A method for associating and orbiting space targets based on dual-star optical observation results

Abstract

This invention discloses a method for associating and orbiting space targets based on binary star optical observations. The method includes: acquiring the observation vectors of a certain space target from the respective fields of view of two observation stars; calculating the shortest distance between the observation vectors; if this distance is consistently less than a threshold over a time series, it is determined that the two observation stars are observing the same space target; calculating the midpoint of the common perpendicular line between the two observation vectors of the same space target as the orbit determination point; and determining the orbit of the space target based on the sequence of orbit determination points. This invention employs a low-cost space-based optical orbit determination method, completes space target association through a computationally inexpensive algorithm, and determines target consistency based on distance constraints between observation vectors. It requires no complex models or large amounts of computing power and can still process data efficiently even with a large number of targets and a large amount of data, demonstrating significant cost and efficiency advantages.

Description

Technical Field

[0001] This invention relates to the field of space target identification and orbit determination technology, and in particular to a method for associating and determining the orbit of space targets based on the results of binary star optical observations. Background Technology

[0002] With the rapid development of aerospace technology, the number of space targets in Earth orbit is constantly increasing, placing higher demands on spacecraft orbit determination and control. Lowering the cost of this technology is therefore essential for the development of commercial aerospace. Space-based optical orbit determination technology, with its unique observation mechanism, has shown great potential in the field of satellite orbit measurement. This technology uses a spaceborne optical camera to image and observe target satellites, and then uses the characteristic information in the optical images to retrieve the target's orbital parameters. Compared to traditional radio observation techniques, it has advantages such as low cost, low energy consumption, no need for active signal transmission, and immunity to atmospheric effects. It is particularly suitable for the observation and orbit determination of low-contrast targets such as microsatellites and space debris.

[0003] Optical orbit determination techniques are mainly divided into two categories: single-eye optical orbit determination and two-eye optical orbit determination. Single-eye optical orbit determination requires only one observation satellite. Based on a continuous sequence of target observations and the known position and attitude of the observation satellite, the target's orbit is calculated using constraints from a perturbation model of the target. Two-eye optical orbit determination uses cameras from two observation satellites. By combining the pose information of each observation satellite, the target's position can be calculated using two images acquired simultaneously. For example, the academic article "Space-based Dual-Satellite Stereoscopic Astronomical Positioning of Space Targets" (doi: 10.37188 / OPE.20212912.2902) calculates the target's three-dimensional position information from two images captured simultaneously based on the direction-finding cross-positioning principle and the least squares method.

[0004] Optical positioning also requires the association and tracking of space targets, a process that can also be achieved based on the principle of binary satellite orbit determination. For example, the academic article "A Space-Based Passive Cooperative Multi-Target Initial Orbit Determination Method in Complex Environments" (DOI:10.12305 / j.issn.1001-506X.2025.05.03) constructs a cost matrix based on the distance between the LOS vectors of multiple targets observed by two observation satellites simultaneously, and calculates the association between targets using the Hungarian optimal allocation algorithm.

[0005] However, existing methods suffer from the following problems: First, they have high computational complexity, especially when there are many targets and a large amount of observation data. Existing orbit determination algorithms may face the problem of low computational efficiency, making it difficult to meet real-time requirements. Second, observation errors have a significant impact. Since observation data inevitably contains noise and errors, these errors will propagate to the orbit determination results, affecting the accuracy of orbit determination. Third, they lack environmental adaptability. Factors such as changes in illumination and occlusion in complex space environments may lead to a decline in the quality of observation data, thereby affecting the stability and accuracy of orbit determination. Therefore, it is necessary to propose a more efficient, accurate, and adaptable optical orbit determination method to address the problems existing in current methods.

[0006] Therefore, a novel space-based passive collaborative multi-target initial orbit determination method is needed in complex environments. This method aims to significantly reduce computational complexity, improve the efficiency of processing large amounts of observation data, and ensure that real-time requirements are met. Summary of the Invention

[0007] To address the aforementioned problems, the present invention aims to provide a method for correlating and orbiting space targets based on binary star optical observation results, thereby improving the efficiency and accuracy of optical orbit determination for space targets.

[0008] The first aspect: a method for correlating and determining the orbit of space targets based on binary star optical observations, including:

[0009] Obtain the observation vectors of a certain space target in the field of view of each of the two observation satellites, calculate the shortest distance between the observation vectors, and if the distance is always less than the threshold within a certain time series, it is determined that the two observation satellites are observing the same space target.

