference between the obtained W TUN-Zero and the average vector is 0.

[0133] If the above matrix C is not the corresponding true value matrix, then the obtained W TUN-Zero and the average vector have a non-zero difference. And when the matrix C is farther away from the corresponding true value matrix, the difference between the obtained W TUN-Zero and the average vector is larger.

[0134] Therefore, the true value loss function loss can be expressed as:

[0135]

[0136] where is the modulus of the difference between the vector calculated from the optical acquisition data for the i-th time and the average vector .

[0137] S243. Determine the coordinate system transformation model based on this true value loss function.

[0138] The control processing unit finally determines the coordinate system transformation model based on the true value loss function. This process includes using numerical optimization algorithms such as gradient descent or Newton's method to minimize the loss function and find the value of the first unknown transformation matrix that makes the loss function reach the minimum. Once this optimal value is determined, the coordinate system transformation model is considered accurate and can be used to describe the precise spatial relationship between the two-axis turntable coordinate system and the collimator coordinate system. This model is crucial for achieving high-precision calibration and alignment, ensuring that the two-axis turntable in the ground test simulation system can accurately align with the beam emitted by the collimator and simulate the real satellite communication environment.

[0139] Specifically, in the coordinate system transformation model, the true value loss function loss is as follows:

[0140]

[0141] Substitute the first angle data and the second angle data into the true value loss function loss to solve for the solution value of the first unknown transformation matrix W TUN-Zero and the true value matrix of the second unknown transformation matrix .

[0142] In this embodiment, the coordinate system transformation model specifically includes the following:

[0143] The mathematical expression for converting the two-axis turntable zero-position coordinate system Tun-Zero to the collimator coordinate system Coll.

[0144] The mathematical expression for converting the two-axis turntable zero-position coordinate system Tun-Zero to the two-axis turntable instantaneous coordinate system Tun-Ins.

[0145] The mathematical expression for converting the theodolite zero-position coordinate system Theo-Zero to the theodolite instantaneous coordinate system Theo-Ins.

[0146] The mathematical expression for converting the two-axis turntable instantaneous coordinate system Tun-Ins to the theodolite zero-position coordinate system Theo-Zero.

[0147] The mathematical expression for the process of converting the two-axis turntable zero-position coordinate system Tun-Zero to the theodolite instantaneous coordinate system Theo-Ins.

[0148] And, the solution function and the true value loss function.

[0149] The above mathematical expressions have been described in the previous text and will not be elaborated here.

[0150] Step 203: Based on the first angle data, the second angle data, and the coordinate system conversion model, determine multiple conversion matrices between the two-axis turntable coordinate system, the theodolite coordinate system of the theodolite, and the collimator coordinate system.

[0151] The control processing unit uses the first angle data (the pitch angle and azimuth angle of the two-axis turntable) and the second angle data (the vertical angle and horizontal angle of the theodolite), and combines the coordinate system conversion model obtained in the above step 202 to determine multiple conversion matrices between the two-axis turntable coordinate system, the theodolite coordinate system, and the collimator coordinate system.

[0152] After determining the coordinate system conversion model based on the above true value loss function, the control processing unit will use this coordinate system conversion model and the collected first angle data (involving the pitch and azimuth rotation angles of the two-axis turntable) and the second angle data (involving the vertical and horizontal rotation angles of the theodolite), and through a series of mathematical operations and optimization algorithms to determine multiple conversion matrices between the two-axis turntable coordinate system, the theodolite coordinate system, and the collimator coordinate system.

[0153] Specifically, the coordinate system conversion model accurately describes the spatial relationship between the two-axis turntable coordinate system (Tun-Zero and Tun-Ins), the theodolite coordinate system (Theo-Zero and Theo-Ins), and the collimator coordinate system (Coll) through a series of mathematical expressions and optimization processes.

[0154] First, using the pitch angle and azimuth angle of the two-axis turntable (the first angle data) and the vertical angle and horizontal angle of the theodolite (the second angle data), the conversion matrix from the two-axis turntable zero-position coordinate system to the instantaneous coordinate system, and the conversion matrix from the theodolite zero-position coordinate system to the instantaneous coordinate system are constructed.

[0155] Next, by solving the function and the truth value loss function, the second unknown transformation matrix from the instantaneous coordinate system of the two-axis turntable to the theodolite zero coordinate system can be calculated. Multiple possible solution values. Through numerical optimization methods such as gradient descent or Newton's method, the truth value loss function is minimized to obtain The optimal solution of, that is, the solution value of the second unknown transformation matrix.

