Quantum communication telescope pointing error calibration method and system

Abstract

The present application relates to the technical field of error correction, and especially relates to a quantum communication telescope pointing error calibration method and system, and the present application proposes the following scheme: calibration observation data of a plurality of target celestial bodies is acquired, target direction information under an inertial navigation platform is obtained based on astronomical coordinates, observation time and inertial navigation attitude information, and an installation error matrix between the inertial navigation and the quantum communication telescope is solved in combination with an encoder observation angle, and then a theoretical pointing angle and a pointing error are determined. Further, before the encoder observation angle is used for calibration, the CCD charge response eccentricity is determined according to a plurality of charge response detection frames, and the encoder observation angle is de-biased, so that the pointing calibration precision under the condition of a weak light of a moving base is improved.

Description

Technical Field

[0001] This invention relates to the field of error correction technology, and in particular to a method and system for calibrating the pointing error of a quantum communication telescope. Background Technology

[0002] In a space-to-ground quantum communication system, a crucial function of a quantum communication telescope on a moving pedestal platform is to point, acquire, and track satellites, establishing and maintaining a link between the satellite and ground stations to facilitate information exchange. The pointing accuracy of a quantum communication telescope on a moving pedestal platform is a key parameter for its ability to acquire satellite targets and reacquire lost targets. Factors affecting the pointing deviation of a quantum communication telescope on a moving pedestal platform mainly include two aspects: First, random errors, including zero-point drift of the gyroscope in the inertial navigation system, random wobbling errors of the telescope's axis during installation, and errors caused by external environmental and temperature changes. Second, systematic errors, including installation errors due to misalignment between the inertial navigation and telescope coordinate systems, zero-point errors during encoder installation, orthogonality errors of the telescope's axis, tube bending and deformation errors, and CCD collimation axis errors. Traditional fixed ground-based telescopes use the coordinates of a target and known celestial objects to establish a pointing model and correct pointing errors. However, because the platform attitude of a quantum communication telescope on a moving pedestal platform is constantly changing, existing astronomical pointing correction methods are insufficient.

[0003] To address the above issues, this application presents a method and system for calibrating the pointing error of a quantum communication telescope. Summary of the Invention

[0004] The technical problem this invention aims to solve is to address the shortcomings of existing technologies by providing a method and system for calibrating the pointing error of a quantum communication telescope. This method acquires calibration observation data from multiple target celestial bodies, obtains the target direction information within the inertial navigation platform frame based on astronomical coordinates, observation time, and inertial navigation attitude information, and solves the installation error matrix between the inertial navigation system and the quantum communication telescope by combining the encoder observation angle. This allows for the determination of the theoretical pointing angle and pointing error. Furthermore, before using the encoder observation angle for calibration, the CCD charge response eccentricity is determined based on multiple charge response detection frames, and the encoder observation angle is de-biased, improving the pointing calibration accuracy under low-light conditions on a moving base.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for calibrating the pointing error of a quantum communication telescope is applied to a calibration device for a moving-base quantum communication telescope. The calibration device includes a moving-base platform, an inertial navigation system (INS), and a quantum communication telescope. The quantum communication telescope and the INS are strapped together and mounted on the moving-base platform. The method includes: Acquire calibration observation data corresponding to multiple target celestial bodies, wherein the calibration observation data includes at least encoder observation angles; Based on the calibration observation data, the target orientation information of each target celestial body under the inertial navigation platform system is obtained; Based on the target orientation information of the inertial navigation system corresponding to each target celestial body and the observation angle of the encoder, the installation error matrix between the inertial navigation system and the quantum communication telescope is determined, and the theoretical pointing angle of the target to be calibrated is obtained based on the installation error matrix. Based on the theoretical pointing angle and the actual encoder angle of the quantum communication telescope relative to the target to be calibrated, the pointing error of the quantum communication telescope is determined, and the pointing angle of the quantum communication telescope is corrected based on the pointing error.

[0006] The calibration observation data also includes the astronomical coordinates of the target celestial body, the observation time information, and the inertial navigation attitude information. The astronomical coordinates are obtained through star catalog data and include the right ascension and declination of the target celestial body at a preset epoch. The observation time information includes the local sidereal time corresponding to the imaging observation of the target celestial body by the quantum communication telescope. The inertial navigation attitude information is obtained through inertial navigation system acquisition and includes the heading angle, pitch angle, and roll angle of the moving base platform at the observation time.

[0007] The encoder observation angle is determined based on the azimuth encoder angle and pitch encoder angle output by the quantum communication telescope after extracting the off-target amount of the target celestial body and stabilizing the closed-loop tracking.

[0008] The methods for determining the target orientation information on the inertial navigation side include: Based on the local sidereal time and the right ascension information, determine the hour angle corresponding to each target celestial body at the observation time; Based on the hour angle, the declination information, and the geographical location information corresponding to the moving base platform, determine the astronomical lateral azimuth and astronomical lateral elevation angles of each target celestial body in the astronomical reference coordinates; Based on the astronomical azimuth and the astronomical elevation angle, construct the astronomical target direction vector corresponding to each target celestial body; Based on the heading angle, pitch angle, and roll angle, construct an attitude transformation matrix from astronomical reference coordinates to the inertial navigation platform system; The coordinate transformation of the astronomical target direction vector is performed by the attitude transformation matrix to obtain the inertial navigation side target direction vector of each target celestial body in the inertial navigation platform system. Based on the inertial navigation side target direction vector, determine the inertial navigation side azimuth and inertial navigation side pitch angle of each target celestial body in the inertial navigation platform system, and use the inertial navigation side azimuth and the inertial navigation side pitch angle as the inertial navigation side target direction information.

[0009] The installation error matrix is ​​determined in the following ways: Based on the inertial navigation side target direction information corresponding to each target celestial body, construct the inertial navigation side target direction vector of each target celestial body in the inertial navigation platform system; Based on the encoder observation angle corresponding to each target celestial body, construct the device-side observation direction vector of each target celestial body under the telescope equipment system; Based on the observation relationship corresponding to the same target celestial body, establish the coordinate transformation relationship between the target direction vector on the inertial navigation side and the observation direction vector on the equipment side; The installation error matrix between the inertial navigation system and the quantum communication telescope is obtained by solving the problem with the residual between the target direction vector on the inertial navigation side, after transformation by the observation equation matrix, and the corresponding observation direction vector on the equipment side, which satisfies a preset convergence condition.

[0010] The methods for determining the pointing error include: Based on the installation error matrix, the inertial navigation side target direction vector corresponding to the target to be calibrated is converted into the theoretical direction vector under the telescope equipment system; Based on the theoretical direction vector, determine the theoretical azimuth and theoretical elevation angles of the target to be calibrated in the telescope equipment system, and use the theoretical azimuth and theoretical elevation angles as the theoretical pointing angles; The actual azimuth encoder angle and actual pitch encoder angle are obtained after the quantum communication telescope extracts the miss distance from the target to be calibrated and stabilizes the closed-loop tracking. The azimuth pointing error is determined based on the difference between the theoretical azimuth angle and the actual azimuth axis encoder angle, and the pitch pointing error is determined based on the difference between the theoretical pitch angle and the actual pitch axis encoder angle. The pointing error of the quantum communication telescope is determined based on the azimuth pointing error and the elevation pointing error.

[0011] The methods for correcting the pointing angle include: Based on the azimuth pointing error, the azimuth axis target control angle of the quantum communication telescope is compensated to obtain the corrected azimuth axis control angle. Based on the pitch pointing error, the pitch axis target control angle of the quantum communication telescope is compensated to obtain the corrected pitch axis control angle. The corrected azimuth control angle and the corrected pitch control angle are used as the corrected pointing angle of the quantum communication telescope.

[0012] The method further includes: Before obtaining the encoder observation angle, determine the charge response eccentricity corresponding to the target celestial body; The encoder observation angle is de-biased based on the charge response eccentricity, and the installation error matrix is ​​determined based on the de-biased encoder observation angle.

[0013] The method for determining the charge response eccentricity includes: Acquire a reference charge response detection frame and multiple perturbation charge response detection frames corresponding to the same target celestial body. Different perturbation charge response detection frames correspond to different CCD electrical acquisition parameters, which include at least one of exposure integration time, readout gain, electronic shutter phase, and dark current subtraction intensity. The electrical sensing axis corresponding to the target celestial body is determined based on at least one of the CCD readout direction, frame transfer direction, and dark current background gradient direction. The centroid drift vector of each disturbance charge response detection frame relative to the reference charge response detection frame is determined, and the centroid drift vector is projected onto the electrical sensing axis to obtain the one-dimensional electrical drift corresponding to each disturbance charge response detection frame; Based on the attitude change information of the inertial navigation system at the acquisition time of each charge response detection frame, geometric drift elimination is performed on each one-dimensional electrical drift to obtain multiple candidate electrical eccentricities. Based on the sign consistency of multiple candidate electrical eccentricities and the perturbation monotonicity between them and the CCD electrical acquisition parameters, the effective candidate electrical eccentricity is determined from multiple candidate electrical eccentricities. Based on the effective candidate electrical eccentricities, the charge response eccentricity corresponding to the target celestial body is determined.

[0014] A quantum communication telescope pointing error calibration system, the system comprising: The observation data acquisition module is used to acquire calibration observation data corresponding to multiple target celestial bodies, and the calibration observation data includes at least the encoder observation angle; The target orientation conversion module is used to obtain the inertial navigation side target orientation information of each target celestial body in the inertial navigation platform system based on the calibration observation data. The installation error calibration module is used to determine the installation error matrix between the inertial navigation system and the quantum communication telescope based on the target direction information of each target celestial body and the observation angle of the encoder, and to obtain the theoretical pointing angle based on the installation error matrix. The pointing correction module is used to determine the pointing error of the quantum communication telescope based on the theoretical pointing angle, and to correct the pointing angle of the quantum communication telescope based on the pointing error.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention utilizes celestial bodies, inertial navigation attitude information, and encoder observation angles to establish a pointing calibration relationship on a moving base platform, eliminating the need for external artificial targets and reducing the workload of calibration preparation. By associating the inertial navigation platform system with the telescope equipment system through an installation error matrix, it can adapt to changes in platform attitude. Furthermore, it corrects encoder observation angle deviations caused by CCD charge response eccentricity, avoiding false centroid contamination of the installation error matrix in weak-light imaging, thus improving the pointing error calibration accuracy and stability of the quantum communication telescope. Attached Figure Description

[0016] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 An exemplary application scenario diagram provided for an embodiment of this application; Figure 2 This is a schematic diagram of the structure of the calibration device for the dynamic base quantum communication telescope provided in the embodiments of this application; Figure 3 A flowchart illustrating a pointing error calibration method for a quantum communication telescope provided in this application embodiment; Figure 4 This is a schematic diagram illustrating the definition of the angular coordinate system for the motion attitude of the moving base provided in an embodiment of this application. Figure 5 A schematic diagram illustrating the installation errors of the inertial navigation platform coordinate system and the telescope equipment coordinate system provided in the embodiments of this application. Detailed Implementation

[0017] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0018] The term "embodiment" as used herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0019] Unless otherwise defined, all technical and scientific terms used in the embodiments of this application have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in the embodiments of this application is for descriptive purposes only and is not intended to limit the scope of this application.

[0020] Before providing a further detailed description of the embodiments of this application, the nouns and terms involved in the embodiments of this application will be explained, and the nouns and terms involved in the embodiments of this application shall be interpreted as follows.

