Optical satellite drift angle accurate calculation and attitude correction method and system

Abstract

The invention discloses an optical satellite drift angle accurate calculation and attitude correction method and system, and relates to the technical field of satellite attitude control, and the method comprises the steps: calculating a prime unitary circle curvature radius according to a WGS84 ellipsoid parameter, and converting the geodetic coordinate of a ground target point into an ECEF rectangular coordinate; calculating Julian days based on UTC time, determining an age difference angle and a nutation angle, and converting an ECEF coordinate into a J2000 coordinate; calculating the projection of the earth rotation angular velocity in a J2000 coordinate system, and determining a relative velocity vector; determining an orthogonalized body coordinate system in combination with a unit vector from the target satellite to the ground target point; and projecting the relative velocity vector to a body coordinate system, calculating a drift angle and a double-rotation-sequence Euler angle, and correcting a real-time execution attitude by rotating a matrix around a Z axis. According to the method, high-precision image motion compensation can be realized, the imaging quality of a high-resolution optical satellite in a complex task scene is improved, and a technical foundation is laid for wide application of sub-meter remote sensing images.

Description

Technical Field

[0001] This invention relates to the field of satellite attitude control technology, and in particular to a method and system for accurate calculation of yaw angle and attitude correction of optical satellites. Background Technology

[0002] The yaw angle is a core factor affecting the imaging quality of optical remote sensing satellites. It refers to the angle between the velocity vectors of the satellite's flight direction (caused by the Earth's rotation) and the actual imaging direction of the TDICCD (Time Delay Integrating Charge-Coupled Device) camera. This angular difference causes lateral image shift during the integration imaging process, severely degrading image quality. Under the combined effects of high-speed satellite flight (typically exceeding 7 km / s) and the Earth's rotation (approximately 465 m / s equatorial linear velocity), ground targets experience complex relative motions with respect to the satellite platform. In pushbroom imaging systems, without precise compensation, the yaw angle causes lateral image shift at the focal plane, resulting in geometric distortion and blurring effects, leading to image blurring and a decrease in MTF (Modulation Transfer Function). Studies show that when the yaw angle residual exceeds 0.05°, pushbroom imaging produces image shift blur exceeding 1.2 pixels, causing a decrease in image MTF value of over 30%, severely impacting the application value of high-resolution remote sensing images.

[0003] Traditional methods for calculating deflection angles mainly rely on static geometric models: in For the deflection angle, This is the Earth's rotational angular velocity (approximately 465 m / s). For satellite latitude, The satellite's orbital velocity is approximately 7,600 m / s. This model assumes a fixed satellite attitude and the target is located at the nadir, and is applicable to traditional pushbroom satellites such as Landsat and SPOT. However, with the development of agile satellite technology, satellites possess rapid three-axis attitude maneuvers, enabling dynamic imaging of targets deviating from their flight path (maneuvering imaging mode). In this mode, the yaw angle originates not only from the Earth's rotation but also from additional components caused by attitude maneuvers. Where t is the time variable of the imaging process. and These are the satellite velocity and ground velocity vectors, respectively.

[0004] Existing technologies suffer from problems such as coordinate system modeling defects and accumulated errors, defects in body coordinate system construction, and limitations in attitude correction mechanisms. Defects in Coordinate System Modeling and Cumulative Errors: Existing technologies generally employ a simplified two-step coordinate transformation model (ECEF Earth-Fixed System → Orbital System → Local System), neglecting precession and nutation effects, leading to attitude calculation biases. A 2006 resolution of the International Astronomical Union (IAU) pointed out that the traditional IAU-1976 model has a precession calculation error of 0.3″ / year, which can cause an attitude deviation of 2.5μrad at an orbital altitude of 500km, equivalent to a 0.125 pixel offset in a 5m resolution image. This defect is further amplified, especially in maneuvering imaging modes. Missing Earth rotation velocity component: Most patents assume ground targets are stationary and do not incorporate the Earth's rotational tangential velocity into relative motion models. NASA research report JPL-PUB-18-3 points out that the Earth's rotational angular velocity... At a 700km orbit, a 0.15° deviation in the flow angle calculation will occur.

[0005] Time base missynchronization: Leap second correction errors between UTC and TAI (International Atomic Time) cause deviations in the ECEF→J2000 transformation matrix. Experimental measurements show that a 1-second time error can cause a 0.01° attitude angle deviation in low-Earth orbit satellite attitude calculations.

[0006] In the European Space Agency's Sentinel-2 mission, such cumulative errors led to a 40% increase in image registration error, with the MTF value dropping from 0.22 to below 0.15, severely limiting the geometric accuracy of the images.

[0007] Defects in constructing the body coordinate system: Traditional methods directly use the Y-axis (negative normal) of the orbital system as the Y-axis of the body system, without considering the non-orthogonal error caused by the Z-axis (pointing to the target point) offset. Experiments at the MIT Space Systems Laboratory have confirmed that when the non-orthogonal error reaches 0.05°, pushbroom imaging produces a 1.2-pixel blur, and the MTF decreases by 25%. Specifically: Y-axis inheritance mechanism defect: When the satellite is side-swinging for imaging, the Y-axis (negative normal) of the VVLH orbital system is not perpendicular to the Z-axis (target pointing) of the system. Direct inheritance will lead to non-orthogonality of the coordinate system, which will destroy the uniqueness of the attitude description.

[0008] The reconstruction algorithm is missing: the existing technology does not introduce the Gram-Schmidt orthogonalization process, and only calculates the temporary X-axis through a single cross product. It does not perform a second orthogonalization correction on the Y-axis, which causes the included angles of each axis of the system to deviate from 90°.

