A data processing method of a track arc segment

Abstract

The application provides a data processing method for track arc segments, which comprises the following steps: obtaining initial track elements of two track arc segments; constructing a geocentric coordinate system and a selenocentric coordinate system, and converting the initial track elements into target position vectors in the geocentric coordinate system and the selenocentric coordinate system respectively; determining target semi-radii corresponding to the first arc segment in the geocentric coordinate system and the selenocentric coordinate system respectively according to the target position vectors; determining target velocity vectors corresponding to the first arc segment according to the target semi-radii and the target position vectors, and determining second track elements corresponding to the first arc segment in the geocentric coordinate system and the selenocentric coordinate system respectively; updating the second track elements by using a pre-constructed observation equation; determining target track elements from the updated second track elements in the geocentric coordinate system and the selenocentric coordinate system, and outputting the correlation results of the two track arc segments. According to the application, the accuracy of the correlation determination of the track arc segments can be improved.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to data processing methods, devices, equipment, and media for orbital arc segments. Background Technology

[0002] With the rapid development of aerospace technology, the Earth-Moon space has become one of the important targets of space exploration.

[0003] In the process of exploring the Earth-Moon space, it is necessary to correlate multiple observed orbital arcs to determine whether these orbital arcs belong to the same Earth-Moon target, so as to achieve accurate orbit determination and cataloging of the Earth-Moon target.

[0004] In related technologies, compared to near-Earth space, the Earth-Moon space area is larger, the observed orbital arcs are sparser, and the observation intervals are significantly longer, especially the coverage capability for detecting non-cooperative targets (such as Earth-Moon space debris) is significantly reduced. Moreover, determining the orbital correlation of Earth-Moon targets involves complex three-body problems, making it extremely difficult to determine the interrelationships between multiple orbital arcs of Earth-Moon targets. Summary of the Invention

[0005] In view of the above problems, a data processing method, apparatus, device, and medium for track arc segments are proposed to overcome or at least partially solve the above problems, including: A data processing method for an orbital arc segment, the method comprising: Obtain the initial orbital elements of two orbital arc segments; wherein, the orbital arcs include the first and second arc segments at different observation times; Construct a geocentric coordinate system and a lunar coordinate system, and convert the initial orbital elements into target position vectors in the geocentric coordinate system and the lunar coordinate system, respectively; Based on the target position vector, determine the target semi-circular diameter corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system, respectively; The target velocity vector corresponding to the first arc segment is determined based on the target semi-circle and the target position vector, and the second orbital elements corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system are determined based on the target position vector and the target velocity vector, respectively. Obtain a pre-constructed observation equation and update the second orbital elements based on the observation equation; wherein the observation equation characterizes the functional relationship between the observations of the Earth-Moon target and the orbital elements; The target orbital elements are determined from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system; Based on the target number of orbital elements, output the correlation result of the two orbital arc segments.

[0006] Optionally, the initial orbital elements include an initial semi-circle, and the step of determining the target semi-circle corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system based on the target position vector includes: The observation duration is determined based on the observation time corresponding to the two orbital arc segments, and the number of orbital cycles between the two orbital arc segments is determined based on the observation duration, the target position vector, and the initial semi-circle. Obtain the pre-constructed Rabert equation; wherein the Rabert equation characterizes the functional relationship between the observation duration, the orbital number, and the auxiliary calculation parameters of the target semi-path; The target solution is obtained by solving the Rabert equation based on the observation duration, the orbital revolution number, and the target position vector. The target value of the auxiliary calculation parameter is determined based on the target solution and the Rabert equation, and the target semi-pipeline is determined based on the target value and the target position vector.

[0007] Optionally, updating the second orbital elements based on the observation equation includes: Determine the linearization condition equation corresponding to the observation equation; wherein the linearization condition equation includes a first state transition matrix with respect to the orbital elements; Based on the second orbital element, the linearized condition equation is iteratively calculated; During the iterative calculation of the linearized condition equation, the second orbital elements are updated according to the first state transition matrix.

[0008] Optionally, updating the second orbital elements based on the first state transition matrix includes: The first state transition matrix is ​​converted into a target expression; wherein the target expression includes the first partial derivatives of the observed relative position vector and velocity vector, the second state transition matrix with respect to the position vector and velocity vector, and the second partial derivatives of the position vector and velocity vector with respect to the orbital elements; Solve for the first state transition matrix based on the target position vector, the target velocity vector, the first partial derivative, the second state transition matrix, and the second partial derivative; The second orbital elements are updated based on the solved first state transition matrix.

[0009] Optionally, determining the target semi-aperture based on the target value and the target position vector includes: The angle difference between the two track segments is determined based on the target position vector; The target semi-circular diameter is determined based on the angle difference and the target value.