[0010] In one embodiment of the present invention, the method further includes: when it is determined that the two observation satellites are observing the same space target, calculating the midpoint of the common perpendicular line of the two observation vectors of the two observation satellites to the same space target as the orbit determination point.

[0011] In one embodiment of the present invention, the parametric equation of the observation vector is:

[0012]

[0013] in, The position coordinates of the observed star, To determine the right ascension of the observation vector, The declination of the observed vector.

[0014] In one embodiment of the present invention, the right ascension and declination The acquisition process includes: obtaining the position information of the observed satellite using GNSS positioning or ground observation stations; determining the attitude information of the observed satellite based on starlight positioning; and combining the installation matrix of the observed satellite's camera, the imaging equation, and the position of the observed satellite relative to the space target in the image to obtain the right ascension of the line of sight from the observed satellite to the space target. and declination .

[0015] In one embodiment of the present invention, the shortest distance between the observation vectors is expressed as:

[0016]

[0017] in, , Let be the position coordinate vectors of the two observed stars. , It is the unit direction vector of the observation vectors of the two observation stars.

[0018] In one embodiment of the present invention, the coordinate vector expression of the midpoint of the common perpendicular of the two observation vectors is:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] in, and The common perpendicular and the two observation vectors and The coordinate vector of the intersection point, and For parameters.

[0025] In one embodiment of the present invention, the orbit determination includes: based on the orbit determination point estimation sequence obtained from binary star observations, determining the initial orbit using the two-point Lambert method, and then combining the perturbed motion model with the least squares method to optimize the data of the entire observation arc segment to achieve orbit determination of the space target.

[0026] In one embodiment of the present invention, the threshold is related to the distance between the space target and the observed star, and the threshold is no greater than 10 km.

[0027] Second aspect: An electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, performs the steps of the method provided in the first aspect.

[0028] Third aspect: A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method provided in the first aspect.

[0029] The beneficial effects of this invention are:

[0030] 1. This invention adopts a low-cost space-based optical orbit determination method, completes the association of space targets through a low-cost algorithm, and judges the consistency of targets based on the distance constraints between observation vectors. It does not require complex models or a lot of computing power, and can still process efficiently when there are many targets and a large amount of data. It has significant advantages in cost and efficiency.

[0031] 2. This invention utilizes a single-moment image of two stars to estimate the target position by observing the midpoint of the common perpendicular of the vectors. Based on images from two moments and combined with two-body model constraints, the initial orbit of the target is quickly determined using the Lambert orbit of two points. Then, by using an image of an observation arc segment, a perturbed motion model (such as J2 term perturbation) is introduced, and the orbit is optimized using the least squares method. This achieves a closed-loop process from association to positioning, initial orbit, and fine orbit, significantly improving work efficiency.

[0032] 3. By integrating observation vector distance constraints with the perturbation motion model, this invention can still filter noise and correct deviations by relying on multiple constraints even in complex spatial environments where changes in illumination and occlusion cause fluctuations in the quality of observation data, thus ensuring the stability and accuracy of target association and orbit determination, and broadening the applicable scenarios of the method. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating the method for correlating and determining the orbit of space targets based on binary star optical observations according to the present invention.

[0034] Figure 2 This is a schematic diagram of binary star optical observation using the method of the present invention;

[0035] Figure 3 This is a schematic diagram of the correlation and orbit determination system structure of the present invention;

[0036] Figure 4 This is a schematic diagram of the structure of the electronic device of the present invention. Detailed Implementation

[0037] Embodiments of the present invention are described in detail below. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar symbols denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0038] Existing space-based dual-satellite optical orbit determination methods have the following drawbacks: First, they have high computational complexity, and when there are many targets and a large amount of data, the orbit determination algorithm is inefficient and it is difficult to meet real-time requirements. Second, observation errors have a significant impact, and data noise and errors will propagate to the orbit determination results, reducing accuracy. Third, they are not very adaptable to the environment. Changes in illumination and occlusion in complex space environments can lead to a decline in data quality, affecting the stability and accuracy of orbit determination.