[0009] Limitations of attitude correction mechanisms: Existing attitude correction systems suffer from two major bottlenecks: single-order output and lack of residual compensation. The Euler angle conversion is limited: traditional methods only provide 321 conversion (ZYX) Euler angle outputs, while most new satellite platforms (such as Pleiades-NEO) use a 123 conversion (XYZ) control architecture. This conversion mismatch requires additional conversion for attitude control, introducing a calculation error of 0.02°~0.05°.

[0010] Uncorrected residual skew angle error: Especially in high-latitude regions, the residual skew angle error increases nonlinearly with latitude. Data from the Tianhui-1 satellite shows that in the 80° latitude region, the residual parallax reaches 101 pixels, causing uncontrolled positioning accuracy to drop from the 10-meter level to the 100-meter level. Current technologies lack on-orbit adaptive compensation mechanisms, relying solely on ground calibration, making it difficult to promptly eliminate sensor performance degradation caused by space irradiation (such as a 30-50% increase in random walk angle in fiber optic gyroscopes).

[0011] Table 1. Influence of deflection angle residuals on imaging quality at different latitudes It is evident that existing technologies suffer from problems such as inconsistent coordinate systems, insufficient compensation for Earth's rotation, and unintuitive attitude descriptions. Summary of the Invention

[0012] The technical problem to be solved by this invention is to address the shortcomings of existing technologies, specifically by providing a method and system for accurate calculation of optical satellite yaw angle and attitude correction, as detailed below: 1) In a first aspect, the present invention provides a method for accurate calculation of the yaw angle and attitude correction of an optical satellite, the specific technical solution of which is as follows: Based on the WGS84 ellipsoid parameters, the radius of curvature of the primordial and maximal orbits is calculated. Based on the radius of curvature of the primordial and maximal orbits, the geodetic coordinates of the collected ground target points are converted into ECEF rectangular coordinates. The Julian day is calculated based on UTC time. The precession angle and nutation angle are determined based on the Julian day. The ECEF rectangular coordinates of the collected ground target points are converted into J2000 coordinates by combining the precession angle and nutation angle. The Earth's rotational angular velocity is projected onto the J2000 coordinate system, and the tangential velocity of the ground target point is calculated to determine the relative velocity vector corresponding to the tangential velocity. Based on the relative velocity vector, and combined with the unit vector from the target satellite to the ground target point, an orthogonalized body coordinate system is determined. The relative velocity vector is projected onto the body coordinate system to obtain the projection component corresponding to the relative velocity vector. The deflection angle and double rotation sequence Euler angle are calculated based on the projection component, and the real-time execution attitude is corrected by combining the rotation matrix around the Z-axis.

[0013] The beneficial effects of the method for accurate calculation of optical satellite velocity angle and attitude correction provided by this invention are as follows: By calculating the radius of curvature of the prime mover circle based on WGS84 ellipsoid parameters and converting the geodetic coordinates of the ground target point to ECEF rectangular coordinates, this invention provides a precise coordinate transformation method, ensuring high accuracy and reliability. This process lays a solid foundation for subsequent coordinate transformations and calculations, avoiding imaging errors caused by inaccurate coordinate transformation. The Julian day is calculated based on UTC time, and the precession and nutation angles are determined based on the Julian day, thereby converting the ECEF rectangular coordinates to J2000 coordinates. This process not only considers the long-term precession (precession) and short-term perturbation (nutation) of the Earth's rotation axis in space but also eliminates the problem of inaccurate coordinate transformation caused by the cumulative errors of precession and nutation in traditional methods. By employing the IAU-2006 model, this invention improves the conversion accuracy from ECEF to J2000 to the 0.001″ level, significantly outperforming traditional methods. This provides accurate inertial coordinates for subsequent Earth rotation velocity vector compensation and yaw angle calculation. The Earth's rotation angular velocity is projected onto the J2000 coordinate system, and the tangential velocity of the ground target point is calculated to determine the relative velocity vector. This process addresses the lack of relative motion modeling in existing technologies, ensuring accurate calculation of the relative velocity vector. By considering the influence of Earth's rotation on the target point, this invention can more accurately describe the relative motion between the satellite and the target point, providing an important basis for accurate yaw angle calculation. Based on the relative velocity vector and the unit vector from the target satellite to the ground target point, orthogonalized body coordinates are determined. By introducing the Gram-Schmidt orthogonalization process, this invention can construct a strictly orthogonal body coordinate system, solving the non-orthogonal error problem caused by the defect of the Y-axis inheritance mechanism in traditional methods. This improvement not only enhances the accuracy of attitude description but also ensures the uniqueness and reliability of attitude control. The relative velocity vector is projected onto the body coordinate system, the yaw angle and dual-rotation-order Euler angles are calculated, and the real-time attitude is corrected using the rotation matrix around the Z-axis. This process not only achieves accurate calculation of the yaw angle but also adapts to the control architecture of different satellite platforms through the output of dual-rotation-order Euler angles, improving the flexibility and compatibility of attitude correction. Through a closed-loop compensation mechanism, this invention can also adjust the yaw angle compensation parameters in real time based on imaging quality assessment feedback, further optimizing imaging quality.

[0014] Based on the above solution, the present invention can be further improved as follows.

[0015] Furthermore, the process of converting the collected ECEF rectangular coordinates of the ground target points into J2000 coordinates is as follows: Based on the precession angle and the nutation angle, construct a rotation matrix from ECEF rectangular coordinates to J2000 coordinates; The coordinate transformation is performed based on the rotation matrix.