[0010] Optionally, determining the target orbital elements from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system includes: Determine the first error index value of the second orbital element in the geocentric coordinate system, and determine the second error index value of the second orbital element in the lunar coordinate system; The target orbital elements are determined from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system based on the first error index and the second error index value.

[0011] Optionally, the step of outputting the correlation result of the two orbital arc segments based on the target orbital elements includes: Based on the comparison between the target error index value corresponding to the target orbital elements and the preset threshold, the correlation result of the two orbital segments is output.

[0012] A data processing device for a track arc segment, the device comprising: An initial orbital element acquisition module is used to acquire the initial orbital elements of two orbital arc segments; wherein, the orbital arc segments include the first and second arc segments at different observation times; The target position vector determination module is used to construct a geocentric coordinate system and a lunar coordinate system, and to convert the initial orbital elements into target position vectors in the geocentric coordinate system and the lunar coordinate system, respectively; The target semi-circular diameter determination module is used to determine the target semi-circular diameter corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system, respectively, based on the target position vector. The second orbital element determination module is used to determine the target velocity vector corresponding to the first arc segment based on the target semi-circle and the target position vector, and to determine the second orbital element corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system based on the target position vector and the target velocity vector, respectively. The second orbital element update module obtains a pre-constructed observation equation and updates the second orbital element based on the observation equation; wherein, the observation equation characterizes the functional relationship between the observations of the Earth-Moon target and the orbital element; The target orbital element determination module is used to determine the target orbital element from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system; The correlation result output module is used to output the correlation result of the two track arc segments based on the target track element number.

[0013] An electronic device includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the above-described data processing method for track arc segments.

[0014] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described data processing method for track arc segments.

[0015] The embodiments of this invention have the following advantages: By converting the initial orbital elements of the two orbital arcs into target position vectors in the geocentric and lunar coordinate systems, respectively, the target semi-path based on the geocentric and lunar coordinate systems is determined, and the second orbital elements corresponding to the first arc in the two coordinate systems are further determined. This achieves an improvement in the accuracy of orbital elements based on multiple gravitational centers (i.e., with the geocentric and lunar centers as gravitational centers respectively). Then, the second orbital elements are updated using the observation equation characterizing the functional relationship between the observations of the Earth-Moon target and the orbital elements, further improving the accuracy of the second orbital elements. Then, the target orbital elements are determined from the updated second orbital elements in the geocentric and lunar coordinate systems. Through multiple levels of accuracy correction, the improved target orbital elements are finally obtained. Based on the high-precision target orbital elements, the accuracy of the correlation results of the two orbital arcs is improved, so as to perform high-precision orbit determination of the Earth-Moon target in the subsequent Earth-Moon three-body problem, solving the problem of autonomous cataloging of non-cooperative targets under the Earth-Moon three-body problem. Attached Figure Description

[0016] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the steps of a data processing method for an orbital arc segment provided in an embodiment of the present invention; Figure 2 This is a structural block diagram of a data processing device for a track arc segment provided in an embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0019] The Earth-Moon space region is a crucial gateway for humanity's exploration of deep space and a hotspot for competition among global spacefaring powers. To effectively support the pre-positioning of deep space resources and ensure the safe operation of deep space assets, it is imperative to possess the capability for effective detection and cataloging of Earth-Moon space debris and to understand the operational status of deep space targets. Compared to near-Earth space, the Earth-Moon space region is more than ten times larger, significantly reducing the detection coverage of non-cooperative space debris, resulting in sparser observation arcs and significantly longer observation intervals. Therefore, determining the correlation between multiple sparse observation arcs of Earth-Moon debris is extremely difficult, making autonomous cataloging with a cold start highly challenging. Furthermore, due to the influence of the Earth-Moon tri-body system, the initial orbit determination accuracy of targets is poor, and the uncertainty of orbit prediction is more pronounced. Moreover, Earth-Moon spacecraft typically perform frequent low-thrust sustaining maneuvers, making the cataloging process prone to interruption. This means a higher frequency of re-correlation and orbit determination, severely limiting accuracy.

[0020] In related technologies, the methods for associating and determining orbits of non-cooperative target arc segments are only applicable to near-Earth space two-body problems and are difficult to adapt to the orbit determination and cataloging requirements of Earth-Moon space debris.

[0021] Reference Figure 1 The diagram illustrates a flowchart of a data processing method for an orbital arc segment according to an embodiment of the present invention, which may specifically include the following steps: Step 101: Obtain the initial orbital elements of the two orbital arcs; wherein the orbital arcs include the first arc and the second arc at different observation times; In practice, the initial number of track elements can be the number of track elements with lower precision and to be corrected corresponding to the two track arcs to be associated, such as the number of six track elements for a conic section track.