[0021] Quantum communication telescope: refers to an optical telescope device used in a space-to-ground quantum communication system to perform target pointing, target acquisition, and target tracking. It can be used in conjunction with components such as optical receiving components, transmitting components, CCD imaging components, azimuth axis drive mechanisms, pitch axis drive mechanisms, and encoders. In the embodiments of this application, the quantum communication telescope is not limited to a telescope that only performs astronomical observations, but refers to a pointing and tracking device used to establish and maintain a space-to-ground quantum communication optical link.

[0022] A mobile pedestal platform refers to an installation platform used to support a quantum communication telescope whose attitude may change, such as a vehicle-mounted platform, ship-mounted platform, mobile ground station platform, or other mobile support platform. A mobile pedestal platform may experience attitude changes in heading, pitch, and roll directions depending on its deployment location, leveling state, or motion state. These attitude changes alter the correspondence between the target celestial object's orientation and the coordinates of the quantum communication telescope equipment.

[0023] Inertial navigation system (INS): refers to an inertial navigation device used to measure the attitude information of a moving base platform. It can output the heading angle, pitch angle, and roll angle of the moving base platform at the observation time. In the embodiments of this application, the INS is strapped in with the quantum communication telescope to provide the attitude angle information required for attitude conversion between the astronomical reference coordinates and the INS platform system.

[0024] Strapdown installation refers to the fixed mounting of the inertial navigation system and the quantum communication telescope on the same moving base platform or the same mounting reference structure, forming a relatively stable mechanical mounting relationship between the two. Strapdown installation does not require the coordinate system of the inertial navigation platform to be completely coincident with the coordinate system of the quantum communication telescope equipment. There may be installation angles, installation zero-position deviations, or axis inconsistencies between the two. The above relative mounting relationship can be characterized by an installation error matrix.

[0025] Target celestial object: refers to a celestial object in the star catalog with known astronomical coordinates that can be imaged and observed by a quantum communication telescope. In the embodiments of this application, the target celestial object is used as a far-field natural calibration source, and its astronomical coordinates can be used to determine the theoretical target direction at the observation time, thereby replacing an external artificial target in the pointing error calibration of the quantum communication telescope.

[0026] The quantum communication telescope pointing error calibration method provided in this application is applicable to quantum communication optical terminals installed on a moving base platform. The moving base platform can be a vehicle-mounted platform, a ship-mounted platform, a mobile ground station platform, or other carrier platform whose attitude changes during deployment, leveling, and attitude maintenance. The quantum communication telescope on the carrier platform is not solely used for astronomical observation, but rather serves as an optical pointing, acquisition, and tracking device in a satellite-to-ground quantum communication link. It is used to point the telescope's optical axis towards the satellite's location during satellite transit and to maintain stable tracking of the weak light quantum signal transmission direction after the link is established. Because quantum communication links typically have characteristics such as small beam divergence angles, narrow receiving fields of view, and limited link margins, even small azimuth and elevation pointing deviations of the telescope can lead to a shortened satellite target acquisition window, repeated loss of tracking, or even prevent the quantum signal from effectively entering the receiving optical path.

[0027] In fixed ground-based telescopes, pointing error calibration can typically be accomplished using a fixed site, a stable base, and pre-set targets. Since the telescope's spatial relationship with the ground remains largely constant, once a pointing model is established using known targets or several celestial objects, subsequent use only requires angle corrections based on a fixed coordinate reference. However, the operating conditions of a moving base platform differ fundamentally from those of a fixed ground-based telescope. Factors such as vehicle parking slope, ship sway, platform leveling errors, minor deformations of the mounting plate, and assembly deviations between the inertial navigation system and the telescope can all cause the telescope's equipment system to lose its fixed correspondence with external astronomical reference coordinates. In such cases, if the calibration approach used for fixed telescopes is still employed, it is often necessary to reposition the targets before each field deployment or forcibly adjust the platform to a near-fixed attitude before calibration. This not only involves cumbersome preparation but also fails to adequately meet the requirements of rapid relocation and temporary deployment of quantum communication mobile stations.

[0028] Furthermore, the pointing error under the moving base platform is not simply a deviation between the telescope encoder angle and the theoretical angle of the target. For the same celestial object, its right ascension and declination in the star catalog provide the target's position in an astronomical sense, while the actual telescope control uses the equipment's azimuth and elevation axis angles. Between these two, there are also multiple levels of coordinate mapping relationships, such as local sidereal time, the geographical location of the observatory, changes in the moving base attitude, and errors in the inertial navigation system (INS) and telescope strapdown installation. If the platform attitude changes and the INS-telescope installation relationship are not included in the same calibration chain, and the pointing error is directly corrected using the telescope observation angle, it is easy to mistake the coordinate changes caused by the platform attitude for the telescope's own errors, or to mix the INS installation deviation, encoder observation deviation, and axis geometric errors into the same compensation amount, causing the calibration results to become invalid after the platform changes location or attitude.

[0029] Based on the above understanding, the embodiments of this application do not rely on an external artificial target as the sole calibration benchmark. Instead, they utilize the high stability of the target celestial body in astronomical coordinates, using the target celestial body as a far-field natural calibration source. Simultaneously, the conversion relationship between the astronomical reference direction and the attitude of the moving base platform is established using the real-time output of the inertial navigation system's heading, pitch, and roll angles. In other words, the target celestial body provides an absolute reference for the target direction, the inertial navigation system provides an intermediate bridge for the attitude changes of the moving base, and the quantum communication telescope encoder provides the actual observation angle on the device side.

[0030] By adopting the above method, the key focus of this application's embodiments is not simply obtaining the angular difference of a single observation, but rather establishing a transferable and reusable calibration relationship between the target celestial body's direction, the inertial navigation platform's direction, and the telescope's direction under conditions where the dynamic base platform's attitude is variable. As long as the mechanical strapdown relationship between the inertial navigation system and the quantum communication telescope remains substantially unchanged, even if the platform's deployment location or attitude changes, the target direction conversion can be re-completed using the inertial navigation attitude information, thereby avoiding the need to re-set up the target or re-establish the fixed-site pointing model for each field use. Therefore, this application's embodiments can better adapt to the pointing error calibration needs of dynamic base quantum communication telescopes under conditions of mobile deployment, temporary link establishment, rapid site transfer, and no target in the field.

[0031] refer to Figure 1 , Figure 1 This is an exemplary application scenario diagram provided for an embodiment of this application.

[0032] like Figure 1 As shown, the quantum communication telescope calibration device is located in an external observation environment capable of observing multiple target celestial bodies. These target celestial bodies may include target celestial body one, target celestial body two, and so on up to target celestial body N, where N is an integer greater than or equal to 2. These target celestial bodies are not used as satellite targets for communication, but rather as far-field natural calibration sources with known astronomical coordinates, providing a directional reference for the pointing error calibration of the quantum communication telescope on the moving base platform.

[0033] exist Figure 1 In the scenario shown, the quantum communication telescope calibration device can be installed on a vehicle-mounted platform, ship-mounted platform, mobile ground station platform, or other moving base platform. Because changes in the deployment location, leveling state, or working attitude of the moving base platform will cause changes in the coordinates of the quantum communication telescope relative to the external astronomical reference direction, relying solely on the pointing model established under a fixed target or fixed site is insufficient to meet the calibration requirements after rapid site transitions. Therefore, this embodiment utilizes the stable positional characteristics of multiple target celestial bodies in astronomical coordinates, using them as calibration observation objects, and combines this with the moving base attitude information output by the inertial navigation system to convert the astronomical orientation of the target celestial bodies to the inertial navigation platform system.

[0034] It should be noted that, Figure 1 This illustration merely presents an exemplary application scenario of using multiple target celestial bodies to calibrate the pointing error of a quantum communication telescope calibration device, and does not constitute a limitation on the number of target celestial bodies, their spatial distribution, the type of the moving base platform, or the type of celestial body to be calibrated. In practical applications, as long as the selected celestial body has obtainable astronomical coordinates and can be imaged and observed by the quantum communication telescope, it can be used as the calibration observation object in this application embodiment.

[0035] refer to Figure 2 , Figure 2 This is a schematic diagram of the structure of the calibration device for the dynamic base quantum communication telescope provided in the embodiments of this application.

[0036] like Figure 2 As shown, the calibration device for the moving-base quantum communication telescope includes a moving-base platform 10, an inertial navigation system 20, and a quantum communication telescope 30. Both the inertial navigation system 20 and the quantum communication telescope 30 are mounted on the moving-base platform 10, allowing them to move together with the attitude changes of the moving-base platform 10, thus forming a strapdown connection.

[0037] The movable base platform 10 serves as a common mounting reference for the inertial navigation system 20 and the quantum communication telescope 30. It can be a mounting base, mounting plate, or load-bearing frame in a vehicle-mounted platform, ship-mounted platform, mobile ground station platform, or other mobile support platform. Since both the inertial navigation system 20 and the quantum communication telescope 30 use the movable base platform 10 as their mounting reference, when the movable base platform 10 undergoes attitude changes in heading, pitch, or roll, the inertial navigation system 20 can output inertial navigation attitude information corresponding to those attitude changes.

[0038] The inertial navigation system 20 is used to acquire the attitude information of the moving base platform 10 at the observation time. The attitude information may include the heading angle, pitch angle, and roll angle. The quantum communication telescope 30 is used to perform imaging observation of the target celestial body or the target to be calibrated, extract the miss distance, and perform closed-loop tracking. After the closed-loop tracking stabilizes, it outputs the encoder observation angle corresponding to the target observation direction. Thus, the inertial navigation system 20 provides the attitude reference of the moving base platform 10, and the quantum communication telescope 30 provides the actual observation angle on the device side. Together, they are used to establish the coordinate transformation relationship between the inertial navigation platform system and the telescope equipment system.

[0039] It should be noted that, Figure 2This illustration only shows an exemplary installation relationship between the moving base platform 10, the inertial navigation system 20, and the quantum communication telescope 30, and does not constitute a limitation on the specific shape, mounting bracket type, connector structure, or relative arrangement of the components. As long as the inertial navigation system 20 and the quantum communication telescope 30 can form a relatively stable strapdown installation relationship based on the same moving base platform 10, the quantum communication telescope pointing error calibration method described in this application embodiment can be applied.

[0040] Example 1: Next, with reference to the accompanying drawings, a method for calibrating the pointing error of a quantum communication telescope provided in Embodiment 1 of this application will be further described. Figure 3 The method shown is applied to the calibration device of the moving-base quantum communication telescope as described above, and the method includes: S1: Acquire calibration observation data corresponding to multiple target celestial bodies, wherein the calibration observation data includes at least the encoder observation angle.

[0041] In this embodiment, the calibration device for the mobile-based quantum communication telescope can be deployed in an open field observation environment. The mobile-based platform can be a vehicle-mounted platform, a ship-mounted platform, or a mobile ground station platform. The inertial navigation and quantum communication telescopes are fixed to the mobile-based platform with the same installation reference. The calibration observation is not performed by selecting a single target celestial body, but by selecting multiple target celestial bodies distributed in different orientations and elevation heights as natural calibration sources, avoiding the problem that a single observation direction can only reflect local pointing deviations.