[0016] The beneficial effects of the above-mentioned further solutions are as follows: Constructing rotation matrices provides a systematic and precise mathematical tool for coordinate transformation. This matrix-based transformation method not only improves computational efficiency but also ensures the accuracy and reliability of the transformation process. By using rotation matrices, complex coordinate transformation problems can be simplified to matrix multiplication operations, thereby reducing computational complexity and improving accuracy. This method is particularly effective when processing large amounts of data, significantly improving the overall system performance. The coordinate transformation process based on rotation matrices also exhibits good scalability and adaptability. Since the construction of rotation matrices is based on precession and nutation angles, which can be obtained through precise astronomical measurements and model calculations, this method can adapt to different time bases and coordinate systems, possessing broad applicability. Whether for high-orbit or low-orbit satellites, and for short-term or long-term missions, this method can provide accurate coordinate transformation results.

[0017] Furthermore, the process of determining the orthogonalized ontological coordinate system is as follows: Based on the position vector of the ground target point relative to the target satellite, the Z-axis of the orthogonalized body coordinate system is determined; The X-axis of the orthogonalized body coordinate system is initialized by the cross product of the target satellite's velocity vector and the Z-axis, thus obtaining the initialized X-axis. By using the Gram-Schmidt method, the projections of the target satellite on the Z-axis and X-axis are removed from the initial Y-axis of the orthogonalized body coordinate system to obtain the reconstructed Y-axis of the orthogonalized body coordinate system. The reconstructed Y is normalized and orthogonalized to determine the Y-axis of the orthogonalized ontological coordinate system; Based on the Z-axis and Y-axis of the orthogonalized body coordinate system, the initial X-axis is reconstructed to obtain the X-axis of the orthogonalized body coordinate system. The X-axis, Y-axis and Z-axis are then integrated to obtain the orthogonalized body coordinate system.

[0018] The beneficial effects of the above-mentioned further solutions are as follows: The Z-axis of the body coordinate system is determined based on the position vector of the ground target point relative to the target satellite, ensuring that the definition of the Z-axis is consistent with the direction from the satellite to the target point, thus providing an accurate reference direction for subsequent coordinate system construction. This process not only improves the accuracy of the coordinate system but also ensures that the orientation of the coordinate system is closely related to the satellite's mission objectives. The X-axis of the body coordinate system is initialized by the cross product of the target satellite's velocity vector and the Z-axis. This method utilizes the satellite's motion characteristics, ensuring that the X-axis is related to the satellite's motion direction and perpendicular to the Z-axis. This initialization method is not only simple and efficient but also provides a good starting point for the subsequent orthogonalization process. The initialized Y-axis is orthogonalized using the Gram-Schmidt method, eliminating the projection of the Y-axis onto the Z-axis and X-axis, thus obtaining a strictly orthogonal Y-axis. This process not only ensures the orthogonality of the coordinate system but also further improves the accuracy and reliability of the coordinate system through normalization and orthogonality verification. This orthogonalization method effectively solves the non-orthogonal error problem caused by the defects in the Y-axis inheritance mechanism in traditional methods, thereby improving the accuracy and uniqueness of attitude description. Based on orthogonalized Y-axis and Z-axis, the initialized X-axis is reconstructed, ensuring the orthogonality of the X-axis with the Y and Z axes. By integrating the X, Y, and Z axes, a strictly orthogonal body coordinate system is obtained. This orthogonalized body coordinate system not only improves the accuracy of attitude control but also provides an accurate coordinate system basis for subsequent yaw angle calculations and attitude corrections. In this way, the present invention can effectively eliminate the impact of non-orthogonal errors on imaging quality, significantly improving the imaging quality of high-resolution optical satellites.

[0019] Furthermore, the process of correcting the real-time execution posture is as follows: Calculate the deflection angle and double-rotation Euler angle based on the projected components, and construct a rotation matrix around the Z-axis based on the deflection angle; Based on the rotation matrix around the Z-axis, the current attitude matrix of the satellite determined according to the double rotation order Euler angles is corrected.

[0020] The beneficial effects of the above-mentioned further solutions are as follows: This scheme achieves dynamic attitude adjustment by correcting the satellite's current attitude matrix through a rotation matrix around the Z-axis. This correction method not only considers the satellite's current attitude state but also dynamically updates it based on real-time calculated yaw angles and Euler angles. This enables the satellite to maintain high-precision attitude control in complex mission scenarios, such as maneuvering imaging modes, thereby significantly improving the stability and reliability of imaging quality.

[0021] Furthermore, it also includes: The current MTF value is acquired in real time, and the error between the current MTF value and the preset optimal MTF value is calculated. The state estimate and covariance matrix of the Kalman filter are updated based on the error, and the compensation parameters for the deflection angle are updated based on the updated Kalman filter.

[0022] The beneficial effects of the above-mentioned further solutions are as follows: By acquiring the current MTF value in real time and calculating the error between it and the preset optimal MTF value, this scheme can directly assess the impact of the current attitude correction on image quality. The MTF value, as a key indicator of image quality, reflects the gap between the current attitude correction and the ideal state. This real-time feedback mechanism enables the system to detect changes in image quality promptly, providing an accurate basis for further attitude adjustments. Based on the error-updated state estimate and covariance matrix of the Kalman filter, this scheme can dynamically adjust the yaw angle compensation parameters. The Kalman filter, as an efficient recursive filtering algorithm, can update the state estimate in real time based on new measurement data, while considering the effects of measurement noise and system noise. In this way, the system can not only respond quickly to changes in image quality but also maintain stable performance in uncertain environments. This dynamic adjustment mechanism allows the yaw angle compensation parameters to be adaptively optimized, thereby further improving image quality.

