Spacecraft relative position correction method based on single-star angle measurement information

Abstract

A spacecraft relative position correction method based on single star angle measurement information, the steps are as follows: (1) based on the initial orbit determination information, recursively calculate the target position of the space target in J2000 system; (2) calculate the estimated value of the relative position of the two stars in the VVLH coordinate system; (3) judge whether the relative position full component error correction condition is satisfied; if the correction condition is satisfied, execute step (4); otherwise, execute step (5); (4) based on the relative position estimate value and the spacecraft line-of-sight angle measurement value, calculate the Moore-Penrose inverse matrix of the first Jacobian matrix of the observation with respect to the relative position, and calculate the spacecraft and space target relative position correction value, complete the spacecraft relative position correction; (5) based on the relative position estimate value and the spacecraft line-of-sight angle measurement value, calculate the inverse matrix of the second Jacobian matrix of the observation with respect to the relative position, and calculate the spacecraft and space target relative position X-axis and Z-axis correction value, complete the spacecraft relative position correction.

Description

Technical Field

[0001] This invention relates to a spacecraft relative position correction method based on single-satellite angle measurement information, belonging to the field of angle-only relative navigation technology for space target observation missions. Background Technology

[0002] With the rapid increase in the number of spacecraft in orbit, the need for accurate measurement, cataloging, and prediction of space target orbits is becoming increasingly urgent. Ground-based observation equipment is limited by deployment area, making continuous and effective observation of space targets difficult. Furthermore, updating target orbits using dynamic recursion during non-observational segments can cause orbit determination errors to diverge. Therefore, it is necessary to utilize the probe payloads of space-based observation equipment to measure the relative state between spacecraft and targets and perform error correction to compensate for the shortcomings of ground-based observations.

[0003] Space-based observation equipment is typically located at a considerable distance from the target, and limitations in payload power and weight make relative distance measurement difficult. When the relative distance between the spacecraft and the target reaches hundreds of kilometers, the spacecraft can only obtain elevation and azimuth measurements using passive optical detection equipment. Since changes in the distance between the target and the spacecraft in the line-of-sight direction do not alter the elevation and azimuth measurements during single-satellite observation, the same set of angle observation data can correspond to countless target trajectories at different relative distances. This leads to a "distance ambiguity" problem in relative navigation algorithms based solely on angle measurement information. Consequently, when using linear relative motion models such as the CW equation for navigation calculations, the state estimation of relative position and relative velocity cannot converge stably, making it difficult to use the relative state between the spacecraft and the target for error correction. To address these issues, common methods include: constructing complex nonlinear relative motion models based on spherical or cylindrical coordinate systems to utilize orbital curvature characteristics to eliminate the "distance ambiguity" problem; and applying orbital maneuvering accelerations to the spacecraft that are not parallel to the line-of-sight pointing towards the target to ensure the system meets observability conditions.

[0004] However, these methods have significant limitations: First, for high-orbit spacecraft, at relative distances on the order of hundreds of kilometers, the curvature of the orbital arc between the spacecraft and the target is low. Even with complex relative motion equations, the nonlinear information they provide is extremely limited and insufficient to help the spacecraft distinguish changes in the line-of-sight angle at different distance scales. Second, for spacecraft not performing specific target observation missions, performing orbital maneuvers to achieve system visibility when encountering a target in the field of view will introduce additional fuel consumption and cause the spacecraft to deviate from its preset orbit. Finally, in high-speed flyby scenarios facing targets with different orbits, the rendezvous window time is insufficient to support the convergence of the filtering algorithm. Therefore, existing methods struggle to accurately calculate the relative positional relationship between the spacecraft and the space target, and cannot obtain accurate relative position correction results. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and provide a spacecraft relative position correction method based on single-satellite angular measurement information. This method utilizes the geometric relationship between the spacecraft and the orbit of a space target, and corrects the error in the relative position between the spacecraft and the space target through projection transformation between different coordinate systems. This solves the problem that existing methods struggle to accurately calculate the relative position relationship between the spacecraft and the space target using single-satellite angular measurement information, thus failing to obtain accurate relative position correction results.