[0156] Finally, by combining all the known transformation matrices and the obtained transformation matrix, the complete transformation matrix from the zero coordinate system of the two-axis turntable to the collimator coordinate system and the transformation matrix from the zero coordinate system of the two-axis turntable to the theodolite instantaneous coordinate system are determined, thus realizing the accurate description of the spatial relationship between the two-axis turntable and the collimator, providing a reliable mathematical basis for equipment alignment in the ground inspection simulation system and satellite communication simulation.

[0157] In this embodiment, multiple transformation matrices between the two-axis turntable coordinate system, the theodolite coordinate system of the theodolite and the collimator coordinate system include known transformation matrices and transformation matrices that need to be calculated.

[0158] Among them, the known transformation matrices include:

[0159] The transformation matrix from the two-axis turntable zero coordinate system Tun-Zero to the two-axis turntable instantaneous coordinate system Tun-Ins, and the transformation matrix from the theodolite zero coordinate system Theo-Zero to the theodolite instantaneous coordinate system Theo-Ins.

[0160] The transformation matrices that need to be calculated and obtained include:

[0161] The transformation matrix from the two-axis turntable instantaneous coordinate system Tun-Ins to the theodolite zero coordinate Theo-Zero. This transformation matrix is obtained through calculation, involving the transformation from the two-axis turntable instantaneous coordinate system to the theodolite zero coordinate system, and needs to be calculated in combination with the angular data of the two-axis turntable and the theodolite and their relative position relationship.

[0162] The transformation matrix from the two-axis turntable instantaneous coordinate system Tun-Ins to the theodolite instantaneous coordinate system Theo-Ins. This transformation matrix also needs to be calculated. It combines the transformation from the two-axis turntable instantaneous coordinate system to the theodolite zero coordinate system and the transformation from the theodolite zero coordinate system to the theodolite instantaneous coordinate system.

[0163] The transformation matrix from the two-axis turntable zero coordinate system Tun-Zero to the collimator coordinate system Coll. This transformation matrix is unknown and needs to be calculated through the calibration process. It involves the transformation from the zero coordinate system of the two-axis turntable to the collimator coordinate system, which usually requires complex geometric and trigonometric calculations and a possible iterative optimization process to minimize the system error.

[0164] Step 204: Determine the conversion relationship between the two-axis turntable and the collimator according to the multiple conversion matrices.

[0165] The control processing unit determines the final conversion relationship between the two-axis turntable and the collimator based on these calculated multiple conversion matrices. This step may involve comprehensive analysis of multiple matrices, including calculating the average value of the matrices or selecting the optimal conversion matrix through an optimization algorithm. The control processing unit will evaluate the consistency and accuracy of these matrices to ensure that the finally determined conversion relationship can truly reflect the spatial relationship between the two-axis turntable and the collimator. This process may require iterative optimization, by continuously adjusting and comparing the predicted results with the actual measurement data to improve the accuracy of the conversion matrix.

[0166] Finally, the control processing unit will determine one or a set of matrices or Euler angles that can accurately describe the conversion relationship between the two-axis turntable coordinate system and the collimator coordinate system. These matrices or Euler angles will be used to guide the actual equipment alignment and calibration work to ensure the accuracy and reliability of the ground test simulation system when simulating satellite communication.

[0167] In some embodiments, this step specifically includes:

[0168] (1) Solve for the solution value of the second unknown conversion matrix according to the true value loss function and the solution value of the first unknown conversion matrix.

[0169] The control processing unit uses the already defined true value loss function and the calculated solution value of the first unknown conversion matrix W TUN-Zero to solve for the solution value of the second unknown conversion matrix . The control processing unit continuously adjusts the parameters of the second unknown conversion matrix through an iterative optimization process to minimize the true value loss function. This process requires the control processing unit to precisely process and analyze data to ensure the accuracy of the solution process. Through this method, the control processing unit can determine the accurate conversion relationship between the instantaneous coordinate system of the two-axis turntable and the zero position coordinate system of the theodolite, which is a key step in achieving accurate calibration.