[0023] 2) In a second aspect, the present invention also provides a system for accurate calculation of the velocity angle and attitude correction of optical satellites, the specific technical solution of which is as follows: The first conversion module is used to: calculate the radius of curvature of the primordial and maximal orbits according to the WGS84 ellipsoid parameters, and convert the geodetic coordinates of the collected ground target points into ECEF rectangular coordinates based on the radius of curvature of the primordial and maximal orbits; The second conversion module is used to: calculate the Julian day based on UTC time, determine the precession angle and nutation angle based on the Julian day, and convert the ECEF rectangular coordinates of the collected ground target points into J2000 coordinates by combining the precession angle and the nutation angle. The first determining module is used to: project the Earth's rotation angular velocity onto the J2000 coordinate system, and simultaneously calculate the tangential velocity of the ground target point, and determine the relative velocity vector corresponding to the tangential velocity; The second determining module is used to: determine an orthogonalized body coordinate system based on the relative velocity vector and the unit vector from the target satellite to the ground target point; The calculation module is used to: project the relative velocity vector onto the body coordinate system to obtain the projection component corresponding to the relative velocity vector, and calculate the deflection angle and double rotation order Euler angle based on the projection component, and correct the real-time execution attitude by combining the rotation matrix around the Z-axis.

[0024] Based on the above solution, the present invention can be further improved as follows.

[0025] Furthermore, the process of converting the collected ECEF rectangular coordinates of the ground target points into J2000 coordinates is as follows: Based on the precession angle and the nutation angle, construct a rotation matrix from ECEF rectangular coordinates to J2000 coordinates; The coordinate transformation is performed based on the rotation matrix.

[0026] Furthermore, the process of determining the orthogonalized ontological coordinate system is as follows: Based on the position vector of the ground target point relative to the target satellite, the Z-axis of the orthogonalized body coordinate system is determined; The X-axis of the orthogonalized body coordinate system is initialized by the cross product of the target satellite's velocity vector and the Z-axis, thus obtaining the initialized X-axis. By using the Gram-Schmidt method, the projections of the target satellite on the Z-axis and X-axis are removed from the initial Y-axis of the orthogonalized body coordinate system to obtain the reconstructed Y-axis of the orthogonalized body coordinate system. The reconstructed Y is normalized and orthogonalized to determine the Y-axis of the orthogonalized ontological coordinate system; Based on the Z-axis and Y-axis of the orthogonalized body coordinate system, the initial X-axis is reconstructed to obtain the X-axis of the orthogonalized body coordinate system. The X-axis, Y-axis and Z-axis are then integrated to obtain the orthogonalized body coordinate system.

[0027] Furthermore, the process of correcting the real-time execution posture is as follows: Calculate the deflection angle and double-rotation Euler angle based on the projected components, and construct a rotation matrix around the Z-axis based on the deflection angle; Based on the rotation matrix around the Z-axis, the current attitude matrix of the satellite determined according to the double rotation order Euler angles is corrected.

[0028] Furthermore, it also includes: The update module is used to: obtain the current MTF value in real time and calculate the error between the current MTF value and the preset optimal MTF value; The state estimate and covariance matrix of the Kalman filter are updated based on the error, and the compensation parameters for the deflection angle are updated based on the updated Kalman filter.

[0029] 3) In a third aspect, the present invention also provides an electronic device, the electronic device including a processor coupled to a memory, the memory storing at least one computer program, the at least one computer program being loaded and executed by the processor to enable the electronic device to perform any of the above methods.

[0030] 4) In a fourth aspect, the present invention also provides a computer-readable storage medium storing at least one computer program, which is loaded and executed by a processor to enable a computer to implement any of the above methods.

[0031] It should be noted that the beneficial effects of the technical solutions of the second to fourth aspects of the present invention and their corresponding possible implementations can be found in the above description of the technical effects of the first aspect and its corresponding possible implementations, and will not be repeated here. Attached Figure Description

[0032] 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 This is a flowchart illustrating a method for accurately calculating the yaw angle and correcting the attitude of an optical satellite according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a four-layer coordinate system transformation chain for a method of accurately calculating the yaw angle and correcting the attitude of an optical satellite according to an embodiment of the present invention; Figure 3 This is a flowchart illustrating the orthogonalization construction of the ontological coordinate system for a method of accurate calculation of optical satellite yaw angle and attitude correction according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the system architecture of a method for accurate calculation of optical satellite yaw angle and attitude correction according to an embodiment of the present invention; Figure 5 This is a structural framework diagram of an electronic device according to the present invention. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0034] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for accurate calculation of the velocity angle and attitude correction of an optical satellite, comprising the following steps: S1. Calculate the radius of curvature of the primordial and maximal orbits based on the WGS84 ellipsoid parameters, and convert the geodetic coordinates of the collected ground target points into ECEF rectangular coordinates based on the radius of curvature of the primordial and maximal orbits. S2, calculate the Julian day based on UTC time, determine the precession angle and nutation angle based on the Julian day, and convert the ECEF rectangular coordinates of the collected ground target points into J2000 coordinates by combining the precession angle and the nutation angle. S3, Project the Earth's rotational angular velocity onto the J2000 coordinate system, and simultaneously calculate the tangential velocity of the ground target point to determine the relative velocity vector corresponding to the tangential velocity; S4. Based on the relative velocity vector, and combined with the unit vector from the target satellite to the ground target point, determine the orthogonalized body coordinate system; S5, the relative velocity vector is projected onto the body coordinate system to obtain the projection component corresponding to the relative velocity vector, and the deflection angle and double rotation sequence Euler angle are calculated based on the projection component. The real-time execution attitude is corrected by combining the rotation matrix around the Z-axis.