[0022] The Earth-Moon space is affected by the gravitational pull of the three bodies, resulting in poor accuracy of the initial orbital elements and a long observation time interval between orbital segments. It is impossible to directly predict from one orbital segment to another for observational matching. It is necessary to first perform joint orbit determination on the two related orbital segments, and then use the orbit determination results to determine whether the two are the same target.

[0023] Therefore, in order to improve the success rate of joint orbit determination, it is necessary to correct the initial orbital elements to obtain more accurate orbital elements.

[0024] In some examples, the observation time of the first arc segment is set to... The observation time of the second arc segment is Then the initial orbital elements of the two orbital arc segments can be: ,in , This represents the semi-major axis of an ellipse, hyperbola, or the semi-broad diameter of a parabola. Indicates the eccentricity. Indicates the orbital inclination angle. Indicates the right ascension of the ascending node. Indicates the angle of perigee. It represents the plan anterior angle of an ellipse or the true anterior angle of a parabola or hyperbola.

[0025] Step 102: Construct a geocentric coordinate system and a lunar coordinate system, and convert the initial orbital elements into target position vectors in the geocentric coordinate system and the lunar coordinate system, respectively; The geocentric coordinate system is a coordinate system established with the Earth's center as the origin, while the lunar coordinate system is a coordinate system established with the Moon's center as the origin.

[0026] In practical applications, the geocentric coordinate system can be the geocentric J2000 inertial coordinate system, and the lunar coordinate system can be the lunar-centered J2000 inertial coordinate system, so as to unify the initial time of the two coordinate systems to the same epoch (J2000).

[0027] A position vector is a vector that points from the Earth's center or the Moon's center to the Earth-Moon target, including information such as its magnitude and direction.

[0028] In practical implementation, orbital elements and position and velocity vectors can be converted to each other. For the target position vector in the geocentric coordinate system, the initial orbital elements can be directly converted to obtain the corresponding position and velocity vectors, thus obtaining the required target position vector. For the target position vector in the lunar coordinate system, the accurate position and velocity of the moon at any time can be calculated using ephemeris. Then, based on the position and velocity of the moon, the position and velocity vectors of the Earth-Moon target in the geocentric coordinate system can be converted to the position and velocity vectors in the lunar coordinate system, thus obtaining the required target position vector.

[0029] Step 103: Based on the target position vector, determine the target semi-circular diameter corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system, respectively; In practical implementation, based on the target position vector, the target semi-circle of the Earth-Moon target's orbit with the Earth's center of gravity as the gravitational center and the Moon's center of gravity as the gravitational center can be calculated using preset algorithms and models, as well as other observations or computational quantities (such as angular momentum, orbital revolutions) required to obtain these algorithms or models. This yields a more accurate Earth-Moon target orbit semi-circle, which is then used to correct the initial orbital elements in subsequent steps based on the target velocity vector obtained from the target semi-circle, resulting in a more accurate second orbital element.

[0030] In some embodiments of the present invention, the initial orbital elements include an initial semi-circular diameter, and the step of determining the target semi-circular diameter corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system according to the target position vector includes: The observation duration is determined based on the observation time corresponding to the two orbital arc segments, and the number of orbital cycles between the two orbital arc segments is determined based on the observation duration, the target position vector, and the initial semi-circle. Obtain the pre-constructed Rabert equation; wherein the Rabert equation characterizes the functional relationship between the observation duration, the orbital number, and the auxiliary calculation parameters of the target semi-path; The target solution is obtained by solving the Rabert equation based on the observation duration, the orbital revolution number, and the target position vector. The target value of the auxiliary calculation parameter is determined based on the target solution and the Rabert equation, and the target semi-pipeline is determined based on the target value and the target position vector.

[0031] The Lambert equations can effectively reorient orbital segments, significantly improving the accuracy of the semi-major axis (or semi-major diameter) by utilizing the long time intervals between segments. In Earth-Moon orbit design, the Lambert equations are sometimes used for mission planning of Earth-Moon transfer orbit segments, but they are difficult to apply effectively when the gravitational influence range of the Earth and Moon within an orbital segment is unclear. Therefore, the Lambert equations are still primarily used for solving elliptical orbit equations under the two-body problem, and are not effective in determining arbitrary conic section orbits under the three-body problem.

[0032] Based on this, the present invention proposes a method for correcting the orbital elements of the conic section Lambert equation based on the assumption of multiple gravitational centers. By using the pre-constructed Lambert equation, a high-precision target semi-circle can be determined under multiple gravitational centers (Earth-center, Moon-center), which can solve the problem of initial orbit correction of Earth-Moon space debris to a certain extent.