[0042] Those skilled in the art will understand that the number, spatial distribution, and observation order of target celestial bodies can be determined based on the visible starry sky, weather conditions, and calibration accuracy requirements. It is sufficient to at least meet the multi-directional observation constraints required for solving the installation error matrix; this application does not impose further limitations. The target celestial body refers to a far-field celestial target with obtainable astronomical coordinate information that can be imaged and observed by a quantum communication telescope. It can be a star, a planet, lunar edge features, an artificial celestial body with a known orbit, or other celestial targets that can provide a stable directional reference. As long as the astronomical coordinate information of the target celestial body can be determined based on star catalog data, astronomical ephemeris data, or orbital prediction data, and can be imaged by a quantum communication telescope at the observation time, it can be used as the calibration observation object in the embodiments of this application.

[0043] S2: Based on the calibration observation data, obtain the target orientation information of each target celestial body under the inertial navigation platform system.

[0044] In this embodiment, the right ascension and declination of the target celestial body in the star catalog are astronomical coordinates and cannot be directly used as the control basis for the azimuth and elevation axes of the quantum communication telescope. Therefore, it is necessary to combine the local sidereal time corresponding to the observation time and the geographical location information of the moving base platform to convert the astronomical coordinates of the target celestial body into astronomical side azimuth and astronomical side elevation angles at the observation location. Subsequently, an astronomical side target direction vector is constructed based on the astronomical side azimuth and astronomical side elevation angles, and an attitude conversion matrix is ​​constructed using the heading angle, elevation angle, and roll angle output by the inertial navigation system to convert the astronomical side target direction vector into the inertial navigation platform frame, obtaining the inertial navigation side target direction vector. The inertial navigation side azimuth and inertial navigation side elevation angles are then determined from the inertial navigation side target direction vector.

[0045] S3: Based on the target direction information of the inertial navigation system corresponding to each target celestial body and the observation angle of the encoder, determine the installation error matrix between the inertial navigation system and the quantum communication telescope, and obtain the theoretical pointing angle of the target to be calibrated based on the installation error matrix.

[0046] In this embodiment, although the inertial navigation system (INS) and the quantum communication telescope are strapdown mounted on the same moving base platform, their coordinate axes are not necessarily completely coincident. Slight angular deviations, installation zero-position differences, or axis inconsistencies may exist during installation. If the target direction under the INS platform system is directly used as the control angle on the telescope equipment side, strapdown installation deviations will be incorporated into the pointing result. Therefore, an INS-side target direction vector can be constructed based on the INS-side target direction information corresponding to each target celestial body, and an equipment-side observation direction vector can be constructed based on the encoder observation angle after closed-loop tracking of the same target celestial body has stabilized. Then, using the correspondence between multiple sets of INS-side target direction vectors and equipment-side observation direction vectors, the installation error matrix from the INS platform system to the telescope equipment system can be solved. This installation error matrix characterizes the stable relative installation relationship between the INS and the quantum communication telescope, rather than a random angle difference in a single observation. After solving, the INS-side target direction information of the target to be calibrated can be converted into a theoretical direction vector under the telescope equipment system via the installation error matrix, and further converted into theoretical azimuth and theoretical elevation angles, which serve as the theoretical pointing angle of the target to be calibrated.

[0047] It should be noted that the target to be calibrated in this application is not entirely the same as the target celestial body. The target celestial body mainly refers to the calibration observation object used to participate in the solution of the installation error matrix. There are usually multiple such objects, which are used to establish the correspondence between the inertial navigation platform system and the telescope equipment system from different observation directions. The target to be calibrated, on the other hand, refers to the target object that needs to be used for theoretical pointing angle calculation, actual closed-loop observation, and pointing error determination after the installation error matrix has been determined. The target to be calibrated can be other observable celestial bodies that are not involved in the solution of the installation error matrix, or it can be a satellite target that needs to be pointed to, captured, or tracked during the space-to-ground quantum communication process. In other words, the target celestial body focuses on the establishment of calibration parameters, while the target to be calibrated focuses on the application or verification of calibration results. As long as the target to be calibrated can obtain the corresponding target direction information on the inertial navigation side and can obtain the actual encoder angle through closed-loop tracking by the quantum communication telescope, it can be used as the target to be calibrated in the embodiments of this application. This application does not impose further limitations on its specific type.

[0048] In some optional implementations, the target to be calibrated can be one or more of the aforementioned target celestial bodies.

[0049] S4: Based on the theoretical pointing angle and the actual encoder angle of the quantum communication telescope to the target to be calibrated, determine the pointing error of the quantum communication telescope, and correct the pointing angle of the quantum communication telescope based on the pointing error.

[0050] In this embodiment, the target to be calibrated can be a celestial object participating in the verification observation, or a satellite target or other far-field target that needs to be pointed to later. After the quantum communication telescope points to the target according to the theoretical pointing angle and completes the miss distance extraction and closed-loop tracking stabilization, the azimuth axis encoder angle and elevation axis encoder angle can be read as the actual encoder angles. The theoretical azimuth angle is compared with the actual azimuth axis encoder angle to obtain the azimuth pointing error, and the theoretical elevation angle is compared with the actual elevation axis encoder angle to obtain the elevation pointing error. Subsequently, the azimuth axis target control angle is compensated according to the azimuth pointing error, and the elevation axis target control angle is compensated according to the elevation pointing error to obtain the corrected azimuth axis control angle and the corrected elevation axis control angle. Thus, the pointing correction does not simply rely on a one-time angle compensation under a fixed target, but rather corrects the control angle on the quantum communication telescope equipment side based on the consideration of star direction, inertial navigation attitude, and strapdown installation relationship. For satellite-to-ground quantum communication link scenarios that require rapid relocation, temporary deployment, or where it is impossible to deploy long-distance targets, the above methods can reduce the amount of preparation for field calibration and improve the reliability of target acquisition and reacquisition under dynamic base conditions.

[0051] Next, we will further elaborate on the technical aspects of the method in this application regarding the calibration of observation data.

[0052] The calibration observation data also includes the astronomical coordinates of the target celestial body, the observation time information, and the inertial navigation attitude information. The astronomical coordinates are obtained through star catalog data and include the right ascension and declination of the target celestial body at a preset epoch. The observation time information includes the local sidereal time corresponding to the imaging observation of the target celestial body by the quantum communication telescope.

[0053] It is understandable that, since the target celestial body is selected from those with known or calculable astronomical positions, the specific calibration observation data does not need to be obtained through additional field targets. For example, the target celestial body can be selected from star catalog data, astronomical ephemeris data, or a pre-established celestial target database. The preset epoch can be J2000 epoch, or other epochs corresponding to the actual star catalog data. The right ascension and declination information of the target celestial body can be obtained through conventional astronomical data query methods after determining the target celestial body's number, name, or orbital prediction data. The local sidereal time can be calculated based on the observation time, the longitude of the moving base platform, and general time information, or it can be directly output by a processing unit with astronomical calculation capabilities. Those skilled in the art will understand that the specific acquisition and conversion of right ascension, declination, and local sidereal time are mature data processing content in astronomical positioning and telescope pointing control. It is sufficient to satisfy the subsequent calculation of the astronomical lateral direction of the target celestial body at the observation time. This application does not impose further limitations on the star catalog type, time reference format, or specific conversion procedures for local sidereal time.

[0054] Furthermore, the inertial navigation attitude information is obtained through the inertial navigation system (INS), and includes the heading angle, pitch angle, and roll angle of the moving base platform at the observation time. How to acquire INS attitude information is a mature inertial measurement and attitude calculation technique in this field. For example, angular velocity and acceleration information can be obtained through the gyroscopes and accelerometers inside the INS, and the attitude angles of the moving base platform relative to the reference coordinates can be obtained through initial alignment, attitude integration, error compensation, or integrated navigation calculation. This application does not improve the attitude calculation algorithm inside the INS, nor does it limit the INS to pure inertial calculation, satellite navigation-assisted calculation, or other integrated navigation methods. It only requires that the INS can output the heading angle, pitch angle, and roll angle corresponding to the observation time during the imaging observation of the target celestial body, so that the astronomical lateral direction of the target celestial body can be converted to the INS platform frame.

[0055] Therefore, the astronomical coordinates and observation time information in the calibration observation data are used to determine the theoretical orientation of the target celestial body under an external astronomical reference, the inertial navigation attitude information is used to describe the attitude state of the moving base platform at the same observation time, and the encoder observation angle is used to describe the actual pointing of the quantum communication telescope on the device side after completing closed-loop tracking of the target celestial body. The acquisition of the above data can be achieved using existing methods in this field. The focus of this application is to establish a correlation between these data corresponding to the same target celestial body and the same observation time, and to use them for the subsequent determination of the target orientation information, installation error matrix, and pointing error of the inertial navigation platform system.

[0056] In yet another example, the encoder observation angle is determined based on the azimuth encoder angle and pitch encoder angle output by the quantum communication telescope after extracting the off-target amount of the target celestial body and stabilizing the closed-loop tracking.

[0057] It should be noted that the "off-target amount" refers to the offset of the target celestial body's imaging position in the quantum communication telescope's imaging field of view relative to a preset field-of-view reference position. This preset reference position can be the center position of the CCD imaging plane and the optical axis calibration position. The CCD is a charge-coupled device used to image the target celestial body to determine its position within the quantum communication telescope's imaging field of view. Specifically, after the quantum communication telescope images the target celestial body, it can extract the target region from the image and determine the image plane coordinates of the target celestial body using methods such as gray-scale centroid method, bright spot center fitting method, peak neighborhood weighting method, or other target center extraction methods. Subsequently, these image plane coordinates are compared with the preset field-of-view reference position to obtain the target celestial body's offset in the horizontal and vertical directions of the image plane. Based on the pixel size and focal length of the imaging component, these horizontal and vertical offsets can be converted into azimuth and elevation off-target amounts. The above-mentioned off-target extraction process is a routine image measurement process in photoelectric tracking equipment. This application does not impose any further restrictions on the specific image filtering method, target center extraction algorithm, or image plane angle conversion method. It is only necessary to obtain the offset of the target celestial body relative to the reference position of the telescope optical axis.

[0058] After obtaining the miss distance, the quantum communication telescope can generate azimuth and elevation axis adjustments based on the miss distances in the azimuth and elevation directions, respectively. It then drives the azimuth and elevation axes to perform closed-loop tracking, gradually bringing the imaged position of the target celestial object closer to the preset field-of-view reference position. Stable closed-loop tracking can be understood as the target celestial object remaining within the allowable miss range during continuous observation windows, and the azimuth and elevation axes of the quantum communication telescope no longer undergoing continuous adjustments exceeding the allowable range.

[0059] Once the closed-loop tracking reaches a stable state, the current azimuth angle output by the azimuth encoder and the current elevation angle output by the elevation encoder can be read as the encoder observation angles corresponding to the target celestial body. To reduce the impact of instantaneous jitter and encoder quantization errors on the observation results, multiple sets of azimuth and elevation encoder angles can be continuously read within a stable time window. These multiple sets of angles are then processed by averaging, median processing, or outlier removal, and the processed azimuth and elevation angles are used as the final encoder observation angles. Therefore, the encoder observation angles are not the instantaneous angles when the target celestial body first enters the field of view, but rather the actual observation angles on the equipment side after the target celestial body has been imaged and identified, the miss distance has been closed-loop converged, and the telescope pointing state is relatively stable. This allows for more accurate calculation of the installation error matrix between the inertial navigation platform system and the telescope equipment system.

[0060] Next, we will further elaborate on the technical content of the method of this application regarding the target orientation information on the inertial navigation side.