[0035] The beneficial effects of the method for accurate calculation of optical satellite velocity angle and attitude correction provided by this invention are as follows: By calculating the radius of curvature of the prime mover circle based on WGS84 ellipsoid parameters and converting the geodetic coordinates of the ground target point to ECEF rectangular coordinates, this invention provides a precise coordinate transformation method, ensuring high accuracy and reliability. This process lays a solid foundation for subsequent coordinate transformations and calculations, avoiding imaging errors caused by inaccurate coordinate transformation. The Julian day is calculated based on UTC time, and the precession and nutation angles are determined based on the Julian day, thereby converting the ECEF rectangular coordinates to J2000 coordinates. This process not only considers the long-term precession (precession) and short-term perturbation (nutation) of the Earth's rotation axis in space but also eliminates the problem of inaccurate coordinate transformation caused by the cumulative errors of precession and nutation in traditional methods. By employing the IAU-2006 model, this invention improves the conversion accuracy from ECEF to J2000 to the 0.001″ level, significantly outperforming traditional methods. This provides accurate inertial coordinates for subsequent Earth rotation velocity vector compensation and yaw angle calculation. The Earth's rotation angular velocity is projected onto the J2000 coordinate system, and the tangential velocity of the ground target point is calculated to determine the relative velocity vector. This process addresses the lack of relative motion modeling in existing technologies, ensuring accurate calculation of the relative velocity vector. By considering the influence of Earth's rotation on the target point, this invention can more accurately describe the relative motion between the satellite and the target point, providing an important basis for accurate yaw angle calculation. Based on the relative velocity vector and the unit vector from the target satellite to the ground target point, orthogonalized body coordinates are determined. By introducing the Gram-Schmidt orthogonalization process, this invention can construct a strictly orthogonal body coordinate system, solving the non-orthogonal error problem caused by the defect of the Y-axis inheritance mechanism in traditional methods. This improvement not only enhances the accuracy of attitude description but also ensures the uniqueness and reliability of attitude control. The relative velocity vector is projected onto the body coordinate system, the yaw angle and dual-rotation-order Euler angles are calculated, and the real-time attitude is corrected using the rotation matrix around the Z-axis. This process not only achieves accurate calculation of the yaw angle but also adapts to the control architecture of different satellite platforms through the output of dual-rotation-order Euler angles, improving the flexibility and compatibility of attitude correction. Through a closed-loop compensation mechanism, this invention can also adjust the yaw angle compensation parameters in real time based on imaging quality assessment feedback, further optimizing imaging quality.

[0036] The WGS84 (World Geodetic System 1984) ellipsoid parameters are mathematical model parameters used to describe the shape and size of the Earth, and are widely used in the Global Positioning System (GPS) and other geographic information systems. The main parameters of the WGS84 ellipsoid model include: semi-major axis (a): 6,378,137 meters, oblateness (f): 1 / 298.257223563, and semi-minor axis (b): 6,356,752.314245 meters (calculated from the semi-major axis and oblateness).

[0037] In another embodiment of this scheme, the process for determining the radius of curvature of the ramusoidal circle is as follows: The square of the first eccentricity e is calculated based on the semi-major axis and the flattening. 2 e 2 =2f-f 2 For any point on the Earth's ellipsoid, the radius of curvature N of the primordial circle and the geographical latitude of that point... The relevant calculation formula is as follows: .

[0038] It should be further explained that the Prime Vertical Circle is the normal section line passing through a point on the Earth's ellipsoid and perpendicular to the meridian plane at that point. Its radius of curvature reflects the degree of curvature of that point in the Prime Vertical direction.

[0039] In another embodiment of this scheme, the process of converting to ECEF rectangular coordinates includes: Longitude is projected using a nonlinear projection formula. ,latitude Convert elevation h to ECEF rectangular coordinates and output ECEF rectangular coordinates: .

[0040] In another embodiment of this solution, the specific process of S2 is as follows: The IAU-2006 resolution model was used to calculate the precession nutation parameters, that is, to calculate the Julian day (JD) using UTC time and to analyze the precession angle. , And zonal angle , .

[0041] Construct the rotation matrix: in, Transformation matrix representing rotation about the Z-axis , Transformation matrix representing rotation about the Y-axis , Transformation matrix representing rotation about the Z-axis , Transformation matrix representing rotation about the X-axis .

[0042] Coordinate transformation: .

[0043] In another embodiment of this solution, the process of S3 is specifically as follows: Eliminate the cumulative error of 0.3″ / year in the traditional IAU-1976 model: Earth's rotation speed vector compensation The Earth's rotational angular velocity ( Projected onto the J2000 series: Calculate the tangential velocity at the target point: ; in, This represents the position vector of the target point in the J2000 system.

[0044] Calculate the relative velocity vector that includes compensation for Earth's rotation: ; in, This represents the satellite's velocity vector in the J2000 system.

[0045] In another embodiment of this scheme, the process of S4 is specifically as follows: Introducing Gram-Schmidt orthogonalization of the loop ( This reduces the orthogonal deviation to <0.0001° and is applicable across the entire angular range.

[0046] The coordinate system construction process includes: Z-axis definition: The unit vector along the satellite to the target point: in, This represents the position vector of the target point in the J2000 system. This represents the satellite's position vector in the J2000 system.

[0047] Initial X-axis: Cross product of the orbital system's Y-axis (negative normal) and Z-axis: Orthogonalizing the Y-axis: Reconstructing it via the Gram-Schmidt process: Final X-axis: Cross product of orthogonal Y-axis and Z-axis: Orthogonality guarantee mechanism Reconstruction using cyclic cross product ( ) Perform double normalization: normalize the norm of the result at each step. Verify the orthogonality condition: .