[0170] Exemplarily, the specific implementation of this step can be as follows:

[0171] 1. Input the initial matrix C, such as the identity matrix, and let

[0172] 2. Calculate W for n groups of data according to TUN-Zero ;

[0173] 3. Calculate the average vector TUN-Zero according to W

[0174] 4. Calculate the true value loss function loss according to ;

[0175] 5. Use the line search algorithm and quasi - Newton method to calculate the first solution C of the matrix ; 1 ;

[0176] 6. Let and loop through the above steps 1 - 5;

[0177] 7. After reaching the iteration termination condition, take the optimal solution C_opt of C as the true value matrix of . C_opt is the solution value of the second unknown transformation matrix to be solved. The iteration termination conditions include: the total number of iterations is greater than the set upper limit value max_times, or the true value loss function loss is less than the threshold ξ.

[0178] (2) Based on the solution value of the second unknown transformation matrix and the solution function, determine the solution value of the third unknown transformation matrix.

[0179] The control processing unit takes the solution value of the second unknown transformation matrix as an input parameter and substitutes it into the solution function to derive the solution value of the third unknown transformation matrix. This step is crucial because it connects the relationships between different coordinate systems and provides the necessary mathematical basis for finally determining the transformation relationship between the two - axis turntable coordinate system and the collimator.

[0180] Specifically, after obtaining the solution value of the second unknown transformation matrix , according to the following two formulas of the solution function:

[0181]

[0182] The calculation formula of the third unknown transformation matrix can be derived:

[0183]

[0184] Since are all known quantities, the solution value of the third unknown transformation matrix can be calculated and used as the true value transformation matrix between the two - axis turntable zero - position coordinate system and the theodolite instantaneous coordinate system.

[0185] (3) According to the solution value of the third unknown transformation matrix, determine the Euler angles between the two - axis turntable and the collimator, and these Euler angles are used to represent the transformation relationship between the two - axis turntable and the collimator.

[0186] Based on the solution values of the third unknown transformation matrix, the control processing unit can determine the Euler angles between the two-axis turntable and the collimator because this transformation matrix contains the complete information about the rotational relationship between the two-axis turntable coordinate system and the collimator coordinate system. By substituting the elements of into the calculation formula of the Euler angles, that is, using the trigonometric function values of specific elements in the matrix to calculate the azimuth angle (ψ), pitch angle (θ), and roll angle (φ), the control processing unit can extract three key angles that describe the spatial rotation between these two coordinate systems. These Euler angles provide an intuitive and accurate way to express the direction change of the two-axis turntable coordinate system relative to the collimator coordinate system. Thus, in the ground test simulation system, no matter how the two-axis turntable adjusts its attitude, it can accurately simulate and predict its alignment state with the collimator, which is crucial for achieving high-precision satellite communication simulation and testing.

[0187] Among them, when the theodolite and the collimator are in the light-alignment state, the telescope of the theodolite is precisely aligned with the light-emitting point of the collimator, forming an accurate optical alignment. At this light-alignment moment, the Euler angles between the zero-position coordinate system Tun-Zero of the two-axis turntable and the instantaneous coordinate system Theo-Ins of the theodolite actually reflect the rotation from the zero-position coordinate system Tun-Zero of the two-axis turntable to the instantaneous coordinate system Theo-Ins of the theodolite. Since in the light-alignment state, the telescope of the theodolite is flush with the light-emitting port pointing to the collimator, this rotation is actually equivalent to the rotation from the zero-position coordinate system Tun-Zero of the two-axis turntable to the collimator coordinate system Coll.

[0188] Therefore, the Euler angles between the zero-position coordinate system Tun-Zero of the two-axis turntable and the instantaneous coordinate system Theo-Ins of the theodolite are actually equal to the Euler angles from the zero-position coordinate system Tun-Zero of the two-axis turntable to the collimator coordinate system Coll.

[0189] Furthermore, in this embodiment, the Euler angles obtained by calculating the solution values of the third unknown transformation matrix are equivalent to the Euler angles from the zero-position coordinate system Tun-Zero of the two-axis turntable to the collimator coordinate system Coll, and thus can represent the transformation relationship between the two-axis turntable and the collimator.

[0190] The specific Euler angle calculation process is as follows. Calculate the Euler angles from the matrix :

[0191]

[0192] The transformation Euler angles from the zero-position coordinate system Tun-Zero of the two-axis turntable to the collimator coordinate system Coll are usually small. Assuming the range of Euler angles is ψ, θ, then the three Euler angles are respectively:

[0193]

[0194] Due to the influence of human measurement errors and measurement noise, based on n groups of matrices n groups of three Euler angles can be solved. To eliminate the influence of measurement noise, the average value of the n groups of Euler angles is used as the final conversion relationship between the two-axis turntable and the collimator.