[0061] It should be noted that the inertial navigation-side target orientation information in this application specifically includes the inertial navigation-side azimuth and inertial navigation-side pitch angles, used to characterize the spatial pointing relationship of the target celestial body relative to the inertial navigation mounting reference within the inertial navigation platform system. In other words, the inertial navigation-side target orientation information is neither the original position of the target celestial body in the star catalog, nor the device angle directly output by the quantum communication telescope encoder. Instead, it is an intermediate orientation expression obtained by combining the astronomical orientation of the target celestial body with the attitude change of the moving base platform at the observation time. By setting this intermediate orientation expression, the external astronomical reference orientation of the target celestial body can be first converted to the inertial navigation platform system that changes together with the moving base platform, and then a correspondence can be established with the device-side observation angle of the quantum communication telescope, avoiding the introduction of platform attitude errors due to direct comparison between astronomical coordinates and telescope encoder angles.

[0062] Specifically, the right ascension, declination, and local sidereal time of the target celestial body can determine its astronomical lateral orientation at the observation location and time. However, the mobile base platform is not necessarily horizontal, due north, or in a fixed attitude. When the vehicle-mounted platform is parked on a slope, the ship-mounted platform is affected by swaying, or the mobile ground station has residual tilt angles after leveling, the orientation of the target celestial body relative to the inertial navigation system (INS) mounting reference will change with the heading angle, pitch angle, and roll angle. Therefore, it is necessary to use the attitude information output by the INS to perform coordinate transformation on the astronomical lateral orientation, so that the orientation of the target celestial body is expressed as the INS lateral azimuth and INS lateral pitch angle in the INS platform frame.

[0063] In one optional implementation, determining the inertial navigation side target orientation information may include: determining the hour angle corresponding to the target celestial body at the observation time based on the local sidereal time and the right ascension information of the target celestial body; determining the astronomical side azimuth and astronomical side pitch angle of the target celestial body in astronomical reference coordinates based on the hour angle, declination information, and the geographical location information of the moving base platform; constructing the astronomical side target orientation vector based on the astronomical side azimuth and astronomical side pitch angle; constructing an attitude transformation matrix based on the heading angle, pitch angle, and roll angle output by the inertial navigation system; performing coordinate transformation on the astronomical side target orientation vector through the attitude transformation matrix to obtain the inertial navigation side target orientation vector in the inertial navigation platform system; and then calculating the inertial navigation side azimuth and inertial navigation side pitch angle based on the inertial navigation side target orientation vector.

[0064] Those skilled in the art will understand that the mutual conversion between astronomical azimuth angle, astronomical pitch angle, and direction vector, as well as the construction of attitude transformation matrices based on heading angle, pitch angle, and roll angle, are all mature processing methods in spatial coordinate transformation. In specific implementation, the corresponding coordinate transformation matrix can be selected according to the coordinate axis definition of the inertial navigation system, the order of attitude angle rotation, and the installation direction of the quantum communication telescope. It is only necessary to be able to convert the direction of the target celestial body in the astronomical reference coordinate system into the direction expression in the inertial navigation platform system. This application does not impose further restrictions on the specific rotation order, matrix arrangement, or the convention of angle sign.

[0065] Specifically, the hour angle of a celestial body is calculated from local sidereal time and right ascension using the following formula: ,in, For celestial hour angles, When it is a local star, The right ascension of a celestial body.

[0066] Astronomical pitch angle of the target celestial body The calculation formula is as follows: , in, The geographical latitude of the observation point where the dynamic base platform is located. The declination of the target celestial body; Astronomical lateral azimuth of the target celestial body The calculation formula is as follows: , Furthermore, the astronomical tilt angle And astronomical lateral azimuth Coordinates in the inertial navigation platform frame are converted into direction vectors. , ,in, The coordinates of the target celestial body in a rectangular coordinate system; like Figure 4 As shown, Figure 4This is a schematic diagram illustrating the definition of the angular coordinate system for the motion posture of the moving base provided in an embodiment of this application.

[0067] The attitude is output by the inertial navigation system, including the heading angle H, roll angle R, and pitch angle P, according to... Figure 4 The transformation sequence is used to calculate the attitude change matrix of the moving base platform. : , Similarly, assuming the target celestial body's coordinates in a Cartesian coordinate system are... According to coordinate transformation, , The azimuth angle of the celestial target in the inertial navigation platform system Pitch angle The calculation formula is as follows: , The above calculation formula provides an exemplary coordinate transformation method for this application. Its essence lies in converting the direction of the target celestial body in astronomical reference coordinates, combined with the attitude change of the moving base platform at the observation time, into a directional expression that can be used to solve the subsequent installation error matrix in the inertial navigation platform system. Through this processing, the right ascension, declination, and local sidereal time of the target celestial body no longer exist merely as astronomical observation data, but are converted into inertial navigation azimuth and pitch angles associated with the inertial navigation installation reference. This allows target celestial body observation data acquired at different observation times and under different platform attitudes to be compared within the same inertial navigation platform system.

[0068] It should be noted that, Figure 4 The coordinate transformation sequence and attitude change matrix shown are only one optional implementation. Since different inertial navigation systems may have different definitions of the positive directions, rotation sequence, and coordinate axis orientations for heading, pitch, and roll angles, in actual implementation, the rotation sequence, angle signs, and matrix arrangement in the attitude change matrix can be adaptively adjusted according to the inertial navigation output protocol, the installation direction of the moving base platform, and the equipment coordinate definition of the quantum communication telescope. As long as the adjusted coordinate transformation relationship can convert the direction of the target celestial body in astronomical reference coordinates into the inertial navigation side target direction information in the inertial navigation platform system, it should be understood as falling within the scope of the coordinate transformation concept described in the embodiments of this application.

[0069] It should be further noted that the astronomical lateral azimuth angle The calculation can be performed using an arctangent function with quadrant determination to avoid ambiguity in the azimuth angle caused by the ordinary arctangent function in different quadrants. For example, the arctangent calculation result can be corrected according to the quadrant in which the target celestial body is located, or the atan2 function can be used to solve the numerator and denominator terms jointly. This application does not impose a unique limitation on the zero direction and positive direction of the azimuth angle; it is sufficient to maintain the same angle convention in the calculation of the astronomical side azimuth angle, the orientation conversion of the inertial navigation platform system, and the subsequent comparison of the encoder observation angles.

[0070] Next, the technical content of the method of this application regarding the installation error matrix will be further elaborated.

[0071] refer to Figure 5 , Figure 5 A schematic diagram illustrating the installation errors of the inertial navigation platform coordinate system and the telescope equipment coordinate system provided in the embodiments of this application.

[0072] like Figure 5 As shown, the coordinate axes of the inertial navigation platform and the telescope equipment do not necessarily have completely identical orientations. Although the inertial navigation and quantum communication telescopes are strapdown mounted on the same moving base platform, factors such as machining errors of the installation reference, fastening and assembly errors, zero-position difference in equipment installation, and installation deviations of the telescope axis system can cause a fixed or approximately fixed angular deviation between the coordinate axes of the inertial navigation platform coordinate system and the coordinate axes of the telescope equipment coordinate system. These angular deviations typically exhibit a stable relative installation relationship when the assembly relationship remains unchanged, and therefore can be characterized by an installation error matrix.

[0073] The inertial navigation platform coordinate system is the inertial navigation coordinate system shown in the figure, and the telescope equipment coordinate system is the telescope coordinate system shown in the figure.

[0074] Understandable Figure 5 In the diagram, Xb, Yb, and Zb represent the three coordinate axes of the inertial navigation platform coordinate system. The Xb, Yb, and Zb axes move together with the inertial navigation installation reference and the attitude change of the moving base platform, representing the spatial component of the target direction on the inertial navigation side. Similarly, Xe, Ye, and Ze represent the three coordinate axes of the telescope equipment coordinate system. The Xe, Ye, and Ze axes move together with the quantum communication telescope body and its azimuth and elevation axis installation references, representing the spatial component of the target direction on the telescope equipment side. Since the inertial navigation platform coordinate system and the telescope equipment coordinate system are established based on the inertial navigation installation reference and the telescope equipment installation reference, respectively, even if they are fixedly installed on the same moving base platform, there may still be slight angles between Xb and Xe, Yb and Ye, and Zb and Ze. Figure 5The relative deflection relationship between the axes of the two coordinate systems is used to illustrate the installation error relationship between the inertial navigation platform coordinate system and the telescope equipment coordinate system. This relationship can be uniformly represented by the installation error matrix.

[0075] In this embodiment, the inertial navigation platform coordinate system is used to express the inertial navigation-side target direction information obtained after attitude transformation, and the telescope equipment coordinate system is used to express the equipment-side observation direction determined by the encoder observation angle after the quantum communication telescope performs closed-loop tracking of the target celestial body. For the same target celestial body, it corresponds to one inertial navigation-side target direction vector in the inertial navigation platform coordinate system and one equipment-side observation direction vector in the telescope equipment coordinate system; both describe the expression results of the same target direction under different coordinate references. Therefore, the coordinate transformation relationship between the inertial navigation platform coordinate system and the telescope equipment coordinate system can be established using the inertial navigation-side target direction vectors and equipment-side observation direction vectors corresponding to multiple target celestial bodies, and the installation error matrix can be obtained by solving for it.

[0076] It should be noted that, Figure 5 The installation error between the two coordinate systems is mainly used to represent the angle transformation relationship caused by the inconsistency of coordinate axis directions, and does not require that the inertial navigation system and the quantum communication telescope have exactly the same origin in space. In the far-field observation scenario of the space-to-ground quantum communication telescope, the distance to the target celestial body or satellite target is much greater than the installation distance between the inertial navigation system and the quantum communication telescope. Therefore, the translation difference between the two has a negligible impact on the target direction expression, or it can be compensated as an additional installation parameter in specific implementation. For the embodiments of this application, it is sufficient to convert the target direction in the inertial navigation platform system to the theoretical direction in the telescope equipment system through the installation error matrix to meet the needs of subsequent theoretical pointing angle determination and pointing error correction.

[0077] In one example, the installation error matrix is ​​determined as follows: Based on the inertial navigation side target direction information corresponding to each target celestial body, construct the inertial navigation side target direction vector of each target celestial body in the inertial navigation platform system; Based on the encoder observation angle corresponding to each target celestial body, construct the device-side observation direction vector of each target celestial body under the telescope equipment system; Based on the observation relationship corresponding to the same target celestial body, establish the coordinate transformation relationship between the target direction vector on the inertial navigation side and the observation direction vector on the equipment side; The installation error matrix between the inertial navigation system and the quantum communication telescope is obtained by solving the problem with the residual between the target direction vector on the inertial navigation side, after transformation by the observation equation matrix, and the corresponding observation direction vector on the equipment side, which satisfies a preset convergence condition.