[0048] In another embodiment of this solution, the process of S5 is specifically as follows: Simultaneously generate 321 / 123 dual-sequence parameters to adapt to different satellite control architectures.

[0049] Projecting the relative velocity onto this system: The deflection angle is calculated using the following formula: ; in, This represents the projection onto the y-axis. This represents the projection onto the X-axis.

[0050] The double Euler angle conversion output includes: 321 Transition (ZYX): Yaw angle ; Pitch angle ; Roll angle ; 123 to sequence (XYZ): Roll angle ; Pitch angle ; Yaw angle .

[0051] Where R represents the rotation matrix of the satellite from its own system to the VVLH orbital system.

[0052] , This represents the satellite's position vector in the VVLH orbital system.

[0053] Construct a rotation matrix around the Z-axis Corrected attitude matrix .

[0054] Furthermore, the process of converting the collected ECEF rectangular coordinates of the ground target points into J2000 coordinates is as follows: Based on the precession angle and the nutation angle, construct a rotation matrix from ECEF rectangular coordinates to J2000 coordinates; The coordinate transformation is performed based on the rotation matrix.

[0055] Furthermore, the process of determining the orthogonalized ontological coordinate system is as follows: Based on the position vector of the ground target point relative to the target satellite, the Z-axis of the orthogonalized body coordinate system is determined; The X-axis of the orthogonalized body coordinate system is initialized by the cross product of the target satellite's velocity vector and the Z-axis, thus obtaining the initialized X-axis. By using the Gram-Schmidt method, the projections of the target satellite on the Z-axis and X-axis are removed from the initial Y-axis of the orthogonalized body coordinate system to obtain the reconstructed Y-axis of the orthogonalized body coordinate system. The reconstructed Y is normalized and orthogonalized to determine the Y-axis of the orthogonalized ontological coordinate system; Based on the Z-axis and Y-axis of the orthogonalized body coordinate system, the initial X-axis is reconstructed to obtain the X-axis of the orthogonalized body coordinate system. The X-axis, Y-axis and Z-axis are then integrated to obtain the orthogonalized body coordinate system.

[0056] Furthermore, the process of correcting the real-time execution posture is as follows: Calculate the deflection angle and double-rotation Euler angle based on the projected components, and construct a rotation matrix around the Z-axis based on the deflection angle; Based on the rotation matrix around the Z-axis, the current attitude matrix of the satellite determined according to the double rotation order Euler angles is corrected.

[0057] Furthermore, it also includes: The current MTF value is acquired in real time, and the error between the current MTF value and the preset optimal MTF value is calculated. The state estimate and covariance matrix of the Kalman filter are updated based on the error, and the compensation parameters for the deflection angle are updated based on the updated Kalman filter.

[0058] In another embodiment of this scheme, real-time imaging MTF value measurement is performed by an imaging sensor onboard the satellite to measure the current imaging MTF value in real time. The MTF value reflects the modulation transfer function of the imaging system and is a key indicator for evaluating imaging quality. A lower MTF value indicates poor imaging quality, and may indicate blurring or distortion.

[0059] The real-time measured MTF value is compared with the preset optimal MTF value to calculate the error. The error value reflects the gap between the current attitude correction and the ideal state. Among them, MTF 目标 It is the expected optimal MTF value, MTF 当前 It is the MTF value measured in real time.

[0060] Kalman filter state update: The deflection angle compensation parameters are optimized online using a Kalman filter. The Kalman filter is a recursive algorithm used to estimate the state of a dynamic system and update the estimates in real time based on new measurement data.

[0061] Based on the error value e, update the state estimate and covariance matrix of the Kalman filter. The state estimate update formula is: Where K is the Kalman gain, used to balance measurement error and prediction error. The formula for calculating the Kalman gain is: Where P is the state covariance matrix, H is the observation matrix, and R is the measurement noise covariance matrix.

[0062] Flow angle compensation parameter update: Using the updated state estimate δ 优化 This new yaw angle compensation parameter is used for subsequent attitude correction. This step ensures that attitude correction can be dynamically adjusted based on real-time imaging quality feedback, thereby optimizing imaging quality.

[0063] Kalman filter parameter update: The covariance matrix P of the Kalman filter is updated to reflect the uncertainty of the new state estimate. The formula for updating the covariance matrix is: Here, I is the identity matrix. This step ensures that the Kalman filter can adjust the uncertainty of its estimate based on new measurement data, thereby providing a more accurate state estimate in subsequent iterations.