[0006] The technical solution of this invention is: A method for correcting the relative position of a spacecraft based on single-satellite angle measurement information, comprising the following steps: (1) Based on the initial target orbit determination values ​​injected from the ground to the spacecraft, obtain the target position of the space target in the J2000 system. ;Execute step (2); (2) Obtain the spacecraft position in the J2000 series. Based on spacecraft position and target location Calculate the relative position of the spacecraft and the space target. ; relative position Transform to the target VVLH coordinate system to obtain the relative position estimate in the target VVLH coordinate system. ;Execute step (3); (3) Estimated relative position based on the target VVLH coordinate system And the difference in orbital inclination between the spacecraft and the space target. Determine whether the relative position full component error correction condition is met; if the relative position full component error correction condition is met, proceed to step (4); otherwise, proceed to step (6). (4) Using measuring equipment, obtain the spacecraft's line-of-sight angle measurement value; and the relative position estimate based on the target's VVLH coordinate system. Using the spacecraft's line-of-sight angle measurement, calculate the first Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. The Moore-Penrose inverse is used to obtain the first Jacobian Moore-Penrose inverse matrix. ;Execute step (5); (5) Based on the first Jacobian Moore-Penrose inverse matrix Calculate the correction value of the relative position between the spacecraft and the space target. The spacecraft's relative position is corrected, and the entire method is completed. (6) Using measuring equipment, obtain the spacecraft's line-of-sight angle measurement value; and the relative position estimate based on the target's VVLH coordinate system. Using the spacecraft's line-of-sight angle measurement, calculate the second Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. The inverse of the second Jacobian inverse matrix is ​​obtained. ; (7) Based on the second Jacobian inverse matrix Calculate the X-axis correction value for the relative position of the spacecraft and the space target. and Z-axis correction value The spacecraft's relative position is corrected, and the entire method is completed.

[0007] Furthermore, in step (1), the target position of the space target in the J2000 system is obtained. Specifically, based on the initial orbit determination values ​​of the spacecraft injected from the ground, the orbital dynamics of the space target are recursively calculated; based on the orbital recursion results, the target position of the space target in the J2000 system at the current moment is calculated. .

[0008] Furthermore, the initial target orbit determination values ​​are injected into the spacecraft by the ground-based orbit determination system; the orbital dynamics recursion takes into account the Earth's non-spherical perturbations. The second-order Runge-Kutta integral method for the term.

[0009] Furthermore, in step (2), the spacecraft's position in the J2000 system is obtained based on the spacecraft's GNSS integrated navigation orbit determination information. ; Relative positions of spacecraft and space targets The calculation formula is

[0010] Relative position estimate of the target in the VVLH coordinate system The calculation formula is

[0011] in, This is the rotation matrix from the J2000 system to the target VVLH system.

[0012] Furthermore, the specific steps for determining whether the relative position full component error correction condition is met in step (3) are as follows: (3.1) Based on the spacecraft's position in the J2000 series Calculate the distance between the spacecraft and the intersection of the two satellite orbits. The formula is

[0013] in, The spatial location of the intersection point between the orbital plane of the spacecraft and the orbit of the space target and the spacecraft's orbit, i.e., the intersection point of the orbits of the two satellites; (3.2) Estimated relative position based on the target VVLH coordinate system The distance between the spacecraft and the intersection of the two satellite orbits Calculate the decision value m The formula is

[0014] in, a It is the ratio of the orbit determination error in the target orbit plane to the orbit plane normal. This represents the relative distance between the spacecraft and the target at the current moment. (3.3) The difference between the decision value m and the orbital inclination angle Compare, if If the condition is met, then the relative position full component error correction condition is satisfied; otherwise, the relative position full component error correction condition is not satisfied.

[0015] Furthermore, in step (4), the first Jacobian Moore-Penrose inverse matrix is ​​obtained. The specific steps are as follows: (4.1) Solve for the first Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. Its expression is:

[0016] in, , and These are the X-axis, Y-axis, and Z-axis components representing the relative positions of the space target and the spacecraft within the spacecraft's own system. The rotation matrix from the target VVLH system to the spacecraft body; For the observation of the spacecraft's elevation angle, ; For azimuth observation of spacecraft, The spacecraft's core system is defined as: origin. Located at the spacecraft's center of mass, The axis points towards the space target. The axis is perpendicular to the orbital plane. The axis points towards the Earth. shaft and axis, The axes form a right-handed rectangular coordinate system; (4.2) Calculate the first Jacobian Moore-Penrose inverse matrix The calculation formula is:

[0017] in, This represents the current elevation angle measurement of the spacecraft. for transpose, for The inverse matrix; Rotation matrix from the target VVLH system to the spacecraft body system The column vector consisting of the elements in the third column , , for The elements in are represented as .