[0078] In one example, the installation error matrix can be solved according to the pairing relationship of the direction vectors of multiple target celestial bodies. For the first... For a target celestial body, let the inertial navigation side target direction vector be obtained by converting the inertial navigation side azimuth and inertial navigation side elevation angles. for: ; in Let be the transpose of the matrix, where and That is, the first The inertial navigation lateral azimuth angle corresponding to each target celestial body. That is, the first The inertial navigation pitch angle corresponding to each target celestial body; Let the observed direction vector on the equipment side be calculated from the angles of the azimuth encoder and the pitch encoder. for: ; in and That is, the first The azimuth encoder angle corresponding to each target celestial body. That is, the first The pitch axis encoder angle corresponding to each target celestial body; Since the true orientation of the same celestial body in space is unique. and The differences mainly stem from the installation deviations between the inertial navigation platform coordinate reference and the telescope equipment coordinate reference. The installation error matrix from the inertial navigation platform frame to the telescope equipment frame is denoted as... , It is a 3×3 matrix, and the matrix elements are as follows:

[0079] ; Then both satisfy Expanding this expression yields the first... The three observation equations contributed by each target celestial body are vertically superimposed in the order of observation to obtain the observation equation matrix Ai. The Ai corresponding to multiple target celestial bodies are then concatenated to form the observation equation matrix. Thus we obtain ,in, The observation result vector is formed by sequentially arranging the observation direction vector components corresponding to each target celestial body from the equipment side. The vector of parameters to be estimated is used to characterize the installation error matrix. All matrix elements in the array.

[0080] The least squares method is a mature parameter estimation method in this field. In this embodiment, it is used to solve the matrix element estimation problem under multiple sets of direction vector constraints, without improving the least squares method itself. Specifically, when there are at least three target celestial bodies and the direction vectors of the multiple target celestial bodies do not have ill-conditioned distributions caused by collinearity or near-coplanarity, the following solution can be obtained: , in The weight matrix is ​​used; if the imaging quality, off-target extraction confidence, and encoder stability of each target celestial body are similar, An identity matrix can be used; if the observation quality of different target celestial bodies is different, the weight of each target celestial body can be set as the reciprocal of the observation variance. For example, the smaller the uncertainty in extracting the centroid of a bright spot and the smaller the fluctuation in the miss distance in consecutive frames, the larger the corresponding weight. (The calculation is then performed.) Then, restore it row by row to form the installation error matrix. Since the ideal installation error matrix represents the rotational relationship between two coordinate references, Orthogonalization processing can usually be performed, for example, by using the mature singular value decomposition processing method. The above orthogonalization processing is used to suppress encoder quantization error, target imaging center extraction error and matrix non-orthogonal deviation caused by platform micro-vibration.

[0081] It should be noted that, in this application, the observation variance can be understood as the degree of dispersion of multiple observations of the same target celestial body within a stable observation window, and it can be calculated using sample variance. Specifically, after the quantum communication telescope stabilizes its closed-loop tracking of the target celestial body, multiple sets of azimuth encoder angles and elevation encoder angles are continuously read. The squared deviation of each set of encoder angles relative to the corresponding average angle is calculated, and the squared deviations are averaged or calculated using the sample variance method to obtain the observation variance corresponding to the target celestial body. If the miss distance or the centroid position of the bright spot is also used for evaluation, the angle sequence after converting the miss distance or centroid of consecutive frames can also be calculated using the same sample variance method. The smaller the observation variance, the more stable the observation results for the target celestial body, and the larger the corresponding weight in the weight matrix.

[0082] The preset convergence conditions can be determined based on the imaging resolution, encoder resolution, and closed-loop tracking stability, rather than being arbitrarily set. Specifically, the transformation residual for each target celestial body can be understood as the angular deviation between the direction obtained by transforming the target direction vector on the inertial navigation side through the installation error matrix and the observation direction on the equipment side corresponding to the same target celestial body; alternatively, the spatial distance deviation between the transformed direction vector and the observation direction vector on the equipment side can be used as an equivalent evaluation quantity. In practical processing, the angular deviation can be prioritized to evaluate the fitting effect of the installation error matrix, so that the residual results can directly correspond to the pointing accuracy index of the quantum communication telescope.

[0083] For example, if the field of view of the imaging component is 0.2° and the image plane width is 2048 pixels, then the angular resolution corresponding to a single pixel is approximately 0.352 arcseconds; if the target centroid extraction error is estimated at 0.3 pixels, then the angular uncertainty on the imaging side is approximately 0.106 arcseconds. If the resolution of the azimuth and pitch encoders is 0.5 arcseconds, then the uncertainty introduced by their quantization is approximately 0.144 arcseconds; if the residual jitter in the azimuth and pitch directions within the closed-loop stabilization window is estimated at 0.2 arcseconds, then the comprehensive standard uncertainty of the observation direction corresponding to a single target object is approximately 0.268 arcseconds. Based on the three-standard-deviation principle, the angular residual threshold for a single target object can be set to approximately 0.8 arcseconds. In engineering implementation, the root mean square angular residual threshold for multiple target objects can also be set to 1 arcsecond, and the maximum allowable angular residual threshold for a single target object can be set to 3 arcseconds, to balance overall fitting accuracy and outlier observation point removal.

[0084] Next, we will further elaborate on the technical aspects of the pointing error in the method of this application.

[0085] In one example, the pointing error is determined by: S4.1: Based on the installation error matrix, the inertial navigation side target direction vector corresponding to the target to be calibrated is converted into the theoretical direction vector under the telescope equipment system.

[0086] Specifically, before entering the pointing error determination process, the target to be calibrated needs to first generate a direction expression corresponding to the inertial navigation platform system. If the target to be calibrated is a celestial object used for verification, the inertial navigation side target direction vector can be obtained based on its astronomical coordinate information, observation time information, geographical location information, and inertial navigation attitude information, following the aforementioned processing method for celestial objects. If the target to be calibrated is a satellite target that needs to be captured or tracked during space-to-ground quantum communication, the direction of the target in astronomical reference coordinates can be obtained first based on orbit prediction data, observation time, dynamic base platform position, and inertial navigation attitude information, and then converted into the inertial navigation side target direction vector in the inertial navigation platform system.

[0087] In this embodiment, the installation error matrix has been obtained by solving observational data from multiple target celestial bodies, and it represents the relative installation relationship between the inertial navigation platform system and the telescope equipment system. After inputting the inertial navigation side target direction vector corresponding to the target to be calibrated into the installation error matrix, the theoretical direction vector under the telescope equipment system can be obtained. Specifically, the inertial navigation side target direction vector of the target to be calibrated can first be normalized to ensure its length is uniform, and then matrix transformation can be performed according to the coordinate axis definition corresponding to the installation error matrix. The transformed theoretical direction vector can also be normalized to reduce the impact of numerical calculation errors or orthogonalization residuals of the installation error matrix on subsequent angle inverse calculations. For implementations using a fixed-decimal-point processor or embedded controller, vector amplitude checks can be set before and after the transformation. For example, if the direction vector length deviates from the unit length by no more than one-thousandth before the transformation, subsequent angle calculations can proceed; if it exceeds this range, re-normalization or triggering observational data verification can be performed.

[0088] S4.2: Based on the theoretical direction vector, determine the theoretical azimuth and theoretical elevation angles of the target to be calibrated in the telescope system, and use the theoretical azimuth and theoretical elevation angles as the theoretical pointing angles.

[0089] Specifically, the theoretical direction vector is typically in three-dimensional rectangular coordinates. However, the pointing control of a quantum communication telescope is usually achieved through both azimuth and elevation axis control angles. Therefore, it is necessary to convert the theoretical direction vector within the telescope's system of reference into theoretical azimuth and elevation angles corresponding to the equipment's control axes. During this conversion, the theoretical azimuth angle can be determined based on the projection of the theoretical direction vector onto the horizontal reference plane, and the theoretical elevation angle can be determined based on the angle between the theoretical direction vector and the horizontal or elevation reference plane. To avoid azimuth angle jumps when the target direction is in different quadrants, the theoretical azimuth angle should preferably be determined using an arctangent method with quadrant-based judgment, rather than relying solely on a single ratio for ordinary arctangent calculation. The theoretical elevation angle can be determined by combining the component of the theoretical direction vector in the optical axis lifting direction with the horizontal projection length, ensuring consistency between the elevation angle and the telescope's elevation axis control definition.

[0090] In this embodiment, the theoretical azimuth and theoretical elevation angles can be normalized before output. For example, the azimuth angle can be normalized to a range of 0 to 360 degrees, or to a range of -180 to +180 degrees; the elevation angle can be limited according to the mechanical allowable range of the quantum communication telescope, for example, limited to a range of -5 to 95 degrees, or limited to other angle ranges that the actual equipment can cover. If the theoretical angle falls outside the mechanical limit, the target to be calibrated can be marked as not being able to point at the target in the current attitude, and will not enter the subsequent actual encoder angle comparison process. If the theoretical angle is close to the mechanical limit, for example, less than 0.5 degrees from the azimuth or elevation axis limit, the drive speed can be reduced or the miss distance stability criterion requirement can be increased during subsequent closed-loop tracking to avoid mechanical backlash and drive hysteresis near the limit affecting the actual encoder angle.

[0091] S4.3: Obtain the actual azimuth encoder angle and the actual pitch encoder angle output by the quantum communication telescope after extracting the miss distance of the target to be calibrated and stabilizing the closed-loop tracking.

[0092] S4.4: Determine the azimuth pointing error based on the difference between the theoretical azimuth angle and the actual azimuth axis encoder angle, and determine the pitch pointing error based on the difference between the theoretical pitch angle and the actual pitch axis encoder angle.

[0093] Specifically, azimuth and pitch pointing errors correspond to the angular deviations on the two control axes of the quantum communication telescope. The azimuth direction is periodic; when the theoretical azimuth angle and the actual azimuth encoder angle are close to zero or the 360-degree boundary, directly subtracting ordinary values ​​may produce a spurious difference close to 360 degrees. Therefore, before calculating the azimuth pointing error, the theoretical azimuth angle and the actual azimuth encoder angle should be unified to the same angular range, and the difference between them should be determined according to the principle of minimum angular distance. For example, when the theoretical azimuth angle is 359.8 degrees and the actual azimuth encoder angle is 0.1 degrees, the azimuth pointing error should be treated as a small angular deviation near 0.3 degrees, rather than 359.7 degrees. The pitch direction usually does not have a complete cycle, but it is necessary to unify the definitions of positive and negative directions. For example, the lift direction can be defined as positive, and the pitch direction as negative, ensuring that the error sign can be directly used for subsequent control angle compensation.

[0094] In this embodiment, before comparing the theoretical angle with the actual encoder angle, a zero-position consistency and unit consistency check can be performed. If the encoder output is a pulse count value, it can be converted into an angle value based on the encoder resolution, transmission ratio, and zero-position calibration value. If the encoder output is already an angle value, it is necessary to confirm that its azimuth zero position and pitch zero position are consistent with the zero position convention of the theoretical pointing angle. For example, when the azimuth axis encoder outputs a 23-digit absolute value code per revolution, the reading can be converted into an angle based on the total count per revolution. If there is a reduction mechanism on the azimuth axis, it is also necessary to convert it to the telescope azimuth axis angle in conjunction with the transmission ratio. For the pitch axis encoder, if the mechanical zero position corresponds to the horizontal optical axis position, this zero position can be used as the pitch zero degree. If the mechanical zero position corresponds to the installation calibration position, it is necessary to subtract the zero-position offset before comparing it with the theoretical pitch angle.

[0095] Among them, the zero-position offset is an angle compensation parameter obtained and stored in advance through encoder zero-position calibration. It is used to uniformly convert the encoder mechanical zero position to the zero-position reference used for theoretical pointing angle. It is a common parameter in encoder angle conversion and shaft calibration in this field.

[0096] S4.5: Determine the pointing error of the quantum communication telescope based on the azimuth pointing error and the elevation pointing error.