[0064] Example 1, Ground target point location: Longitude 107.876°, Latitude 43.9586°, Elevation 0.5km; UTC time: 2025-07-04 15:16:55; Position and velocity of satellite J2000 series: pos_J2000 = [ -1474.850837 -5241.498388 4243.207524]'km vel_J2000 = [0.060085 4.770849 5.914162]'km / s; like Figures 2 to 4 As shown, the present invention mainly includes the following steps: Step 1: Precise transformation from geodetic coordinate system to ECEF; The target point has the following rectangular coordinates on ECEF: [-1411.709 4377.003 4405.129] km; Step 2: ECEF → J2000 inertial frame conversion; The target point's rectangular coordinates in the J2000 system; Target point J2000 location: [-814.165, -4524.258, 4407.320] km; Target point J2000 speed: [0.330, -0.060, -0.001] km / s; Earth's rotation velocity vector compensation; Relative velocity vector: [-0.270, 4.831, 5.915] km / s; Step 3: Orthogonalize and construct the ontological coordinate system; The X-axis of the body coordinate system is: [-0.145266, -0.091599, 0.985143]. The Y-axis of the body coordinate system is: [0.729736, -0.682301, 0.044164]. The body coordinate system Z-axis is defined as: [0.668119, 0.725310, 0.165959]. Step 4: Calculation of drift angle and attitude correction; Relative velocity projected onto this system: ; The relative velocity of this system is: [5.424, -3.232, 4.305] km / s; Deflection angle calculation; ; Deflection angle = -30.789628°; Step 5: Output the double Euler angles in sequence; The staring attitude Euler angles of this system relative to the VVLH orbital system (321 rotation sequence); Roll angle: -33.353531°; Pitch angle: 44.921134°; Yaw angle: 0.000000°; The staring attitude Euler angles of this system relative to the VVLH orbital system (123 rotation sequence); Roll angle: -42.909875°; Pitch angle: 36.144840°; Yaw angle: 28.735605°; Step 6: Attitude correction; The corrected attitude Euler angles of this system relative to the VVLH orbital system (321 rotation sequence); Roll angle: -49.638090°; Pitch angle: 24.036914°; Yaw angle: -27.915903°; The corrected attitude Euler angles of this system relative to the VVLH orbital system (123 rotation sequence); Roll angle: -42.909875°; Pitch angle: 36.144840°; Yaw angle: -2.054023°.

[0065] In the above embodiments, although the steps are numbered S1, S2, etc., they are only specific embodiments given by the present invention. Those skilled in the art can adjust the execution order of S1, S2, etc. according to the actual situation, which is also within the protection scope of the present invention. It can be understood that in some embodiments, some or all of the above embodiments may be included.

[0066] This invention also provides a system for accurate calculation of the velocity angle and attitude correction of optical satellites, the specific technical solution of which is as follows: The first conversion module is used to: calculate the radius of curvature of the primordial and maximal orbits according to the WGS84 ellipsoid parameters, and convert the geodetic coordinates of the collected ground target points into ECEF rectangular coordinates based on the radius of curvature of the primordial and maximal orbits; The second conversion module is used to: calculate the Julian day based on UTC time, determine the precession angle and nutation angle based on the Julian day, and convert the ECEF rectangular coordinates of the collected ground target points into J2000 coordinates by combining the precession angle and the nutation angle. The first determining module is used to: project the Earth's rotation angular velocity onto the J2000 coordinate system, and simultaneously calculate the tangential velocity of the ground target point, and determine the relative velocity vector corresponding to the tangential velocity; The second determining module is used to: determine an orthogonalized body coordinate system based on the relative velocity vector and the unit vector from the target satellite to the ground target point; The calculation module is used to: project the relative velocity vector onto the body coordinate system to obtain the projection component corresponding to the relative velocity vector, and calculate the deflection angle and double rotation order Euler angle based on the projection component, and correct the real-time execution attitude by combining the rotation matrix around the Z-axis.

[0067] It should be noted that the beneficial effects of the optical satellite yaw angle accurate calculation and attitude correction system provided in the above embodiments are the same as those of the optical satellite yaw angle accurate calculation and attitude correction method described above, and will not be repeated here. Furthermore, the system provided in the above embodiments is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the system can be divided into different functional modules according to the actual situation to complete all or part of the functions described above. In addition, the system and method embodiments provided in the above embodiments belong to the same concept, and their specific implementation process is detailed in the method embodiments, and will not be repeated here.

[0068] like Figure 5 As shown, an electronic device 300 according to an embodiment of the present invention includes a processor 320 coupled to a memory 310. The memory 310 stores at least one computer program 330, which is loaded and executed by the processor 320 to enable the electronic device 300 to implement any of the above-mentioned methods. Specifically: The electronic device 300 can vary considerably due to differences in configuration or performance. It may include one or more processors 320 (Central Processing Units, CPUs) and one or more memories 310. The memories 310 store at least one computer program 330, which is loaded and executed by the processors 320 to enable the electronic device 300 to implement the method for accurate calculation of optical satellite yaw angle and attitude correction provided in the above embodiments. Of course, the electronic device 300 may also have wired or wireless network interfaces, a keyboard, and input / output interfaces for input and output. It may also include other components for implementing device functions, which will not be elaborated upon here.

[0069] An embodiment of the present invention provides a computer-readable storage medium storing at least one computer program, which is loaded and executed by a processor to enable a computer to implement any of the above-described methods.

[0070] Alternatively, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a compact disc read-only memory (CD-ROM), magnetic tape, a floppy disk, and an optical data storage device, etc.

[0071] In an exemplary embodiment, a computer program product or computer program is also provided, which includes computer instructions stored in a computer-readable storage medium. A processor of an electronic device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the electronic device to perform any of the methods described above.

[0072] It should be noted that the terms "first" and "second" in the specification and claims of this application are used to distinguish similar objects and represent a limitation on a specific order or sequence. Where appropriate, the order of use for similar objects can be interchanged so that the embodiments of this application described herein can be implemented in an order other than that shown or described.

[0073] Those skilled in the art will recognize that this invention can be implemented as a system, method, or computer program product. Therefore, this disclosure can be specifically implemented in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, the invention can also be implemented as a computer program product contained in one or more computer-readable media, which includes computer-readable program code.