[0033] In practical implementation, taking the geocentric coordinate system as an example, the process of calculating the target semi-circle of the Earth-Moon target in the geocentric coordinate system is as follows: Define parameters , , , ,in, For the observation time The observed target position vector in the geocentric coordinate system for the orbital arc segment. For the observation time The target position vector in the geocentric coordinate system of the orbital arc segment observed at all times. , The 2-norm of a vector; Then the observation duration According to Euler's equations, we get: (1) In equation (1), This is the Earth's central gravitational constant (or the Moon's central gravitational constant for a lunar coordinate system). Based on equation (1), the orbital revolutions between the two orbital segments... for: (2) In equation (2), The initial semi-pivot diameter in the initial orbital elements. Represents absolute value. Indicates rounding down; Furthermore, obtain pre-built, to The Lambert equation with as the independent variable characterizes the orbital revolutions. Observation duration And auxiliary calculation parameters for the target semi-pipe diameter The functional relationship between them is as follows: (3) In equation (3), , It is a hypergeometric function; Based on equation (3), the observation duration relatively The partial derivatives are: (4) In equation (4), For about Auxiliary variables; combining equations (3) and (4), and the known... , Observation duration and orbital circles Equation (3) is solved iteratively using the Newton-Raphson method. When the preset convergence condition is met, the result is obtained. The target solution; Furthermore, Substituting the target solution into equation (3), we obtain the auxiliary calculation parameters of the target semi-major axis. Target value; Furthermore, based on the target position vector and the target value, the target semi-circular diameter in the geocentric coordinate system can be calculated using a pre-constructed relational formula; The calculation method for the target semi-circular diameter in the lunar coordinate system is the same, and will not be repeated here.

[0034] In some embodiments of the present invention, determining the target semi-aperture based on the target value and the target position vector includes: The angle difference between the two track segments is determined based on the target position vector; The target semi-circular diameter is determined based on the angle difference and the target value.

[0035] In practical implementation, taking the geocentric coordinate system as an example, For the observation time The observed target position vector in the geocentric coordinate system for the orbital arc segment. For the observation time The target position vector in the geocentric coordinate system of the orbital arc segment observed at each moment, let , , , The angle difference between the two track segments for: (5) Furthermore, adopt Auxiliary calculation parameters The target value is obtained by the following formula (6) in the geocentric coordinate system. : (6) The calculation method for the target semi-circular diameter in the lunar coordinate system is the same, and will not be repeated here.

[0036] Step 104: Determine the target velocity vector corresponding to the first arc segment based on the target semi-circle and the target position vector, and determine the second orbital elements corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system based on the target position vector and the target velocity vector, respectively. In practical implementation, the target velocity vector can be determined based on the preset relationship by using the target semi-circular diameter and the target position vector. Then, based on the characteristic that the orbital elements, velocity vector, and target position vector can be converted into each other, the target position vector and target velocity vector can be converted into the second orbital elements in the geocentric coordinate system and the lunar coordinate system, respectively, thereby correcting the initial orbital elements and obtaining more accurate orbital elements.

[0037] In some examples, using a geocentric coordinate system, the target semi-circular diameter is... , For the observation time The observed target position vector in the geocentric coordinate system for the orbital arc segment. For the observation time The target position vector in the geocentric coordinate system of the orbital arc segment observed at each moment, let , Earth's central gravitational constant The angle difference between the two track arcs Then the observation time The orbital arc of the Earth-Moon target, and the target velocity vector in the geocentric coordinate system. for: (7) Furthermore, based on , The observation time can then be converted. The first arc segment of the Earth-Moon target, at the observation time The second orbital element number can specifically be the six elements of a conic section orbital. .

[0038] The same applies to the target velocity vector in the lunar coordinate system, which will not be elaborated here.

[0039] Step 105: Obtain the pre-constructed observation equation and update the second orbital elements based on the observation equation; wherein, the observation equation characterizes the functional relationship between the observations of the Earth-Moon target and the orbital elements; In practical implementation, taking the geocentric coordinate system as an example, the observation equation can be shown in equation (8): (8) In equation (8), For observation purposes, Represents the observation time, among which The specific observations can include information such as elevation angle and azimuth angle. For to be estimated The orbital elements at time 10:00 From orbital elements at time Forecast The observation function at time, The random difference of the observations; Observation function It can be defined according to the actual needs, for example, based on a high-precision orbital model. The second orbital element is used as the basis for equation (8). The initial values ​​are obtained by iteratively solving the observation equations to update the second orbital elements.

[0040] The update of the second orbital elements in the lunar coordinate system is similar and will not be elaborated here.

[0041] Finally, the second orbital elements with higher accuracy were obtained in both the geocentric and lunar coordinate systems.

[0042] In some embodiments of the present invention, updating the second orbital elements based on the observation equation includes: Determine the linearization condition equation corresponding to the observation equation; wherein the linearization condition equation includes a first state transition matrix with respect to the orbital elements; Based on the second orbital element, the linearized condition equation is iteratively calculated; During the iterative calculation of the linearized condition equation, the second orbital elements are updated according to the first state transition matrix.