[0097] Specifically, the pointing error of a quantum communication telescope can be retained as components on both control axes simultaneously, or it can be formed into a comprehensive angle evaluation quantity according to application needs. The component forms include azimuth pointing error and pitch pointing error, suitable for direct compensation of the azimuth and pitch axis target control angles; the comprehensive angle evaluation quantity is suitable for determining whether the current calibration result meets the requirements for establishing a satellite-to-ground quantum communication link. For a quantum communication telescope, the azimuth and pitch axis errors correspond to different actuators, and it is not advisable to use only a single composite value to replace the two axial errors during control compensation. Based on this, in this embodiment, the pointing error includes at least azimuth pointing error and pitch pointing error, and may include error statistics, observation timestamps, target identification for calibration, and observation quality information.

[0098] In another example, the correction method for the pointing angle includes: compensating for the azimuth axis target control angle of the quantum communication telescope based on the azimuth pointing error to obtain a corrected azimuth axis control angle; compensating for the pitch axis target control angle of the quantum communication telescope based on the pitch pointing error to obtain a corrected pitch axis control angle; and using the corrected azimuth axis control angle and the corrected pitch axis control angle as the corrected pointing angle of the quantum communication telescope.

[0099] It should be noted that, given the azimuth and pitch pointing errors, pointing angle correction can be achieved using the axial error compensation method commonly used in photoelectric tracking devices, astronomical telescopes, and servo turntables in this field. Specifically, the meaning of the pointing error sign can be pre-defined; for example, the difference between the theoretical pointing angle and the actual encoder angle can be defined as the pointing error, or the difference between the actual encoder angle and the theoretical pointing angle can be defined as the pointing error. After determining the sign convention, additive or subtractive compensation is performed on the azimuth axis target control angle and the pitch axis target control angle according to the same sign convention. For example, if the azimuth pointing error represents the deviation of the theoretical azimuth angle from the actual azimuth axis encoder angle, the azimuth axis target control angle can be corrected in the opposite direction to this deviation, making the corrected azimuth axis control angle closer to the actual azimuth angle corresponding to the quantum communication telescope in a stable tracking state; the pitch axis target control angle can also be processed according to the same rule. Thus, the pointing error is not merely output as a calibration result, but is converted into a control angle compensation amount that can directly act on the azimuth and pitch axes.

[0100] In this embodiment, if the calibration scenario only requires correction of the target pointing in a single deployment attitude, a direct axial compensation method can be used. Specifically, the theoretical azimuth angle of the target to be calibrated is used as the original target control angle for the azimuth axis, and the theoretical pitch angle is used as the original target control angle for the pitch axis. Then, azimuth axis compensation and pitch axis compensation are generated based on the azimuth pointing error and pitch pointing error, respectively. The compensation amount can be the same as the pointing error value, or a proportional coefficient can be set according to the response characteristics of the servo controller. For example, when there is no significant overshoot in the azimuth and pitch axes of the quantum communication telescope, the proportional coefficient can be set to 1, making the compensation amount equal to the corresponding axial pointing error; when there is a slight overshoot or mechanical hysteresis in the servo axis, the proportional coefficient can be set to 0.8 to 0.95, so that the compensation process approximates the target angle conservatively. After compensation, the corrected azimuth axis control angle and the corrected pitch axis control angle can be sent to the servo controller of the quantum communication telescope, and the miss distance and encoder angle after closed-loop tracking can be read again for verification. If both the azimuth and elevation pointing errors obtained from the verification are less than the preset allowable error thresholds, for example, both less than 5 arcseconds or 10 arcseconds, then the current corrected pointing angle can be considered usable for subsequent target acquisition or tracking. If they still exceed the allowable error thresholds, compensation can be performed again based on the remaining error until the accuracy requirements are met or the preset number of iterations is reached. The preset allowable error thresholds can be determined based on the acquisition field of view of the quantum communication telescope, the receiving field of view of the communication link, and the encoder accuracy. For example, when the half-angle of the acquisition field of view is 50 arcseconds, the single-axis allowable error can be set to no more than one-fifth of the half-angle of the acquisition field of view, i.e., about 10 arcseconds.

[0101] Furthermore, when calibration results need to be used continuously over a large sky area, mature model compensation methods for pointing correction in astronomical telescopes can also be adopted. These model compensation methods are existing optical telescope calibration techniques; this embodiment only illustrates their specific application in this application. During model construction, the theoretical azimuth and elevation angles corresponding to multiple targets to be calibrated or multiple verification targets can be used as model inputs, and the azimuth and elevation pointing errors obtained from corresponding observations can be used as model output samples. Subsequently, following commonly used pointing error modeling methods for optical telescopes, azimuth correction models and elevation correction models are established respectively. Model inputs may include theoretical azimuth, theoretical elevation, the sine and cosine components of the theoretical azimuth, the tangent or secant component of the theoretical elevation, and may further include the heading angle, elevation angle, roll angle, temperature information, or platform vibration level information of the moving base platform at the observation time. Model outputs are azimuth axis compensation and elevation axis compensation. Model parameters can be determined by least squares fitting, weighted least squares fitting, or partitioned lookup table interpolation. Among these, least squares fitting and lookup table interpolation are both mature telescope pointing correction methods in this field.

[0102] When using model compensation, several sets of verification observation data can be collected first within different azimuth and elevation angle ranges to ensure the sample covers the actual working area of ​​the quantum communication telescope. For example, verification targets can be selected every 30 to 60 degrees in azimuth and every 10 to 20 degrees in elevation. If the number of visible targets is limited, targets covering low, medium, and high elevation areas can be prioritized to allow the model to describe the error variations in different pointing regions. For each set of verification observation data, the theoretical pointing angle is calculated, the actual encoder angle is read, and the azimuth and elevation pointing errors are obtained as described above. Then, the above samples are substituted into the azimuth correction model and the elevation correction model to solve for the model coefficients. After obtaining the model coefficients, a new target to be pointed to only needs to be input into the model based on its theoretical azimuth and theoretical elevation angles to obtain the corresponding azimuth axis compensation and elevation axis compensation. The original target control angle is then compensated to obtain the corrected azimuth axis control angle and the corrected elevation axis control angle.

[0103] After the model is built, a portion of the verification targets can be reserved as validation samples to determine whether the model compensation is suitable for the current deployment status. For example, 70% of all verification observation data can be used for parameter fitting, and 30% for validation. If the root mean square values ​​of the azimuth and pitch errors corresponding to the validation samples are both less than the preset threshold, and the validation error is greater than or equal to the preset threshold, the number of verification targets can be increased, or the sky area can be partitioned for modeling, for example, establishing correction models for the low pitch and high pitch regions respectively. For scenarios where the attitude of the moving base platform changes rapidly, the change in inertial navigation attitude can also be used as a trigger condition for model updates. For example, when the change in heading angle, pitch angle, or roll angle relative to the modeling time exceeds 0.5 degrees or 1 degree, several verification targets are re-acquired and the model coefficients are updated. The above model compensation process does not change the calibration chain proposed in this application, which is "determining the theoretical pointing angle from the target celestial body, inertial navigation attitude, and installation error matrix, and then determining the pointing error based on the actual encoder angle." It only changes the fact that after the pointing error has been formed, a mature error compensation model in this field is used to convert the error into a control angle correction amount that is more suitable for continuous pointing.

[0104] The preset threshold can be pre-set based on the pointing accuracy index of the quantum communication telescope, the allowable error of target acquisition, or the error statistics in the historical qualified calibration data. It is a conventional threshold in the field for calibration and acceptance judgment based on the accuracy requirements of the equipment. For example, if it is less than 5 arcseconds or 10 arcseconds, the model compensation result can be used for subsequent target pointing. This application will not elaborate on this point.

[0105] In one example, this application embodiment provides a quantum communication telescope pointing error calibration system, the system comprising: The observation data acquisition module is used to acquire calibration observation data corresponding to multiple target celestial bodies, and the calibration observation data includes at least the encoder observation angle; The target orientation conversion module is used to obtain the inertial navigation side target orientation information of each target celestial body in the inertial navigation platform system based on the calibration observation data. The installation error calibration module is used to determine the installation error matrix between the inertial navigation system and the quantum communication telescope based on the target direction information of each target celestial body and the observation angle of the encoder, and to obtain the theoretical pointing angle based on the installation error matrix. The pointing correction module is used to determine the pointing error of the quantum communication telescope based on the theoretical pointing angle, and to correct the pointing angle of the quantum communication telescope based on the pointing error.

[0106] Example 2: Based on Example 1, this application further provides a method for calibrating the pointing error of a quantum communication telescope based on CCD charge response eccentric stripping.

[0107] It should be noted that when calibrating the pointing error of the quantum communication telescope on a moving pedestal platform, the target celestial object usually appears as a faint point in the CCD imaging field of view. The quantum communication telescope uses the CCD miss distance extraction result for closed-loop tracking, and after the closed-loop tracking stabilizes, it reads the azimuth and elevation encoder angles. This process implicitly assumes that the position of the star's barycenter output by the CCD can accurately represent the optical imaging center of the star.

[0108] In real-world environments, this premise does not always hold true. The charge accumulation process of a star's image on a CCD pixel is influenced by exposure time, electronic shutter timing, readout direction, pixel dark current, background level, low-light signal-to-noise ratio, local charge tailing, and micro-vibrations of the moving base. In such cases, the star's centroid in the CCD image may not be the true optical center, but rather an "electrical offset" caused by charge response distortion. Since closed-loop tracking actively pulls this electrically offset centroid towards the center of the field of view, the angle ultimately recorded by the encoder is not the telescope pointing angle corresponding to the star's true incident direction, but rather a servo-stabilized angle that compensates for the CCD's charge offset.

[0109] The resulting errors are highly concealed. The image appears to be closed-loop stabilized, and the encoder output is also stable, but the observation direction vector used to solve the installation error matrix already includes CCD charge response bias. When multiple stellar samples are used in the solution, this bias is mistakenly absorbed into the installation error matrix between the inertial navigation and quantum communication telescopes, leading to inconsistencies in calibration results under different magnitudes, exposure sequences, or background levels.

[0110] Furthermore, to identify the aforementioned electrical eccentricity, directly performing full two-dimensional centroid fitting on the star point images in multiple charge response detection frames, and further solving for multiple parameters including exposure time, readout gain, dark current background, frame transfer time, and inertial navigation attitude changes, would significantly increase computational complexity. Especially when the moving platform experiences continuous attitude micro-motion, the longer the acquisition window of the charge response detection frames, the more significant the impact of platform attitude changes on centroid drift, making it easier to mix geometric drift caused by attitude perturbations into the charge response eccentricity, thus distorting the eccentricity removal results. Therefore, this embodiment does not employ full two-dimensional joint fitting on all detection frames. Instead, it utilizes the characteristic that CCD charge response eccentricity typically exhibits directional accumulation along the readout direction, frame transfer direction, or dark current background gradient direction. First, the electrical sensitive axis is determined, and then the multi-frame two-dimensional centroid drift is compressed into a one-dimensional electrical drift along the electrical sensitive axis, thereby reducing the difficulty of locking the charge response eccentricity.