[0018] Furthermore, the relative position correction value between the spacecraft and the space target in step (5) The calculation formula is:

[0019] in, This represents the current elevation angle measurement of the spacecraft. This is the current azimuth angle measurement of the spacecraft; The rotation matrix from the target VVLH system to the spacecraft body; This represents the projection of the three-axis positions of the two satellites within the spacecraft's own system onto the measurement space.

[0020] Furthermore, in step (6), the second Jacobian inverse matrix is ​​obtained. The specific steps are as follows: (6.1) Solve for the second Jacobian matrix of the relative position of the target in the VVLH coordinate system. Its expression is:

[0021] in, , and These are the X-axis, Y-axis, and Z-axis components representing the relative positions of the space target and the spacecraft within the spacecraft's own system. The matrix formed by the first and third rows of the rotation matrix from the target VVLH system to the spacecraft body system; For the observation of the spacecraft's elevation angle, ; For azimuth observation of spacecraft, The spacecraft's core system is defined as: origin. Located at the spacecraft's center of mass, The axis points towards the space target. The axis is perpendicular to the orbital plane. The axis points towards the Earth. shaft and axis, The axes form a right-handed rectangular coordinate system; (6.2) Calculate the second Jacobian inverse matrix The calculation formula is:

[0022] in, This represents the current elevation angle measurement of the spacecraft. , , for The elements in are represented as , Rotation matrix from the target VVLH system to the spacecraft body system The column vector consisting of the elements in the third column x , y and z These are the estimated relative positions of the target in the VVLH coordinate system. The X-axis component, Y-axis component, and Z-axis component. .

[0023] Furthermore, the X-axis correction value of the relative position between the spacecraft and the space target in step (7) and Z-axis correction value The calculation formula is:

[0024] in, x and z These are the estimated relative positions of the target in the VVLH coordinate system. The X-axis and Z-axis components; This represents the current elevation angle measurement of the spacecraft. This is the current azimuth angle measurement of the spacecraft; This represents the projection of the three-axis positions of the two satellites within the spacecraft's own system onto the measurement space.

[0025] Secondly, the present invention also proposes a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the aforementioned spacecraft relative position correction method based on single-star angle measurement information.

[0026] The advantages of this invention compared to the prior art are: (1) This invention utilizes the geometric relationship between the spacecraft and the space target orbit, and corrects the error of the relative position between the spacecraft and the space target through projection transformation between different coordinate systems, thereby obtaining a unique relative position correction result, which effectively avoids the problem of non-convergence of state estimation results caused by the "distance ambiguity" of traditional filtering methods.

[0027] (2) The calculation process of the present invention is a geometric operation between the measurement space and the position space. Error correction can be completed in a single step, eliminating the need for multiple operation cycles and iterations to converge the error in the traditional filtering algorithm. Attached Figure Description

[0028] Figure 1 This is a flowchart of a spacecraft relative position correction method based on single-satellite angle measurement information according to the present invention. Figure 2 This is a schematic diagram of the orbital spatial relationship and coordinate system in a spacecraft relative position correction method based on single-satellite angle measurement information according to the present invention; Figure 3 This is a schematic diagram of the geometric relationship for error correction when the spacecraft relative position correction method based on single-star angle measurement information of the present invention satisfies the condition for full component error correction of relative position; Figure 4 This is a diagram illustrating the effect of error correction when the spacecraft relative position correction method based on single-star angle measurement information of the present invention satisfies the condition for full component error correction of relative position. Figure 5 This is a geometric diagram illustrating the error correction process when the spacecraft relative position correction method based on single-star angle measurement information does not meet the conditions for full component error correction of relative position. Figure 6 This diagram illustrates the effect of error correction when the spacecraft relative position correction method based on single-star angle measurement information does not meet the conditions for full component error correction of relative position. Detailed Implementation

[0029] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0030] like Figure 1 As shown, this invention provides a method for correcting the relative position of a spacecraft based on single-satellite angle measurement information, the steps of which are as follows: (1) Based on the initial target orbit determination values ​​injected from the ground to the spacecraft, obtain the target position of the space target in the J2000 system. ;Execute step (2); In step (1), the target position of the space target in the J2000 system is obtained. Specifically, based on the initial orbit determination values ​​of the spacecraft injected from the ground, the orbital dynamics of the space target are recursively calculated; based on the orbital recursion results, the target position of the space target in the J2000 system at the current moment is calculated. .