[0043] In practical implementation, taking the geocentric coordinate system as an example, based on the observation equation of equation (8), the corresponding linearization condition equation is shown in equation (9): (9) in, for time According to the precise orbit model prediction The orbital elements at time 10:00 The correction value after the initial orbit iteration is the result of stopping the iteration, which is the updated second orbital element and the first state transition matrix. ; The second orbital element is taken as The initial value is used to perform iterative calculations on equation (9) (e.g., Newton iteration calculations). In each round of iterative calculation, the correction value for each iteration can be obtained by solving the first state transition matrix and substituting the solved first state transition matrix into equation (9). ; When the iterative operation on equation (9) reaches the preset convergence condition, the orbital elements in equation (8) are finally obtained. That is, the updated number of second orbital elements.

[0044] The update of the second orbital elements in the lunar coordinate system is similar and will not be elaborated here.

[0045] In some embodiments of the present invention, updating the second orbital elements according to the first state transition matrix includes: The first state transition matrix is ​​converted into a target expression; wherein the target expression includes the first partial derivatives of the observed relative position vector and velocity vector, the second state transition matrix with respect to the position vector and velocity vector, and the second partial derivatives of the position vector and velocity vector with respect to the orbital elements; Solve for the first state transition matrix based on the target position vector, the target velocity vector, the first partial derivative, the second state transition matrix, and the second partial derivative; The second orbital elements are updated based on the solved first state transition matrix.

[0046] In this embodiment, the solution of the first state transition matrix of equation (9) differs from that of the traditional two-body problem in two main ways: First, the six-element method of the orbit of the conic section is adopted, which has a clearer physical meaning than the position vector and velocity vector, and is convenient for determining the threshold of convergence of orbit determination iteration; Second, considering the influence of the three-body problem, it is necessary to solve the geocentric coordinate system and the lunar coordinate system separately.

[0047] In practical implementation, taking the geocentric coordinate system as an example, the first state transition matrix B based on equation (9) can be transformed into the following objective expression: (10) in, , They are respectively orbital elements at time The corresponding target position vector and velocity vector, target position vector Target velocity vector , ; In equation (10), the first partial derivatives of the observed relative position vector and velocity vector are: (11) The second state transition matrix for the position vector and velocity vector is: (12) The second partial derivatives of the position vector and velocity vector with respect to the orbital elements are: (13) For equation (12), it can be based on known... , It can be obtained through numerical integration or estimated through analytical methods; For equation (13) Specifically, it can be the number of six elements of the orbit of a conic section ( Indicates the semi-nominal diameter. Indicates the eccentricity. Indicates the orbital inclination angle. Indicates the right ascension of the ascending node. Indicates the angle of perigee. (representing the true anterior angle), the solution process of equation (13) is as follows: Set the following vector: , , (14) And the following formula (15): (15) Based on respectively , right Taking the partial derivative, we get: (16) (17) Furthermore, substitute equation (14) into equation (16), and substitute equations (14) and (15) into equation (17); then substitute equations (16) and (17) into equation (13) to solve; Furthermore, substitute equation (10) back into equation (9) to solve for the first state transition matrix; for example, by iteratively solving using the least squares method. Finally, the second orbital elements are updated based on the solved first state transition matrix.

[0048] The update of the second orbital elements in the lunar coordinate system is similar and will not be elaborated here.

[0049] In practical applications, to accommodate the switching between ellipses, parabolas, and hyperbolas during the iteration process, the orbital element format of the parabola can be uniformly set, and then adjusted to the corresponding orbital element formats of the ellipse, parabola, and hyperbola after the iteration is completed. This process is relatively convenient.

[0050] Step 106: Determine the target orbital elements from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system; In practical implementation, after obtaining the updated second orbital elements in both the geocentric and lunar coordinate systems, the target orbital element can be determined by selecting the better one from the two using preset evaluation algorithms and analysis methods. For example, the one with higher precision can be selected as the target orbital element. The target orbital element is the final orbital element determined after improvement for the Earth-Moon target corresponding to the first arc segment.

[0051] In some embodiments of the present invention, determining the target orbital element from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system includes: Determine the first error index value of the second orbital element in the geocentric coordinate system, and determine the second error index value of the second orbital element in the lunar coordinate system; The target orbital elements are determined from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system based on the first error index and the second error index value.

[0052] In practical implementation, the first and second error index values ​​can be residual values. Specifically, the time corresponding to the updated second orbital elements is the initial time. Using the updated second orbital elements as the initial value, the expected observations after the initial time are predicted through the observation equation. The residual values ​​are calculated by comparing these predictions with the actual observations obtained from the actual observations; these residual values ​​are the first and second error index values. Then, the first and second error index values ​​are compared, and the one with the smaller error index value is determined as the target orbital elements.