[0111] In one example, the method further includes: A1: Before obtaining the encoder observation angle, determine the charge response eccentricity corresponding to the target celestial body; A2: The encoder observation angle is de-biased based on the charge response eccentricity, and the installation error matrix is ​​determined based on the de-biased encoder observation angle. In this embodiment, by first determining the charge response eccentricity corresponding to the target celestial body and then de-biasing the encoder observation angle, the problem of weak stars being misidentified as stable centers by closed-loop tracking after being deflected by the CCD's electrical response under a moving base platform can be solved. Especially when the target star magnitude is low, the background level fluctuates significantly, or there is residual trailing in the CCD readout direction, the de-biased encoder observation angle can more closely approximate the angle value under true optical axis alignment, thereby improving the consistency of the installation error matrix solution and the reliability of subsequent quantum communication telescope pointing angle correction.

[0112] In yet another example, the method for determining the charge response eccentricity includes: A1.1: Acquire a reference charge response detection frame and multiple perturbation charge response detection frames corresponding to the same target celestial body. Different perturbation charge response detection frames correspond to different CCD electrical acquisition parameters, which include at least one of exposure integration time, readout gain, electronic shutter phase, and dark current subtraction intensity.

[0113] Specifically, once the target celestial body has entered the CCD imaging field of view and completed closed-loop tracking stabilization, if the encoder observation angle is read immediately, the closed-loop control may actually lock the centroid position after the CCD charge response has taken effect. To separate this type of electrical eccentricity from the conventional miss distance, this embodiment acquires a set of charge response detection frames for the same target celestial body without actively changing the target control angles on the azimuth and elevation axes. The reference charge response detection frame records the centroid position of the target celestial body under normal closed-loop tracking parameters, while the perturbed charge response detection frame records the centroid position of the target celestial body after the CCD electrical acquisition parameters have been controlled and changed. Since the telescope's mechanical pointing remains unadjusted within the acquisition window, the true incident directions of the same target celestial body are comparable in a short time, making it easier to identify differences in the centroid position caused by the CCD electrical acquisition parameters.

[0114] In this embodiment, the reference charge response detection frame can use the exposure integration time, readout gain, electronic shutter phase, and dark current subtraction intensity currently used during closed-loop tracking stabilization. The perturbation charge response detection frames can be acquired using a paired perturbation method, meaning that each perturbation charge response detection frame changes only one CCD electrical acquisition parameter relative to the reference charge response detection frame, while other acquisition parameters remain unchanged. For example, the exposure integration time can be set to 80%, 120%, and 150% of the reference exposure integration time; the readout gain can be reduced by 3 dB and increased by 3 dB respectively based on the reference readout gain; the electronic shutter phase can be offset by one-quarter or one-half of a frame period relative to the reference phase; and the dark current subtraction intensity can be reduced by 10% and increased by 10% respectively based on the reference dark current estimate. The perturbation amplitude is not a fixed value; those skilled in the art can adjust it according to the CCD full-well capacity, the grayscale distribution of weak star points, and the closed-loop tracking frame rate, as long as the perturbation frame can cause an observable difference in charge response without causing large-scale saturation or deviation from the centroid extraction window of the target celestial object image.

[0115] A1.2: Determine the electrical sensing axis corresponding to the target celestial body based on at least one of the CCD readout direction, frame transfer direction, and dark current background gradient direction.

[0116] Specifically, CCD charge response eccentricity typically does not exhibit a completely random two-dimensional diffusion on the image plane, but rather is related to pixel charge transfer paths, row and column readout order, frame transfer direction, and uneven distribution of background levels. If all perturbed frames are directly fitted together on the two-dimensional image plane, the true optical drift, readout direction tail, dark current gradient shift, and local pixel anomalies in centroid drift are easily mixed together. Based on this, this embodiment first determines the electrical sensitive axis corresponding to the target celestial body, and then focuses the subsequent centroid drift analysis on the direction where charge response is more likely to accumulate. The electrical sensitive axis can be understood as the direction on the image plane that is more sensitive to changes in CCD electrical acquisition parameters. Extracting the eccentricity along this direction can reduce interference caused by star flicker, attitude micro-motion, or random noise in the vertical direction.

[0117] In this embodiment, the electrical sensing axis can be directly determined based on the CCD hardware configuration file or adaptively determined based on the detection frame data. For row-transfer readout CCDs, the row readout direction can be used as a candidate electrical sensing axis; for frame-transfer CCDs, the frame transfer direction can be used as a candidate electrical sensing axis; for cases with significant dark current background inhomogeneity, the dark current background gradient direction can be determined based on the average background level difference between adjacent rows or columns in the dark current correction frame, and this dark current background gradient direction can be used as a candidate electrical sensing axis. The background level difference can be obtained by pre-setting a background ring around the centroid of the target celestial body. The background ring can be located within a range of three to six half-widths outside the centroid of the star point, avoiding the core region of the star point, and then calculating the average gray level of each row or column. If the background level change in a certain direction continuously exceeds twice the root mean square value of the camera readout noise, and maintains the same direction of change in at least three adjacent pixel rows or pixel columns, then it can be considered that there is a usable dark current background gradient in that direction.

[0118] A1.3: Determine the centroid drift vector of each disturbance charge response detection frame relative to the reference charge response detection frame, and project the centroid drift vector onto the electrical sensing axis to obtain the one-dimensional electrical drift corresponding to each disturbance charge response detection frame.

[0119] Specifically, both the reference charge response detection frame and the perturbation charge response detection frame contain point images of the same target celestial body. However, due to differences in CCD electrical acquisition parameters, the grayscale distribution of the target celestial body may undergo slight variations. To avoid the single centroid extraction method being affected by local grayscale anomalies, this embodiment can simultaneously extract the grayscale-weighted centroid, the background-subtracted centroid, and the contour-constrained centroid for each frame. The grayscale-weighted centroid reflects the energy center after pixel charge accumulation, the background-subtracted centroid reduces the offset of the centroid by dark current and background inhomogeneity, and the contour-constrained centroid is used to reference the geometric center of the star point diffusion contour. If the maximum distance between the three centroids is less than a preset centroid consistency threshold, the average value of the three centroids is taken as the target centroid of the current frame; if the grayscale-weighted centroid deviates significantly from the other two centroids along the readout direction, this deviation information is retained, and the current frame is marked as a detection frame that may have charge tailing. The centroid consistency threshold can be pre-calibrated according to the CCD pixel size and the equivalent focal length of the telescope. For example, it can be set to 0.2 to 0.5 pixels.

[0120] In this embodiment, the centroid drift vector of each disturbed charge response detection frame relative to the reference charge response detection frame can be obtained from the image plane displacement between the centroid position and the reference centroid position. To reduce the influence of random noise, the reference charge response detection frame can also use the average centroid of two or three consecutive normally acquired parameter images as the reference centroid position; if the centroid of the star point still has a small periodic oscillation after the closed-loop stabilization, the reference frame closest to the acquisition time of the disturbed frame can be selected as the control frame. After obtaining the two-dimensional centroid drift vector, it is not directly put into two-dimensional fitting, but is projected onto the aforementioned main electrical sensing axis to form a one-dimensional electrical drift. The positive and negative directions of the projection direction can be defined according to the direction from the CCD readout start point to the readout end point, or the direction can be defined according to the dark current background level, as long as it remains consistent in all detection frames of the same target celestial body.

[0121] A1.4: Based on the attitude change information of the inertial navigation system at the acquisition time of each charge response detection frame, geometric drift elimination is performed on each one-dimensional electrical drift to obtain multiple candidate electrical eccentricities.

[0122] Specifically, even if the moving base platform maintains the telescope target control angle without actively changing it for a short period, the platform itself may still experience slight attitude changes. These attitude changes cause geometric drift in the true incident direction of the target celestial body on the CCD image plane. Both geometric drift and CCD charge response eccentricity manifest as changes in the center of mass position in the image. If not distinguished, true optical drift can easily be mistaken for electrical eccentricity. Therefore, this embodiment utilizes the heading, pitch, and roll angles output by the inertial navigation system (INS) at each frame acquisition moment to perform geometric drift elimination on the one-dimensional electrical drift. The INS attitude information and the CCD frame acquisition moment can be correlated using a unified timescale, such as using the CCD exposure start time, exposure midpoint time, or frame readout latch time as the attitude corresponding moment for the current detection frame. For detection frames with short exposure times, the INS attitude at the exposure midpoint time can be used; for long exposure detection frames, the average or weighted result of the INS attitude over the exposure time period can be used.

[0123] In this embodiment, the geometric drift caused by attitude changes on the CCD image plane can be estimated based on the inertial navigation attitude change between adjacent detection frames, the equivalent focal length of the quantum communication telescope, and the CCD pixel size. In actual implementation, a mapping relationship between attitude and CCD image plane displacement can be pre-established during the device's factory calibration stage, mapping attitude changes in different directions to pixel displacements in the row and column directions of the CCD image plane. During operation, after acquiring the attitude change of each perturbation frame relative to the reference frame, the above mapping relationship is called to obtain the corresponding image plane geometric drift vector, and then the image plane geometric drift vector is projected onto the main electrical sensing axis to obtain the one-dimensional geometric drift compensation amount.

[0124] Furthermore, after deducting the corresponding one-dimensional geometric drift compensation from the one-dimensional electrical drift for each perturbation frame, candidate electrical eccentricities are obtained. To ensure the reliability of the candidate electrical eccentricities, perturbation frames with excessive attitude changes can be restricted. For example, if the displacement of a perturbation frame relative to the reference frame, calculated onto the CCD image plane, is greater than or equal to a pixel threshold, or exceeds 50% of the current one-dimensional electrical drift, it can be considered that the geometric drift proportion in that frame is high, and the relevant candidate electrical eccentricities will have their weight reduced or will not participate in subsequent validity judgments. The aforementioned pixel threshold can be determined based on the telescope focal length, CCD pixel size, and closed-loop stabilization accuracy. Under high-precision calibration conditions, it can be set to 0.5 pixels, and under low-light or low-frame-rate conditions, it can be relaxed to one pixel. After eliminating geometric drift through inertial navigation attitude change information, the candidate electrical eccentricities are closer to the centroid offset caused by the CCD electrical acquisition link itself.

[0125] A1.5: Determine the effective candidate electrical eccentricity from the multiple candidate electrical eccentricities based on the sign consistency of the multiple candidate electrical eccentricities and the disturbance monotonicity between them and the CCD electrical acquisition parameters.

[0126] Specifically, even after geometric drift elimination, candidate electrical eccentricities may still contain effects such as random noise, local dead pixels, star flicker, and readout transient anomalies. If the final eccentricity is determined directly based on a single frame of candidate electrical eccentricities, overcompensation or miscompensation is likely to occur. Therefore, this embodiment further utilizes two verifiable features of charge response eccentricity for screening: sign consistency and perturbation monotonicity. Sign consistency confirms whether multiple candidate electrical eccentricities shift in the same direction along the main electrical sensing axis; perturbation monotonicity confirms whether candidate electrical eccentricities change accordingly with the increase or decrease of CCD electrical acquisition parameters. Compared to simple threshold elimination, the above screening method can utilize the correspondence between CCD electrical perturbation and centroid shift to retain eccentricity results with more electrical origin characteristics from multiple candidate quantities.