[0195] The method provided in the above embodiment can be executed by a control processing unit, which is an electronic device. The following describes this electronic device in the embodiments of the present invention from the perspective of hardware processing. Please refer to Figure 3 which is a schematic structural diagram of an entity device of the electronic device in the embodiments of the present invention.

[0196] It should be noted that Figure 3 the structure of the electronic device shown is only an example and should not impose any limitations on the functions and usage scope of the embodiments of the present invention.

[0197] As Figure 3 shown, the electronic device includes a central processing unit (CPU) 401, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 402 or the program loaded from the storage section 408 into the random access memory (RAM) 403, such as executing the method described in the above embodiment. In the RAM 403, various programs and data required for system operation are also stored. The CPU 401, ROM 402, and RAM 403 are connected to each other through a bus 404. The input / output (I / O) interface 405 is also connected to the bus 404.

[0198] The following components are connected to the I / O interface 405: an input section 406 including an audio input device, a button switch, etc.; an output section 407 including a liquid crystal display (LCD), an audio output device, an indicator light, etc.; a storage section 408 including a hard disk, etc.; and a communication section 409 including a network interface card such as a LAN (Local Area Network) card, a modem, etc. The communication section 409 performs communication processing via a network such as the Internet. The drive 410 is also connected to the I / O interface 405 as required. A removable medium 411, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 410 as required so that a computer program read therefrom can be installed into the storage section 408 as required.

[0199] Specifically, according to an embodiment of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, an embodiment of the present invention includes a computer program product that includes a computer program carried on a computer-readable medium, and the computer program includes a computer program for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through the communication section 409, and / or installed from the removable medium 411. When the computer program is executed by the central processing unit (CPU) 401, various functions defined in the present invention are executed.

[0200] It should be noted that specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fibers, portable compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above. In the present invention, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0201] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present invention. Each block in the flowchart or block diagram may represent a module, a segment of a program, or a part of code, and the above-mentioned module, segment of a program, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that marked in the accompanying drawings.

[0202] Specifically, the electronic device in this embodiment includes a processor and a memory. The memory is coupled to one or more processors, and the memory is used to store computer program code. The computer program code includes computer instructions, and one or more processors call the computer instructions to cause the electronic device to execute the method provided in the above-mentioned embodiment.

[0203] On the other hand, the present invention also provides a computer-readable storage medium. This storage medium may be included in the electronic device described in the above-mentioned embodiment; or it may exist separately and not be assembled into the electronic device. The above storage medium carries one or more computer programs. When the one or more computer programs are executed by a processor of the electronic device, the electronic device is caused to implement the method provided in the above-mentioned embodiment.

[0204] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the various embodiments of the present invention.

[0205] As used in the above embodiments, depending on the context, the term "when..." may be interpreted to mean "if...", or "after...", or "in response to determining...", or "in response to detecting...". Similarly, depending on the context, the phrase "when determining..." or "if detecting (the stated condition or event)" may be interpreted to mean "if determining...", or "in response to determining...", or "when detecting (the stated condition or event)", or "in response to detecting (the stated condition or event)".

[0206] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by relevant hardware instructed by a computer program. This program can be stored in a computer-readable storage medium. When this program is executed, it can include the processes of the above method embodiments. The foregoing storage medium includes: various media such as ROM or random access memory RAM, magnetic disks, or optical discs that can store program codes.

Claims

1. A method for calibrating the relationship between a two-axis turntable and a collimator, characterized in that: A control processing unit applied to a ground inspection simulation system, wherein the ground inspection simulation system further comprises a two-axis turntable, a collimator and a theodolite, wherein the two-axis turntable comprises a pitch rotation assembly and a horizontal azimuth rotation assembly, wherein the theodolite comprises a base rotatable in the horizontal azimuth and a telescope rotatable in the vertical direction, wherein the base is connected to the pitch rotation assembly, and the telescope is arranged opposite to a light outlet of the collimator, wherein the method comprises: When the theodolite and the collimator are in an alignment condition, obtaining first angle data of the two-axis turntable and second angle data of the theodolite; the alignment condition indicates that the alignment point of the telescope coincides with the alignment point of the collimator; In the case where the two-axis turntable coordinate system of the two-axis turntable, the theodolite coordinate system of the theodolite and the collimator coordinate system of the collimator are defined, a coordinate system conversion model is constructed according to the first angle data and the second angle data, specifically including: determining a first known conversion matrix between the two-axis turntable zero-position coordinate system and the two-axis turntable instantaneous coordinate system, and a second known conversion matrix between the theodolite zero-position coordinate system and the theodolite instantaneous coordinate system; defining the representation form of the first unit vector of the x-axis in the collimator coordinate system in the two-axis turntable zero-position coordinate system as a first unknown conversion matrix, and the conversion matrix between the two-axis turntable instantaneous coordinate system and the theodolite zero-position coordinate system as a second unknown conversion matrix; under the lighting condition, when the second unit vector of the x-axis in the instantaneous coordinate system of the theodolite coincides with the first unknown conversion matrix, determining the mathematical relationship between the second unit vector, the first known conversion matrix, the second known conversion matrix, the first unknown conversion matrix and the second unknown conversion matrix; and constructing a coordinate system conversion model according to the first angle data, the second angle data and the mathematical relationship; Determine a plurality of conversion matrices between the two-axis turntable coordinate system, the theodolite coordinate system of the theodolite, and the collimator coordinate system based on the first angle data, the second angle data, and the coordinate system conversion model; The conversion relationship between the two-axis turntable and the collimator is determined according to the multiple conversion matrices.