[0053] In some examples, the observation time is set. The updated second orbital elements in the geocentric coordinate system are: The first error index value can then be calculated using the following formula. : (18) The updated second orbital elements in the lunar coordinate system are: The second error index value can then be calculated using the following formula. : (19) In equations (18) and (19), , For actual observation, For observation functions; Furthermore, in comparison and The updated second orbital element corresponding to the smaller value is determined as the target orbital element. .

[0054] Step 107: Output the correlation result of the two track segments based on the target number of track elements.

[0055] In the specific implementation, since the target orbital elements corresponding to the first arc segment are obtained through joint orbit determination of the first and second arc segments, orbit prediction can be performed based on the target orbital elements. If the prediction results meet the accuracy requirements, it can be considered that the first and second arc segments have a high correlation and belong to the same Earth-Moon target; if the prediction results do not meet the accuracy requirements, it can be considered that the first and second arc segments have a low correlation and do not belong to the same Earth-Moon target. Finally, the correlation results are output.

[0056] In some embodiments of the present invention, the step of outputting the correlation result of the two orbital arc segments based on the target orbital elements includes: Based on the comparison between the target error index value corresponding to the target orbital elements and the preset threshold, the correlation result of the two orbital segments is output.

[0057] In the specific implementation, the preset threshold can be a precision error threshold. If the target error index value is greater than or equal to the preset threshold, it is considered that the correlation between the two orbital arcs is low and that the two orbital arcs do not belong to the same Earth-Moon target, and the corresponding correlation result is output. If the target error index value is less than the preset threshold, it is considered that the correlation between the two orbital arcs is high and that the two orbital arcs belong to the same Earth-Moon target, and the corresponding correlation result is output.

[0058] In some examples, the target error index is... The preset threshold can be the maximum positional error corresponding to the measurement accuracy of the observed quantity. ,like If the two orbital arcs are not identical, then they belong to the same Earth-Moon target; otherwise, they do not belong to the same Earth-Moon target.

[0059] In some embodiments of the present invention, a simulated observation of a target with a lunar orbit of 7000 km is performed based on a near-Earth sun-synchronous orbit space-based optical monitoring platform. Two orbital arc segments are simulated, each with an arc length of approximately 25 minutes and an interval of approximately 15 hours. The observation accuracy of right ascension and declination is approximately 2 arcseconds. Using the data processing method for orbital arc segments provided in one embodiment of the present invention, the short-arc orbit determination results (orbital elements) and orbit determination errors for non-cooperative Earth-Moon space targets affected by the gravitational pull of the three bodies are shown in Table 1. Table 1

[0060] It is evident that Lambert's initial orbit correction using multiple gravitational centers can improve orbital velocity accuracy from 163.76 m / s to 67.69 m / s. Building upon this, further high-precision orbit determination can be achieved using conic section orbit improvement methods, with a positional accuracy of 7569.98 m and a velocity accuracy of 3.44 m / s. Therefore, it is confirmed that the two orbital arcs belong to the same Earth-Moon target, supporting accurate matching and continuous orbit improvement for subsequent new observation arcs. This provides an effective approach for autonomous and stable cataloging of Earth-Moon space, demonstrating significant application prospects.

[0061] The embodiments of this invention have the following advantages: By converting the initial orbital elements of the two orbital arcs into target position vectors in the geocentric and lunar coordinate systems, respectively, the target semi-path based on the geocentric and lunar coordinate systems is determined. This further determines the second orbital elements corresponding to the first arc in both coordinate systems, thereby improving the accuracy of the orbital elements based on multiple gravitational centers (i.e., with the geocentric and lunar centers as gravitational centers respectively). Then, by using the observation equation characterizing the functional relationship between the observations of the Earth-Moon target and the orbital elements, the second orbital elements are updated, further improving their accuracy. Next, the target orbital elements are determined from the updated second orbital elements in the geocentric and lunar coordinate systems. Through multiple levels of accuracy improvement, the improved target orbital elements are finally obtained. Based on the high-precision target orbital elements, the accuracy of the correlation results of the two orbital arcs is improved, enabling high-precision orbit determination of the Earth-Moon target and solving the problem of autonomous cataloging of non-cooperative targets under the Earth-Moon three-body problem.

[0062] It should be noted that, for the sake of simplicity, the method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of the present invention are not limited to the described order of actions, because according to the embodiments of the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions involved are not necessarily essential to the embodiments of the present invention.