[0039] To address the aforementioned problems, this invention provides a method for correlating and determining the orbit of space targets based on binary star optical observations. Figure 1 This is a flowchart illustrating the orbit determination method provided in an embodiment of the present invention. The method includes:

[0040] First, obtain the observation vector of a certain space target in the field of view of each of the two observation stars.

[0041] The observation satellite obtains its own orbital position information through GNSS positioning or orbit determination results from ground observation stations. Then, it determines its own attitude information through starlight positioning. Combining the camera mounting matrix, imaging equation, and the position of the observation satellite relative to the space target in the image, the right ascension of the line of sight from the observation satellite to the space target can be obtained. and declination .

[0042] Based on the position coordinates and right ascension of the observed star and declination Calculate the parametric equations of the observed vectors.

[0043] For example: The position coordinates of the observed star in the J2000 celestial coordinate system are: The right ascension of the observed vector is Declination is The parametric equation of the observed vector is:

[0044]

[0045] Then, calculate the shortest distance between the observed vectors.

[0046] Let the position coordinates of the observed star be respectively , The unit direction vectors of the two observation vectors are , .

[0047] The expression for calculating the shortest distance between two lines is:

[0048]

[0049] Then, based on the shortest distance obtained, if the distance is always less than the threshold within a certain time series, it is determined that the two observation stars are observing the same space target.

[0050] For example, if the distance between the observed vectors during the observation period is consistently less than a given threshold of 5 kilometers, then it is considered that the two observed satellites are observing the same space target.

[0051] The selection of the threshold is related to the distance between the space target and the observed satellite, and takes into account factors such as observation error, target motion characteristics, and the accuracy of the observation equipment. In practical applications, the threshold is often determined through extensive experimental data and statistical analysis to ensure the accuracy of the correlation. An excessively high threshold may lead to false correlations, that is, misidentifying different space targets as the same target; while an excessively low threshold may lead to false correlations, that is, failing to correctly correlate data of the same space target under different observations. The threshold is generally selected to be no greater than 10 km.

[0052] The above method enables the correlation of two observation satellites with the same space target, thus providing an accurate data foundation for subsequent space target orbit determination. This method not only improves the accuracy of space target correlation but also effectively reduces the risk of false and missed correlations. In practical applications, combined with advanced observation equipment and data processing technologies, it can achieve efficient and accurate observation and tracking of space targets. Furthermore, this method has good adaptability and scalability, and can be widely applied to different types of space target observation missions, providing strong technical support for space science research, spacecraft navigation and positioning, and other fields.

[0053] If two observation satellites are successfully associated with a space target in time observations, the midpoint of the common perpendicular of the two observation vectors is calculated. This midpoint is the closest point to the two observation vectors and is used as the orbit determination point.

[0054] Common perpendicular and two observation vectors and The parametric equations for the intersection point coordinates are as follows:

[0055]

[0056]

[0057] Parameters in the formula and They are respectively:

[0058]

[0059]

[0060] When two observed vectors are parallel, there is no unique common perpendicular between the two parallel lines. In this case, the above expression is meaningless, but this situation is unlikely to occur in real-world scenarios.

[0061] The coordinate expression of the midpoint of the common perpendicular is:

[0062]

[0063] Using the midpoint of the common perpendicular as the orbit determination point, a spatial target position estimation sequence is formed over a time series. Then, based on the estimation sequence, the initial orbit is determined using the two-point Lambert method. Finally, combined with the perturbed motion model, the data of the entire observation arc is optimized using the least squares method to achieve orbit determination of the spatial target.

[0064] The initial orbit of a space target is achieved using the two-point Lambert orbit method. The Lambert orbit is a classic method that uses two known position points and corresponding times to solve for the transfer orbit between two points. It is suitable for quickly obtaining the initial orbital parameters of the target (such as semi-major axis, orbital inclination, etc.).

[0065] For the entire observation arc (i.e., continuous observation data over a period of time), the "least squares method" is used to optimize the target's position and velocity information. The least squares method refines the orbital parameters by minimizing the sum of squared errors between the observed values ​​and the model predictions, reducing the impact of observation errors and improving orbital accuracy.

[0066] Therefore, this invention fully considers various constraints, as shown in Table 1:

[0067] Table 1. Constraints for Space Target Orbit Determination

[0068]

[0069] The entire process incorporates the influence of the perturbation model of the space target, that is, it takes into account the influence of perturbation factors such as the non-spherical nature of the Earth's gravitational field (such as the J2 term) and the gravitational forces of other celestial bodies on the target's motion, so that the orbit calculation is more in line with the actual motion law, rather than being based solely on the ideal two-body model.