[0031] The initial target orbit determination values ​​are fed to the spacecraft by the ground-based orbit determination system; the orbital dynamics recursion takes into account the Earth's non-spherical perturbations. The second-order Runge-Kutta integral method for the term.

[0032] The spacecraft will use the target orbit information at the time of injection as the initial value. As the target star orbits the Earth, it is affected not only by Earth's gravity but also by various perturbations. Its equation of motion is as follows:

[0033] in, For the target in the J2000 series (defined as follows) Figure 2 The position vector shown below, The perturbation acceleration experienced by the target star includes perturbations from Earth's non-spherical shape, atmospheric drag, solar and lunar gravitational forces, and light pressure. Due to the limited computing power of onboard computers, generally only the terms of Earth's non-spherical perturbation are considered. The satellite perturbation equation at this point is:

[0034] in, .

[0035]

[0036] The perturbation equations of satellite motion are complex and nonlinear. The most common method for solving these equations is numerical integration. Considering the computational conditions on the satellite, a second-order Runge-Kutta method is adopted, and its algorithm is as follows:

[0037] Based on the above steps, Recursively calculating to the moment when the detection device acquires the target, we obtain .

[0038] The accuracy of ground-based orbit determination has the following characteristics: the accuracy of orbit determination for the position component within the target orbit plane is lower than the accuracy of orbit determination for the normal position component of the target orbit.

[0039] Based on the above characteristics of ground-based orbit determination, the initial error of the target orbit state can be expressed as:

[0040] in, , , The three-axis components of the initial trajectory error of the target measured on the ground in the target's VVLH coordinate system are respectively: Located within the target orbital plane ( axis, The orbit determination error in the axial direction is relative to the target orbital plane ( The multiple of the orbit determination error (axis direction), which is usually determined based on the characteristics of ground-based orbit determination error. .

[0041] Ignoring the effects of velocity error and perturbation factors, the variation law of relative position error in near-circular orbit, derived from on-board orbit recursion, is as follows:

[0042] in, The time span for performing orbit recursion on the satellite; The target orbital angular velocity.

[0043] At the current moment, the three-axis components of the initial position error of the algorithm satisfy the following relationship:

[0044] (2) Obtain the spacecraft position in the J2000 series. Based on spacecraft position and target location Calculate the relative position of the spacecraft and the space target. ; relative position Transform to the target VVLH coordinate system to obtain the relative position estimate in the target VVLH coordinate system. A schematic diagram of the relationships between the orbits is shown below. Figure 2 As shown; execute step (3); execute step (3); In step (2), the spacecraft's position in the J2000 system is obtained based on the spacecraft's GNSS integrated navigation orbit determination information. ; Relative positions of spacecraft and space targets The calculation formula is

[0045] Relative position estimate of the target in the VVLH coordinate system The calculation formula is

[0046] in, This is the rotation matrix from the J2000 system to the target VVLH system.

[0047] The target VVLH coordinate system is defined as: origin. Located at the spacecraft's center of mass, The axis points to the Earth's center. The axis is perpendicular to the orbital plane. The axis points in the direction of the spacecraft's flight. shaft and shaft and The axes form a right-handed rectangular coordinate system.

[0048] (3) Estimated relative position based on the target VVLH coordinate system And the difference in orbital inclination between the spacecraft and the space target. Determine whether the relative position full component error correction condition is met; if the relative position full component error correction condition is met, proceed to step (4); otherwise, proceed to step (6). The specific steps for determining whether the relative position full component error correction condition is met in step (3) are as follows: (3.1) Based on the spacecraft's position in the J2000 series Calculate the distance between the spacecraft and the intersection of the two satellite orbits. The formula is

[0049] in, The spatial location of the intersection point between the orbital plane of the spacecraft and the orbit of the space target and the spacecraft's orbit, i.e., the intersection point of the orbits of the two satellites; (3.2) Estimated relative position based on the target VVLH coordinate system The distance between the spacecraft and the intersection of the two satellite orbits Calculate the decision value m The formula is

[0050] in, a It is the ratio of the orbit determination error in the target orbit plane to the orbit plane normal. This represents the relative distance between the spacecraft and the target at the current moment. (3.3) The difference between the decision value m and the orbital inclination angle Compare, if If the condition is met, then the relative position full component error correction condition is satisfied; otherwise, the relative position full component error correction condition is not satisfied.