[0074] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0075] 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. An optical satellite drift angle accurate calculation and attitude correction method, characterized in that, The method comprises the following steps: According to the WGS84 ellipsoid parameters, the colure curvature radius is calculated, and the geodetic coordinates of the collected ground target point are converted into ECEF rectangular coordinates based on the colure curvature radius; According to the UTC time, the Julian day is calculated, the precession angle and the nutation angle are determined based on the Julian day, and the ECEF rectangular coordinates of the collected ground target point are converted into J2000 coordinates in combination with the precession angle and the nutation angle; The earth rotation angular velocity is projected into the J2000 coordinate system, and the tangential velocity of the ground target point is calculated, and the relative velocity vector corresponding to the tangential velocity is determined; Based on the relative velocity vector, the orthogonal body coordinate system is determined in combination with the unit vector from the target satellite to the ground target point; The relative velocity vector is projected into the body coordinate system to obtain the projection component corresponding to the relative velocity vector, and the drift angle and the double rotation order Euler angle are calculated based on the projection component, and the real-time execution attitude is corrected in combination with the rotation matrix around the Z-axis.

2. The method of claim 1, wherein the method comprises: The process of converting the collected ECEF rectangular coordinates of the ground target point into J2000 coordinates is specifically as follows: Based on the precession angle and the nutation angle, a rotation matrix from ECEF rectangular coordinates to J2000 coordinates is constructed; Based on the rotation matrix, the coordinate conversion is completed.

3. The method of claim 1, wherein the method further comprises: calculating the satellite's position and velocity based on the satellite's ephemeris data; calculating the satellite's position and velocity based on the satellite's optical observation data; and calculating the satellite's position and velocity based on the satellite's radar observation data. The determination process of the orthogonal body coordinate system is specifically as follows: Based on the position vector of the ground target point relative to the target satellite, the Z-axis of the orthogonal body coordinate system is determined; The X-axis of the orthogonal body coordinate system is initialized by the cross product of the satellite velocity vector of the target satellite and the Z-axis to obtain the initialized X-axis; The projection of the target satellite on the Z-axis and the X-axis is removed from the initialized Y-axis of the orthogonal body coordinate system by the Gram-Schmidt method to obtain the reconstructed Y-axis of the orthogonal body coordinate system; The reconstructed Y is unitized and orthogonality verified to determine the Y-axis of the orthogonal body coordinate system; Based on the Z-axis and the Y-axis of the orthogonal body coordinate system, the initialized X-axis is reconstructed to obtain the X-axis of the orthogonal body coordinate system, and the X-axis, the Y-axis and the Z-axis are integrated to obtain the orthogonal body coordinate system.

4. The method of claim 3, wherein the method further comprises: The process of correcting the real-time execution attitude is specifically as follows: The drift angle and the double rotation order Euler angle are calculated according to the projection component, and the rotation matrix around the Z-axis is constructed according to the drift angle; Based on the rotation matrix around the Z-axis, the satellite current attitude matrix determined according to the double rotation order Euler angle is corrected.

5. The method of claim 1, wherein the method further comprises: Further comprising: The current MTF value is obtained in real time, and the error between the current MTF value and the preset optimal MTF value is calculated; The state estimation and the covariance matrix of the Kalman filter are updated according to the error, and the compensation parameter update of the drift angle is performed based on the updated Kalman filter.

6. An optical satellite drift angle accurate calculation and attitude correction system, characterized in that, The first conversion module is used to calculate the colure curvature radius according to the WGS84 ellipsoid parameters, and convert the geodetic coordinates of the collected ground target point into ECEF rectangular coordinates based on the colure curvature radius. ​ The second conversion module is configured to: calculate a Julian day according to a UTC time, determine an equation of the equinoxes and a nutation angle based on the Julian day, and convert the collected ECEF rectangular coordinates of the ground target point into J2000 coordinates in combination with the equation of the equinoxes and the nutation angle; The first determination module is configured to: project an angular velocity of the earth rotation into a J2000 coordinate system, calculate a tangential velocity of the ground target point, and determine a relative velocity vector corresponding to the tangential velocity; The second determination module is configured to: determine an orthogonal body coordinate system based on the relative velocity vector and in combination with a unit vector from the target satellite to the ground target point; The calculation module is configured to: project the relative velocity vector into the body coordinate system to obtain a projection component corresponding to the relative velocity vector, calculate a drift angle and a double rotation sequence Euler angle based on the projection component, and correct a real-time execution attitude in combination with a rotation matrix around a Z axis.

7. The optical satellite drift angle accurate calculation and attitude correction system according to claim 6, characterized in that, The process of converting the collected ECEF rectangular coordinates of the ground target point into J2000 coordinates specifically includes: Based on the equation of the equinoxes and the nutation angle, a rotation matrix from ECEF rectangular coordinates to J2000 coordinates is constructed; The coordinate conversion is completed based on the rotation matrix.

8. The optical satellite drift angle accurate calculation and attitude correction system according to claim 6, characterized in that, The determination process of the orthogonal body coordinate system specifically includes: Based on a position vector of the ground target point relative to the target satellite, a Z axis of the orthogonal body coordinate system is determined; An initialization X axis of the orthogonal body coordinate system is obtained by taking the cross product of a satellite velocity vector of the target satellite and the Z axis; A reconstructed Y axis of the orthogonal body coordinate system is obtained by removing the projection of the target satellite on the Z axis and the X axis in the initialization Y axis of the orthogonal body coordinate system through the Gram-Schmidt method; The Y axis of the orthogonal body coordinate system is determined by unitizing and verifying the orthogonality of the reconstructed Y; Based on the Z axis and the Y axis of the orthogonal body coordinate system, the initialization X axis is reconstructed to obtain the X axis of the orthogonal body coordinate system, and the X axis, the Y axis, and the Z axis are integrated to obtain the orthogonal body coordinate system.

9. An electronic device, comprising: The electronic device includes a processor coupled with a memory, and the memory stores at least one computer program, which is loaded and executed by the processor to enable the electronic device to implement the method of any one of claims 1 to 5.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores at least one computer program, which is loaded and executed by the processor to enable the computer to implement the method of any one of claims 1 to 5.

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