[0070] The orbit determination method of this invention realizes the complete logic from initial positioning to precise orbit determination, taking into account both computational efficiency and accuracy requirements.

[0071] Example 1:

[0072] Based on the aforementioned publicly disclosed method for correlating and determining the orbit of space targets using binary star optical observations, such as... Figure 2As shown, taking the optical observation correlation of a single spatial target point with two observation satellites as an example, it includes:

[0073] At a certain moment: the J2000 coordinates (unit: meters, the same below) of observed star 1 are 6878140.0X, 0.001Y, -1.526Z, the right ascension of the observed vector is 108.511°, and the declination is 7.170°;

[0074] The coordinates of the observation satellite 2 (J2000) are 3501030.112X, 5639509.799Y, 1802089.688Z, and the right ascension and declination of the observation vector are -33.743° and -27.951°.

[0075] Using the method of this invention, the coordinates of the space target J2000 were calculated to be 5418956.639X, 4358316.172Y, and 578202.584Z.

[0076] The true J2000 coordinates of the observed space target are 5418986.653X, 4358292.793Y, and 578191.535Z.

[0077] The error between the calculated coordinates of the spatial target and the actual coordinates is about 40 meters. Considering the rounding error in the parameters of the input algorithm, especially right ascension and declination, the positioning accuracy of the method of this invention is effective.

[0078] Example 2:

[0079] Based on the aforementioned publicly disclosed method for correlating and determining the orbit of space targets using binary star optical observations, taking the determination of the initial orbit using two orbit determination points as an example, the method includes:

[0080] Based on Example 1, after 60 seconds:

[0081] The position of observation star 1 changes to 6862958.709X, 380602.363Y, 251913.122Z, the right ascension of the observation vector changes to 111.942°, and the declination changes to 6.668°;

[0082] The position of observation star 2 changes to 3187982.948X, 5711627.713Y, 2126655.383Z, the right ascension of the observation vector changes to -28.514°, and the declination changes to -30.994°.

[0083] The new positions of the observed space target calculated according to the method of the present invention are 5143286.682X, 4649368.067Y, and 789930.073Z.

[0084] Using the Lambert orbital formula, the initial velocity of the observed space target is calculated to be -4406.964X, 5007.712Y, and 3551.632Z.

[0085] The actual velocities of the observed space target at the initial moment are -4407.116X, 5008.531Y, and 3551.514Z.

[0086] The calculated value is close to the actual result. After converting it to the six orbital elements, the satellite's semi-major axis is 6,977,061.798 meters, which is about 1,000 meters off from the actual value of 6,978,140 meters. This meets the accuracy expectation of Lambert's orbital design.

[0087] As illustrated in Examples 1 and 2, the method of the present invention can not only effectively correlate observation results of the same space target from different observation stations, but also accurately calculate the orbital parameters of the space target. In practical applications, this method demonstrates high accuracy and stability, especially when processing complex observation data, where its advantages are even more pronounced. Furthermore, the method of the present invention also features high computational efficiency and strong adaptability, making it suitable for various types of space target observation and orbit determination missions. Therefore, the method of the present invention has broad application prospects in fields such as space target monitoring and spacecraft tracking.

[0088] Furthermore, this invention also discloses a system for correlating and determining the orbit of space targets based on binary star optical observations, such as... Figure 3 As shown, the system includes: an observation data acquisition module, a space target association module, a target position estimation module, and a trajectory determination and refinement module, among which:

[0089] The observation data acquisition module is used to collect synchronous optical observation data from the two observation stars, including the position and attitude information of the observation stars themselves, as well as the position information of the target in the image.

[0090] The observed satellite obtains its position coordinates in the J2000 celestial coordinate system through GNSS positioning or orbit determination results from ground observation stations.

[0091] ,

[0092] By determining its own attitude information through starlight positioning, and combining this with the camera mounting matrix and imaging equation, the target's right ascension is extracted from the image. Declination is This generates an observation vector pointing to the space target.

[0093] ,

[0094] The space target association module is used to determine whether the target observed by two observation satellites is the same space target. The core basis is whether the shortest distance between the observation vectors meets the threshold condition.