[0051] (4) Using measuring equipment, obtain the spacecraft's line-of-sight angle measurement value; and the relative position estimate based on the target's VVLH coordinate system. Using the spacecraft's line-of-sight angle measurement, calculate the first Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. The Moore-Penrose inverse is used to obtain the first Jacobian Moore-Penrose inverse matrix. ;Execute step (5); In step (4), the first Jacobian Moore-Penrose inverse matrix is ​​obtained. The specific steps are as follows: (4.1) Solve for the first Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. Its expression is:

[0052] in, , and These are the X-axis, Y-axis, and Z-axis components representing the relative positions of the space target and the spacecraft within the spacecraft's own system. The rotation matrix from the target VVLH system to the spacecraft body; For the observation of the spacecraft's elevation angle, ; For azimuth observation of spacecraft, The spacecraft's core system is defined as: origin. Located at the spacecraft's center of mass, The axis points towards the space target. The axis is perpendicular to the orbital plane. The axis points towards the Earth. shaft and axis, The axes form a right-handed rectangular coordinate system; The elevation angle of a space target is the angle between the line connecting the space target and the spacecraft and the XOY plane of the spacecraft's own system; the azimuth angle of a space target is the angle between the projection of the space target's line of sight onto the XOY plane of the spacecraft's own system and the X-axis. (4.2) Calculate the first Jacobian Moore-Penrose inverse matrix The calculation formula is:

[0053] in, This represents the current elevation angle measurement of the spacecraft. for transpose, for The inverse matrix; Rotation matrix from the target VVLH system to the spacecraft body system The column vector consisting of the elements in the third column , , for The elements in are represented as .

[0054] (5) Based on the first Jacobian Moore-Penrose inverse matrix Calculate the correction value of the relative position between the spacecraft and the space target. Once the relative position of the spacecraft is corrected, the entire method is complete; at this point, the geometric relationship diagram of the error correction is as follows: Figure 3 As shown, the correction results are as follows: Figure 4 As shown; The relative position correction value between the spacecraft and the space target in step (5) The calculation formula is:

[0055] in, This represents the current elevation angle measurement of the spacecraft. This is the current azimuth angle measurement of the spacecraft; The rotation matrix from the target VVLH system to the spacecraft body; This represents the projection of the three-axis positions of the two satellites within the spacecraft's own system onto the measurement space. The projection method is as follows: for a three-dimensional space vector ,have .

[0056] (6) Using measuring equipment, obtain the spacecraft's line-of-sight angle measurement value; and the relative position estimate based on the target's VVLH coordinate system. Using the spacecraft's line-of-sight angle measurement, calculate the second Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. The inverse of the second Jacobian inverse matrix is ​​obtained. ; In step (6), the second Jacobian inverse matrix is ​​obtained. The specific steps are as follows: (6.1) Solve for the second Jacobian matrix of the relative position of the target in the VVLH coordinate system. Its expression is:

[0057] in, , and These are the X-axis, Y-axis, and Z-axis components representing the relative positions of the space target and the spacecraft within the spacecraft's own system. The matrix formed by the first and third rows of the rotation matrix from the target VVLH system to the spacecraft body system; For the observation of the spacecraft's elevation angle, ; For azimuth observation of spacecraft, The spacecraft's core system is defined as: origin. Located at the spacecraft's center of mass, The axis points towards the space target. The axis is perpendicular to the orbital plane. The axis points towards the Earth. shaft and axis, The axes form a right-handed rectangular coordinate system; (6.2) Calculate the second Jacobian inverse matrix The calculation formula is:

[0058] in, This represents the current elevation angle measurement of the spacecraft. , , for The elements in are represented as , Rotation matrix from the target VVLH system to the spacecraft body system The column vector consisting of the elements in the third column x , y and z These are the estimated relative positions of the target in the VVLH coordinate system. The X-axis component, Y-axis component, and Z-axis component. .