[0063] Reference Figure 2 The diagram shows a structural schematic of a data processing device for a track arc segment according to an embodiment of the present invention, which may specifically include the following modules: The initial orbital element acquisition module 201 is used to acquire the initial orbital elements of two orbital arc segments; wherein, the orbital arc segments include the first arc segment and the second arc segment at different observation times; The target position vector determination module 202 is used to construct a geocentric coordinate system and a lunar coordinate system, and to convert the initial orbital elements into target position vectors in the geocentric coordinate system and the lunar coordinate system, respectively; The target semi-circular diameter determination module 203 is used to determine the target semi-circular diameter corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system, respectively, based on the target position vector. The second orbital element determination module 204 is used to determine the target velocity vector corresponding to the first arc segment based on the target semi-circle and the target position vector, and to determine the second orbital element corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system based on the target position vector and the target velocity vector, respectively. The second orbital element update module 205 acquires a pre-constructed observation equation and updates the second orbital element based on the observation equation; wherein the observation equation characterizes the functional relationship between the observations of the Earth-Moon target and the orbital element. The target orbital element determination module 206 is used to determine the target orbital element from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system; The correlation result output module 207 is used to output the correlation result of the two track arc segments according to the target track element number.

[0064] In some embodiments of the present invention, the initial orbital elements include an initial semi-circular diameter, and the target semi-circular diameter determination module 203 includes: The duration and orbit number processing submodule is used to determine the observation duration based on the observation time corresponding to the two orbital arcs, and to determine the orbital orbit number between the two orbital arcs based on the observation duration, the target position vector, and the initial semi-path. The Rabert equation acquisition submodule is used to acquire pre-constructed Rabert equations; wherein, the Rabert equations characterize the functional relationship between the observation duration, the orbital cycle number, and the auxiliary calculation parameters of the target semi-path; The target solution determination submodule is used to solve the Rabert equation based on the observation duration, the orbital cycle number, and the target position vector to obtain the target solution. The target semi-path determination submodule is used to determine the target value of the auxiliary calculation parameter based on the target solution and the Rabert equation, and to determine the target semi-path based on the target value and the target position vector.

[0065] In some embodiments of the present invention, the second orbital element update module 205 includes: A linearization condition equation determination submodule is used to determine the linearization condition equation corresponding to the observation equation; wherein, the linearization condition equation includes a first state transition matrix with respect to the orbital elements; The iterative operation submodule is used to perform iterative operations on the linearized condition equation based on the second orbital root number; The second orbital element update submodule is used to update the second orbital element according to the first state transition matrix during the iterative operation of the linearized condition equation.

[0066] In some embodiments of the present invention, the second orbital element update submodule includes: The target expression conversion unit is used to convert the first state transition matrix into a target expression; wherein, the target expression includes the first partial derivatives of the observed relative position vector and velocity vector, the second state transition matrix with respect to the position vector and velocity vector, and the second partial derivatives of the position vector and velocity vector with respect to the orbital elements; The first state transition matrix solving unit is used to solve the first state transition matrix based on the target position vector, the target velocity vector, the first partial derivative, the second state transition matrix, and the second partial derivative. The second orbital element update unit is used to update the second orbital element based on the solved first state transition matrix.

[0067] In some embodiments of the present invention, the target semi-pipe diameter determination submodule includes: An angle difference determination unit is used to determine the angle difference between the two track segments based on the target position vector. The target semi-aperture determination unit is used to determine the target semi-aperture based on the angle difference and the target value.

[0068] In some embodiments of the present invention, the target orbital element determination module 206 includes: The error index value determination submodule is used to determine the first error index value of the second orbital element in the geocentric coordinate system and the second error index value of the second orbital element in the lunar coordinate system. The target orbital element determination submodule is used to determine the target orbital element from the updated second orbital element in the geocentric coordinate system and the lunar coordinate system based on the first error index and the second error index value.

[0069] In some embodiments of the present invention, the correlation result output module 207 includes: The correlation result output submodule is used to output the correlation result of the two track segments based on the comparison result between the target error index value corresponding to the target track element number and the preset threshold.

[0070] Some embodiments of the present invention also provide an electronic device, which may include a processor, a memory, and a computer program stored in the memory and capable of running on the processor. When the computer program is executed by the processor, it implements the data processing method for the above-mentioned track arc segment.

[0071] Some embodiments of the present invention also provide a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, it implements the data processing method for the above-mentioned track arc segment.

[0072] Some embodiments of the present invention also provide a computer program product, including a computer program that, when executed by a processor, implements the data processing method for the above-mentioned track arc segment.

[0073] As the device embodiment is basically similar to the method embodiment, the description is relatively simple, and relevant parts can be found in the description of the method embodiment.

[0074] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data that have been agreed to by the user or fully accepted by all parties. Furthermore, the collection, use and processing of the relevant data must comply with the relevant laws, regulations and standards of the relevant regions, and corresponding operation portals are provided for users to choose to agree or refuse.

[0075] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0076] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, embodiments of the present invention can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0077] Embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.

[0078] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0079] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0080] Although preferred embodiments of the present invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.

[0081] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes the aforementioned element.