2. The method according to claim 1, characterized in that The first angle data includes a plurality of first pitch angles and a plurality of first azimuth angles, and the second angle data includes a plurality of second pitch angles and a plurality of second azimuth angles; The two-axis turntable coordinate system includes a two-axis turntable zero-position coordinate system when the first pitch angle and the first azimuth angle are both 0, and a two-axis turntable instantaneous coordinate system when at least one of the first pitch angle and the first azimuth angle is not 0; The theodolite coordinate system includes a theodolite zero-position coordinate system when the second elevation angle and the second azimuth angle are both 0, and a theodolite instantaneous coordinate system when at least one of the second elevation angle and the second azimuth angle is not 0.

3. The method according to claim 2, characterized in that The mathematical relationship between the second unit vector, the first known transformation matrix, the second known transformation matrix, the first unknown transformation matrix and the second unknown transformation matrix specifically includes: The third unknown transformation matrix between the two-axis turntable zero-position coordinate system and the theodolite instantaneous coordinate system is equal to the product of the first known transformation matrix, the second unknown transformation matrix and the second known transformation matrix; The first unknown transformation matrix is ​​equal to the product of the third unknown transformation matrix and the second unit vector.

4. The method according to claim 3, characterized in that The step of constructing a coordinate system conversion model according to the first angle data, the second angle data and the mathematical relationship comprises: Constructing a solution function for the first unknown transformation matrix according to a mathematical relationship between the first unknown transformation matrix and the first known transformation matrix, the second unknown transformation matrix, and the second known transformation matrix; Determine a truth loss function of a truth matrix corresponding to the first unknown transformation matrix based on the first angle data, the second angle data and the solution function; A coordinate system transformation model is determined based on the truth loss function.

5. The method according to claim 4, characterized in that The determining, based on the first angle data, the second angle data and the solution function, a truth loss function corresponding to the first unknown transformation matrix comprises: Substituting the first angle data and the second angle data into the solution function to calculate and obtain a plurality of first unknown transformation matrix solution values; Calculate an average value of a plurality of first unknown transformation matrix solution values ​​to obtain an average vector; A true value loss function is determined based on the differences between the plurality of first unknown transformation matrix solution values ​​and the average vector.

6. The method according to claim 5, characterized in that The step of determining the conversion relationship between the two-axis turntable and the collimator according to the multiple conversion matrices comprises: Solving the solution of the second unknown transformation matrix according to the truth loss function and the solution of the first unknown transformation matrix; Determine the solution value of the third unknown transformation matrix based on the solution value of the second unknown transformation matrix and the solution function; The Euler angles between the two-axis turntable and the collimator are determined according to the solution value of the third unknown transformation matrix, and the Euler angles are used to represent the transformation relationship between the two-axis turntable and the collimator.

7. An electronic device, characterized in that: including one or more processors and memory; The memory is coupled to the one or more processors, and the memory is used to store computer program codes, wherein the computer program codes include computer instructions, and the one or more processors call the computer instructions to enable the electronic device to execute the method according to any one of claims 1 to 6.

8. A computer-readable storage medium storing computer instructions, characterized in that: When the computer instructions are executed on an electronic device, the electronic device is caused to execute the method as claimed in any one of claims 1 to 6.

9. A computer program product, characterized in that When the computer program product is executed on an electronic device, the electronic device is enabled to execute the method according to any one of claims 1 to 6.

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