[0059] (7) Based on the second Jacobian inverse matrix Calculate the X-axis correction value for the relative position of the spacecraft and the space target. and Z-axis correction value Once the relative position of the spacecraft is corrected, the entire method is complete; at this point, the geometric relationship diagram of the error correction is as follows: Figure 5 As shown, the correction results are as follows: Figure 6 As shown; The X-axis correction value of the relative position between the spacecraft and the space target in step (7) and Z-axis correction value The calculation formula is:

[0060] in, x and z These are the estimated relative positions of the target in the VVLH coordinate system. The X-axis and Z-axis components; This represents the current elevation angle measurement of the spacecraft. This is the current azimuth angle measurement of the spacecraft; This represents the projection of the three-axis positions of the two satellites within the spacecraft's own system onto the measurement space.

[0061] Through the above process, this invention utilizes the geometric relationship between the spacecraft and the space target's orbit, and corrects the error in the relative position between the spacecraft and the space target through projection transformation between different coordinate systems, thereby obtaining a unique relative position correction result. This effectively avoids the problem of non-convergence of state estimation results caused by "distance ambiguity" in traditional filtering methods. In addition, the calculation process of this invention is a geometric operation between the measurement space and the position space, which can complete the error correction in a single step, eliminating the need for multiple operation cycles and iterative process steps for error convergence required by traditional filtering algorithms.

[0062] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A method for correcting the relative position of a spacecraft based on single-satellite angular measurement information, characterized in that... The steps are as follows: (1) Based on the initial target orbit determination values ​​injected from the ground to the spacecraft, obtain the target position of the space target in the J2000 system. ;Execute step (2); (2) Obtain the spacecraft position in the J2000 series. Based on spacecraft position and target location Calculate the relative position of the spacecraft and the space target. ; relative position Transform to the target VVLH coordinate system to obtain the relative position estimate in the target VVLH coordinate system. ;Execute step (3); (3) Estimated relative position based on the target VVLH coordinate system And the difference in orbital inclination between the spacecraft and the space target. Determine whether the relative position full component error correction condition is met; if the relative position full component error correction condition is met, proceed to step (4); otherwise, proceed to step (6). (4) Using measuring equipment, obtain the spacecraft's line-of-sight angle measurement value; and the relative position estimate based on the target's VVLH coordinate system. Using the spacecraft's line-of-sight angle measurement, calculate the first Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. The Moore-Penrose inverse is used to obtain the first Jacobian Moore-Penrose inverse matrix. ;Execute step (5); (5) Based on the first Jacobian Moore-Penrose inverse matrix Calculate the correction value of the relative position between the spacecraft and the space target. The spacecraft's relative position is corrected, and the entire method is completed. (6) Using measuring equipment, obtain the spacecraft's line-of-sight angle measurement value; and the relative position estimate based on the target's VVLH coordinate system. Using the spacecraft's line-of-sight angle measurement, calculate the second Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system, representing the relative position of the spacecraft and the space target. The inverse of the second Jacobian inverse matrix is ​​obtained. ; (7) Based on the second Jacobian inverse matrix Calculate the X-axis correction value for the relative position of the spacecraft and the space target. and Z-axis correction value The spacecraft's relative position is corrected, and the entire method is completed.

2. The spacecraft relative position correction method based on single-satellite angle measurement information according to claim 1, characterized in that: In step (1), the target position of the space target in the J2000 system is obtained. Specifically, based on the initial orbit determination values ​​of the spacecraft injected from the ground, the orbital dynamics of the space target are recursively calculated; based on the orbital recursion results, the target position of the space target in the J2000 system at the current moment is calculated. .

3. The spacecraft relative position correction method based on single-satellite angle measurement information according to claim 2, characterized in that: The initial target orbit determination values ​​are fed to the spacecraft by the ground-based orbit determination system; the orbital dynamics recursion takes into account the Earth's non-spherical perturbations. The second-order Runge-Kutta integral method for the term.

4. The spacecraft relative position correction method based on single-satellite angle measurement information according to claim 1, characterized in that: In step (2), the spacecraft's position in the J2000 system is obtained based on the spacecraft's GNSS integrated navigation orbit determination information. ; Relative positions of spacecraft and space targets The calculation formula is Relative position estimate of the target in the VVLH coordinate system The calculation formula is in, This is the rotation matrix from the J2000 system to the target VVLH system.