[0127] In this embodiment, sign consistency can be determined based on the positive and negative directions of candidate electrical eccentricities on the main electrical sensing axis. If at least two-thirds of the candidate electrical eccentricities under the same disturbance category have the same direction, or if the top few candidate electrical eccentricities with larger amplitudes have the same direction, then sign consistency can be considered satisfied. If the direction of the candidate electrical eccentricities changes frequently, it indicates that the current centroid drift may be dominated by random noise or attitude disturbances. Two-thirds can be used as an exemplary ratio and can also be adjusted according to the number of detection frames. For example, when the number of detection frames is four, at least three frames may be required to have the same direction; when the number of detection frames is six to eight, at least 70% of the candidate quantities may be required to have the same direction. If the amplitude of the candidate electrical eccentricity is lower than the centroid repetition error threshold, even if the direction is the same, it may not be considered a valid candidate quantity to avoid treating measurement noise as charge response eccentricity.

[0128] The centroid repetition error threshold can be determined by a large number of experiments conducted by those skilled in the art.

[0129] Furthermore, the monotonicity of the perturbation can be determined in conjunction with specific CCD electrical acquisition parameters. For exposure integration time perturbation, if the candidate electrical eccentricity increases along the readout direction or background gradient direction when the exposure time changes from short to long, it can be considered that there is a stable relationship between the exposure perturbation and charge accumulation eccentricity. For readout gain perturbation, if the amplitude of the candidate electrical eccentricity increases after the readout gain is increased, and decreases after the readout gain is decreased, it can be considered that the readout gain perturbation satisfies a monotonic relationship. For dark current subtraction intensity perturbation, if the candidate electrical eccentricity changes repeatably along the background gradient direction when the subtraction intensity increases or decreases, it can also be considered that the perturbation monotonicity is satisfied. A certain tolerance can be allowed for the monotonicity judgment. The tolerance can be twice the centroid repetition error, or between 0.1 and 0.2 pixels. For candidate quantities that satisfy sign consistency but not perturbation monotonicity, the weight can be reduced; for candidate quantities that satisfy neither sign consistency nor perturbation monotonicity, they can be eliminated from the effective candidate electrical eccentricities. Through this screening, the eccentricity values ​​that enter the final statistics are no longer simple multi-frame centroid differences, but effective candidate values ​​with electrical disturbance response characteristics.

[0130] A1.6: Determine the charge response eccentricity corresponding to the target celestial body based on the effective candidate electrical eccentricities.

[0131] Specifically, after determining the effective candidate electrical eccentricities, multiple effective candidate quantities need to be fused into the charge response eccentricity corresponding to the target celestial body. The fusion process should not directly use ordinary arithmetic averaging, because individual perturbation frames in low-light stellar images may still be affected by local pixel anomalies, short-term background fluctuations, or readout transients. To improve the stability of the eccentricity, this embodiment can perform robust statistics based on the dispersion of the effective candidate quantities, the degree of monotonicity agreement of the perturbation, and the signal-to-noise ratio of the corresponding detection frames. For cases with a small number of effective candidate quantities, the median value can be used as the charge response eccentricity; for cases with a large number of effective candidate quantities, the maximum and minimum values ​​can be removed first, and then the average of the remaining candidate quantities can be calculated; for cases where effective candidate quantities exist for different perturbation categories, different candidate quantities can be weighted and fused according to the degree of monotonicity agreement of the perturbation and the star point signal-to-noise ratio.

[0132] In this embodiment, the charge response eccentricity can be represented as a one-dimensional eccentricity value on the main electrical sensing axis, or it can be further reduced to a two-dimensional eccentricity vector in the CCD image plane coordinate system. If subsequent back-off of the encoder observation angle in azimuth and elevation directions is only required, the one-dimensional eccentricity value can be reduced to an image plane eccentricity vector along the main electrical sensing axis. Then, combining the installation relationship between the CCD image plane coordinate system and the telescope equipment coordinate system (the relative installation relationship described in the previous embodiment), the image plane eccentricity vector is converted into azimuth and elevation eccentricity angles. During the conversion, the CCD pixel size, the telescope equivalent focal length, the CCD installation rotation angle, and the image plane coordinate origin position can be used. The CCD installation rotation angle can be obtained through assembly calibration, or it can be obtained by the correspondence between the image plane displacement direction and the azimuth and elevation axis control directions when the telescope is pointing at a known stellar target. The azimuth and elevation eccentricity angles obtained in this way can be directly used for encoder observation angle back-off.

[0133] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for calibrating the pointing error of a quantum communication telescope, applied to a calibration device for a moving-base quantum communication telescope, characterized in that, The calibration device for the moving-base quantum communication telescope includes a moving-base platform, an inertial navigation system, and a quantum communication telescope. The quantum communication telescope and the inertial navigation system are strapped together and mounted on the moving-base platform. The method includes: Acquire calibration observation data corresponding to multiple target celestial bodies, wherein the calibration observation data includes at least encoder observation angles; Based on the calibration observation data, the target orientation information of each target celestial body under the inertial navigation platform system is obtained; Based on the target orientation information of the inertial navigation system corresponding to each target celestial body and the observation angle of the encoder, the installation error matrix between the inertial navigation system and the quantum communication telescope is determined, and the theoretical pointing angle of the target to be calibrated is obtained based on the installation error matrix. Based on the theoretical pointing angle and the actual encoder angle of the quantum communication telescope to the target to be calibrated, the pointing error of the quantum communication telescope is determined, and the pointing angle of the quantum communication telescope is corrected based on the pointing error. The method further includes: determining the charge response eccentricity corresponding to the target celestial body before acquiring the encoder observation angle; performing de-eccentricity processing on the encoder observation angle based on the charge response eccentricity; and determining the installation error matrix based on the de-eccentricated encoder observation angle. The method for determining the charge response eccentricity includes: Acquire a reference charge response detection frame and multiple perturbation charge response detection frames corresponding to the same target celestial body. Different perturbation charge response detection frames correspond to different CCD electrical acquisition parameters, which include at least one of exposure integration time, readout gain, electronic shutter phase, and dark current subtraction intensity. The electrical sensing axis corresponding to the target celestial body is determined based on at least one of the CCD readout direction, frame transfer direction, and dark current background gradient direction. The centroid drift vector of each disturbance charge response detection frame relative to the reference charge response detection frame is determined, and the centroid drift vector is projected onto the electrical sensing axis to obtain the one-dimensional electrical drift corresponding to each disturbance charge response detection frame; Based on the attitude change information of the inertial navigation system at the acquisition time of each charge response detection frame, geometric drift elimination is performed on each one-dimensional electrical drift to obtain multiple candidate electrical eccentricities. Based on the sign consistency of multiple candidate electrical eccentricities and the perturbation monotonicity between them and the CCD electrical acquisition parameters, the effective candidate electrical eccentricity is determined from multiple candidate electrical eccentricities. Based on the effective candidate electrical eccentricities, the charge response eccentricity corresponding to the target celestial body is determined.

2. The method according to claim 1, characterized in that, The calibration observation data also includes the astronomical coordinates of the target celestial body, the observation time information, and the inertial navigation attitude information. The astronomical coordinates are obtained through star catalog data and include the right ascension and declination of the target celestial body at a preset epoch. The observation time information includes the local sidereal time corresponding to the imaging observation of the target celestial body by the quantum communication telescope. The inertial navigation attitude information is obtained through inertial navigation system acquisition and includes the heading angle, pitch angle, and roll angle of the moving base platform at the observation time.

3. The method according to claim 1, characterized in that, The encoder observation angle is determined based on the azimuth encoder angle and pitch encoder angle output by the quantum communication telescope after extracting the off-target amount of the target celestial body and stabilizing the closed-loop tracking.

4. The method according to claim 2, characterized in that, The methods for determining the target orientation information on the inertial navigation side include: Based on the local sidereal time and the right ascension information, determine the hour angle corresponding to each target celestial body at the observation time; Based on the hour angle, the declination information, and the geographical location information corresponding to the moving base platform, determine the astronomical lateral azimuth and astronomical lateral elevation angles of each target celestial body in the astronomical reference coordinates; Based on the astronomical azimuth and the astronomical elevation angle, construct the astronomical target direction vector corresponding to each target celestial body; Based on the heading angle, pitch angle, and roll angle, construct an attitude transformation matrix from astronomical reference coordinates to the inertial navigation platform system; The coordinate transformation of the astronomical target direction vector is performed by the attitude transformation matrix to obtain the inertial navigation side target direction vector of each target celestial body in the inertial navigation platform system. Based on the inertial navigation side target direction vector, determine the inertial navigation side azimuth and inertial navigation side pitch angle of each target celestial body in the inertial navigation platform system, and use the inertial navigation side azimuth and the inertial navigation side pitch angle as the inertial navigation side target direction information.

5. The method according to claim 1, characterized in that, The installation error matrix is ​​determined in the following ways: Based on the inertial navigation side target direction information corresponding to each target celestial body, construct the inertial navigation side target direction vector of each target celestial body in the inertial navigation platform system; Based on the encoder observation angle corresponding to each target celestial body, construct the device-side observation direction vector of each target celestial body under the telescope equipment system; Based on the observation relationship corresponding to the same target celestial body, establish the coordinate transformation relationship between the target direction vector on the inertial navigation side and the observation direction vector on the equipment side; The installation error matrix between the inertial navigation system and the quantum communication telescope is obtained by solving the problem with the residual between the target direction vector on the inertial navigation side, after transformation by the observation equation matrix, and the corresponding observation direction vector on the equipment side, which satisfies a preset convergence condition.

6. The method according to claim 5, characterized in that, The methods for determining the pointing error include: Based on the installation error matrix, the inertial navigation side target direction vector corresponding to the target to be calibrated is converted into the theoretical direction vector under the telescope equipment system; Based on the theoretical direction vector, determine the theoretical azimuth and theoretical elevation angles of the target to be calibrated in the telescope equipment system, and use the theoretical azimuth and theoretical elevation angles as the theoretical pointing angles; The actual azimuth encoder angle and actual pitch encoder angle are obtained after the quantum communication telescope extracts the miss distance from the target to be calibrated and stabilizes the closed-loop tracking. The azimuth pointing error is determined based on the difference between the theoretical azimuth angle and the actual azimuth axis encoder angle, and the pitch pointing error is determined based on the difference between the theoretical pitch angle and the actual pitch axis encoder angle. The pointing error of the quantum communication telescope is determined based on the azimuth pointing error and the elevation pointing error.

7. The method according to claim 6, characterized in that, The methods for correcting the pointing angle include: Based on the azimuth pointing error, the azimuth axis target control angle of the quantum communication telescope is compensated to obtain the corrected azimuth axis control angle. Based on the pitch pointing error, the pitch axis target control angle of the quantum communication telescope is compensated to obtain the corrected pitch axis control angle. The corrected azimuth control angle and the corrected pitch control angle are used as the corrected pointing angle of the quantum communication telescope.

8. A quantum communication telescope pointing error calibration system, implemented based on the quantum communication telescope pointing error calibration method as described in any one of claims 1-7, characterized in that, The system includes: The observation data acquisition module is used to acquire calibration observation data corresponding to multiple target celestial bodies, and the calibration observation data includes at least the encoder observation angle; The target orientation conversion module is used to obtain the inertial navigation side target orientation information of each target celestial body in the inertial navigation platform system based on the calibration observation data. The installation error calibration module is used to determine the installation error matrix between the inertial navigation system and the quantum communication telescope based on the target direction information of each target celestial body and the observation angle of the encoder, and to obtain the theoretical pointing angle based on the installation error matrix. The pointing correction module is used to determine the pointing error of the quantum communication telescope based on the theoretical pointing angle, and to correct the pointing angle of the quantum communication telescope based on the pointing error.

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