[0082] The above provides a detailed description of the data processing method, apparatus, equipment, and medium for track arc segments. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A data processing method for a track arc segment, characterized in that, The method includes: Obtain the initial orbital elements for the two orbital arcs; where the orbital radians include the first and second arcs at different observation times; Construct a geocentric coordinate system and a lunar coordinate system, and convert the initial orbital elements into target position vectors in the geocentric coordinate system and the lunar coordinate system, respectively; Based on the target position vector, determine the target semi-circular diameter corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system, respectively; The target velocity vector corresponding to the first arc segment is determined based on the target semi-circle and the target position vector, and the second orbital elements corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system are determined based on the target position vector and the target velocity vector, respectively. Obtain a pre-constructed observation equation and update the second orbital elements based on the observation equation; wherein the observation equation characterizes the functional relationship between the observations of the Earth-Moon target and the orbital elements; The target orbital elements are determined from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system; Based on the target number of orbital elements, output the correlation result of the two orbital arc segments.

2. The method according to claim 1, characterized in that, The initial orbital elements include the initial semi-circular diameter. The step of determining the target semi-circular diameter corresponding to the first arc segment in both the geocentric and lunar coordinate systems based on the target position vector includes: The observation duration is determined based on the observation time corresponding to the two orbital arc segments, and the number of orbital cycles between the two orbital arc segments is determined based on the observation duration, the target position vector, and the initial semi-circle. Obtain the pre-constructed Rabert equation; wherein the Rabert equation characterizes the functional relationship between the observation duration, the orbital number, and the auxiliary calculation parameters of the target semi-path; The target solution is obtained by solving the Rabert equation based on the observation duration, the orbital revolution number, and the target position vector. The target value of the auxiliary calculation parameter is determined based on the target solution and the Rabert equation, and the target semi-pipeline is determined based on the target value and the target position vector.

3. The method according to claim 1, characterized in that, The update of the second orbital elements based on the observation equation includes: Determine the linearization condition equation corresponding to the observation equation; wherein the linearization condition equation includes a first state transition matrix with respect to the orbital elements; Based on the second orbital element, the linearized condition equation is iteratively calculated; During the iterative calculation of the linearized condition equation, the second orbital elements are updated according to the first state transition matrix.

4. The method according to claim 3, characterized in that, The step of updating the second orbital elements according to the first state transition matrix includes: The first state transition matrix is ​​converted into a target expression; wherein the target expression includes the first partial derivatives of the observed relative position vector and velocity vector, the second state transition matrix with respect to the position vector and velocity vector, and the second partial derivatives of the position vector and velocity vector with respect to the orbital elements; Solve for the first state transition matrix based on the target position vector, the target velocity vector, the first partial derivative, the second state transition matrix, and the second partial derivative; The second orbital elements are updated based on the solved first state transition matrix.

5. The method according to claim 2, characterized in that, Determining the target semi-aperture based on the target value and the target position vector includes: The angle difference between the two track segments is determined based on the target position vector; The target semi-circular diameter is determined based on the angle difference and the target value.

6. The method according to any one of claims 1-5, characterized in that, Determining the target orbital elements from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system includes: Determine the first error index value of the second orbital element in the geocentric coordinate system, and determine the second error index value of the second orbital element in the lunar coordinate system; The target orbital elements are determined from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system based on the first error index and the second error index value.

7. The method according to claim 6, characterized in that, The step of outputting the correlation result of the two orbital arc segments based on the target orbital elements includes: Based on the comparison between the target error index value corresponding to the target orbital elements and the preset threshold, the correlation result of the two orbital segments is output.

8. A data processing device for a track arc segment, characterized in that, The device includes: The initial orbital element acquisition module is used to obtain the initial orbital elements of two orbital arc segments; wherein, the orbital arc includes the first arc segment and the second arc segment at different observation times; The target position vector determination module is used to construct a geocentric coordinate system and a lunar coordinate system, and to convert the initial orbital elements into target position vectors in the geocentric coordinate system and the lunar coordinate system, respectively; The target semi-circular diameter determination module is used to determine the target semi-circular diameter corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system, respectively, based on the target position vector. The second orbital element determination module is used to determine the target velocity vector corresponding to the first arc segment based on the target semi-circle and the target position vector, and to determine the second orbital element corresponding to the first arc segment in the geocentric coordinate system and the lunar coordinate system based on the target position vector and the target velocity vector, respectively. The second orbital element update module obtains a pre-constructed observation equation and updates the second orbital element based on the observation equation; wherein, the observation equation characterizes the functional relationship between the observations of the Earth-Moon target and the orbital element; The target orbital element determination module is used to determine the target orbital element from the updated second orbital elements in the geocentric coordinate system and the lunar coordinate system; The correlation result output module is used to output the correlation result of the two track arc segments based on the target track element number.

9. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the data processing method for the orbital arc segment as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, which, when executed by a processor, implements the data processing method for the orbital arc segment as described in any one of claims 1 to 7.

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