5. The spacecraft relative position correction method based on single-satellite angle measurement information according to claim 1, characterized in that: The specific steps for determining whether the relative position full component error correction condition is met in step (3) are as follows: (3.1) Based on the spacecraft's position in the J2000 series Calculate the distance between the spacecraft and the intersection of the two satellite orbits. The formula is in, The spatial location of the intersection point between the orbital plane of the spacecraft and the orbit of the space target and the spacecraft's orbit, i.e., the intersection point of the orbits of the two satellites; (3.2) Estimated relative position based on the target VVLH coordinate system The distance between the spacecraft and the intersection of the two satellite orbits Calculate the decision value m The formula is in, a It is the ratio of the orbit determination error in the target orbit plane to the orbit plane normal. This represents the relative distance between the spacecraft and the target at the current moment. (3.3) The difference between the decision value m and the orbital inclination angle Compare, if If the condition is met, then the relative position full component error correction condition is satisfied; otherwise, the relative position full component error correction condition is not satisfied.

6. The spacecraft relative position correction method based on single-satellite angle measurement information according to claim 1, characterized in that: In step (4), the first Jacobian Moore-Penrose inverse matrix is ​​obtained. The specific steps are as follows: (4.1) Solve for the first Jacobian matrix of the spacecraft's line-of-sight angle observation relative to the target's VVLH coordinate system to determine the relative position of the spacecraft and the space target. Its expression is: in, , and These are the X-axis, Y-axis, and Z-axis components representing the relative positions of the space target and the spacecraft within the spacecraft's own system. The rotation matrix from the target VVLH system to the spacecraft body; For the observation of the spacecraft's elevation angle, ; For azimuth observation of spacecraft, The spacecraft's core system is defined as: origin. Located at the spacecraft's center of mass, The axis points towards the space target. The axis is perpendicular to the orbital plane. The axis points towards the Earth. shaft and axis, The axes form a right-handed rectangular coordinate system; (4.2) Calculate the first Jacobian Moore-Penrose inverse matrix The calculation formula is: in, This represents the current elevation angle measurement of the spacecraft. for transpose, for The inverse matrix; Rotation matrix from the target VVLH system to the spacecraft body system The column vector consisting of the elements in the third column , , for The elements in are represented as .

7. The spacecraft relative position correction method based on single-satellite angle measurement information according to claim 1, characterized in that: The relative position correction value between the spacecraft and the space target in step (5) The calculation formula is: in, This represents the current elevation angle measurement of the spacecraft. This is the current azimuth angle measurement of the spacecraft; The rotation matrix from the target VVLH system to the spacecraft body; This represents the projection of the three-axis positions of the two satellites within the spacecraft's own system onto the measurement space.

8. The spacecraft relative position correction method based on single-satellite angle measurement information according to claim 1, characterized in that: In step (6), the second Jacobian inverse matrix is ​​obtained. The specific steps are as follows: (6.1) Solve for the second Jacobian matrix of the relative position of the target in the VVLH coordinate system. Its expression is: in, , and These are the X-axis, Y-axis, and Z-axis components representing the relative positions of the space target and the spacecraft within the spacecraft's own system. The matrix formed by the first and third rows of the rotation matrix from the target VVLH system to the spacecraft body system; For the observation of the spacecraft's elevation angle, ; For azimuth observation of spacecraft, The spacecraft's core system is defined as: origin. Located at the spacecraft's center of mass, The axis points towards the space target. The axis is perpendicular to the orbital plane. The axis points towards the Earth. shaft and axis, The axes form a right-handed rectangular coordinate system; (6.2) Calculate the second Jacobian inverse matrix The calculation formula is: in, This represents the current elevation angle measurement of the spacecraft. , , for The elements in are represented as , Rotation matrix from the target VVLH system to the spacecraft body system The column vector consisting of the elements in the third column x , y and z These are the estimated relative positions of the target in the VVLH coordinate system. The X-axis component, Y-axis component, and Z-axis component. .

9. A spacecraft relative position correction method based on single-satellite angular measurement information according to claim 1, characterized in that: The X-axis correction value of the relative position between the spacecraft and the space target in step (7) and Z-axis correction value The calculation formula is: in, x and z These are the estimated relative positions of the target in the VVLH coordinate system. The X-axis and Z-axis components; This represents the current elevation angle measurement of the spacecraft. This is the current azimuth angle measurement of the spacecraft; This represents the projection of the three-axis positions of the two satellites within the spacecraft's own system onto the measurement space.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the steps of the spacecraft relative position correction method based on single-star angle measurement information as described in any one of claims 1 to 9.

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