[0095] Specific process: Calculate the shortest distance d between the two observed vectors, and determine whether the two vectors are parallel. or Using different formulas:

[0096]

[0097] If the distance d within the statistical observation time series is always less than a set threshold (such as 5 kilometers), it is determined to be the same target.

[0098] The target position estimation module is used to calculate the position estimate of the spatial target after successful association, using the midpoint of the common perpendicular of the two observation vectors as the position reference.

[0099] Solve for the parameters of the intersection point of the common perpendicular and the two vectors. and Based on the observed star position and vector direction, parameters are calculated using formulas. and The coordinates of the midpoint of the common perpendicular are:

[0100]

[0101] A target position estimation sequence is formed based on the midpoint of the common perpendicular.

[0102] The orbit determination and refinement module calculates and optimizes the orbit of the space target based on the position estimation sequence, and is divided into two stages: initial orbit determination and orbit optimization.

[0103] Initial trajectory determination: Using the two-point Lambert trajectory method, based on the position estimates at two time points, the initial trajectory parameters of the target (such as semi-major axis, velocity, etc.) are solved.

[0104] Orbit optimization: For the position sequence of the entire observation arc segment, combined with the perturbation motion model of the space target (considering perturbation factors such as J2), the least squares method is used to optimize the position and velocity information of the target and refine the orbit results.

[0105] This system coordinates various modules in the order of observation data acquisition, target association, position estimation, and trajectory determination and refinement. It achieves target association through observation vector distance constraints, constructs position sequences using the midpoint of the common perpendicular, and finally outputs a high-precision trajectory by combining the perturbation model and optimization algorithm. It fully covers the entire process of space target association and orbit determination, and has the characteristics of low cost and low computational complexity.

[0106] The present invention also provides an electronic device, Figure 4This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention, such as... Figure 4 As shown, the electronic device may include a processor, a communications interface, memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions from the memory, for example, to execute the following method:

[0107] Obtain the observation vectors of a certain space target in the field of view of each of the two observation satellites, calculate the shortest distance between the observation vectors, and if the distance is always less than the threshold within a certain time series, it is determined that the two observation satellites are observing the same space target.

[0108] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0109] This invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, is implemented to perform the methods provided in the above embodiments, including, for example:

[0110] Obtain the observation vectors of a certain space target in the field of view of each of the two observation satellites, calculate the shortest distance between the observation vectors, and if the distance is always less than the threshold within a certain time series, it is determined that the two observation satellites are observing the same space target.

[0111] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0112] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for correlating and determining the orbit of space targets based on binary star optical observations, characterized in that, include: Obtain the observation vector of a certain space target in the field of view of each of the two observation satellites, calculate the shortest distance between the observation vectors, and if the distance is always less than the threshold within a certain time series, it is determined that the two observation satellites are observing the same space target. When it is determined that two observation satellites are observing the same space target, the midpoint of the common perpendicular line of the two observation vectors of the two observation satellites to the same space target is calculated as the orbit determination point. The parametric equation of the observed vector is: in, The position coordinates of the observed star, To determine the right ascension of the observation vector, The declination of the observed vector; The right ascension and declination Acquisition includes: The position information of the observed satellite is obtained using GNSS positioning or observation from a ground observation station. The attitude information of the observed satellite is determined based on starlight positioning. Combined with the installation matrix of the observed satellite's camera, the imaging equation, and the position of the observed satellite relative to the space target in the image, the right ascension of the line of sight from the observed satellite to the space target is obtained. and declination ; The shortest distance between the observed vectors is expressed as: in, , Let be the position coordinate vectors of the two observed stars. , This is the unit direction vector of the observation vectors of the two observation stars; The coordinate vector expression for the midpoint of the common perpendicular of the two observation vectors is: in, and The common perpendicular and the two observation vectors and The coordinate vector of the intersection point, and For parameters; The orbit determination includes: Based on the orbit determination point estimation sequence obtained from binary star observations, the initial orbit is determined by the two-point Lambert method. Then, combined with the perturbed motion model, the data of the entire observation arc is optimized using the least squares method to achieve orbit determination of the space target.

2. The method according to claim 1, characterized in that, The threshold is related to the distance between the space target and the observed star, and the threshold is no greater than 10 km.

3. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 2.

4. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 2.

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