Method for precise orbit determination of unknown target by space-based dual multi-satellite coordinated observation with ultra-short-arc

Abstract

This invention discloses a space-based, multi-satellite collaborative observation method for precise orbit determination of unknown targets in ultra-short arcs, belonging to the field of space situational awareness. Addressing the problem of ill-conditioned and unstable solutions in initial orbit determination using only angular measurement data in ultra-short arc segments, this invention utilizes collaborative observation data from two or more space-based optical platforms on the same target. A discrete target position sequence is constructed using line-of-sight convergence least-squares positioning. The Lambert problem is solved by combining multiple points from the beginning and end of the sequence, and the optimal initial orbit is selected by combining physical constraints and the root mean square of the residuals. The orbital region is determined based on the initial orbit, and corresponding dynamic model parameters are configured. Finally, observation equations are constructed using all collaborative angular measurement data, and the orbital state is refined through iterative least-squares analysis. This invention fully utilizes the complementary spatial geometry of multiple satellites, significantly improving the stability and accuracy of initial orbit determination under ultra-short arc conditions, achieving orbit determination accuracy on the order of tens of meters.

Description

Technical Field

[0001] This invention belongs to the field of space situational awareness, and more specifically, relates to a technology for determining the ultra-short arc precise orbit of unknown targets under space-based dual / multi-satellite collaborative observation conditions, specifically a method for ultra-short arc precise orbit determination of unknown targets under space-based dual / multi-satellite collaborative observation. Background Technology

[0002] The Low Earth Orbit (LEO) region is the most active area in space situational awareness research, with an orbital altitude ranging from 200km to 2000km, and is home to a large number of satellites and space debris. With the rapid development of constellation deployments (such as the Starlink constellation), the number of near-Earth space targets is increasing exponentially, and the orbital environment is becoming increasingly complex, placing higher demands on space situational awareness capabilities.

[0003] To ensure the safety of near-Earth space operations and assets, it is urgent to build an independent and controllable space situational awareness system. The core tasks of near-Earth space situational awareness include: space target detection, orbit determination and prediction, and space rendezvous early warning. Among these, the construction of a space target orbit catalog is fundamental to achieving high-precision situational awareness, and its key technology includes Initial Orbit Determination (IOD).

[0004] In near-Earth space observation systems, due to the finite field of view (FOV) typically present by ground-based or space-based observation equipment, a single observation platform often struggles to achieve continuous target tracking. Therefore, dual / multi-satellite co-observation has gradually become an important means of improving observation coverage. Under dual / multi-satellite co-observation conditions, the same target can be observed simultaneously by two or more space-based observation platforms within a similar timeframe, thus forming a co-observation arc. However, dual / multi-satellite co-observation also presents new challenges: on the one hand, the sources of observation data are diverse and exhibit time asynchrony and measurement error differences; on the other hand, in high-density target environments, the initial orbit determination problem still faces uncertainties and insufficient robustness under short-arc or ultra-short-arc observation conditions (observation arc length less than 1% of the target's orbital period), easily generating trivial solutions. These orbital solutions are sensitive to observation errors, affecting subsequent cataloging accuracy. Summary of the Invention

[0005] To address the problem of ill-conditioned and unstable solutions in determining the initial orbit of an ultra-short arc using only angular measurement data under space-based dual / multi-satellite collaborative observation, this invention provides a precise orbit determination method for unknown targets under ultra-short arc conditions using space-based dual / multi-satellite collaborative observation. By using multi-platform line-of-sight positioning, Lambert initial orbit determination through multi-point combination of the beginning and end points, and iterative least-squares orbit refinement, stable and high-precision orbit determination under ultra-short arc conditions is achieved, with orbit determination position accuracy reaching tens of meters.

[0006] According to one aspect of the present invention, a method for precise orbit determination of an unknown target using ultra-short arcs through space-based dual-multi-satellite collaborative observation is provided, comprising: By utilizing the collaborative observation data of two or more space-based optical observation platforms on the same unknown target, the spatial position and angle observations of each platform are obtained, a line-of-sight direction unit vector is constructed, a linear observation equation is constructed using vector collinearity constraints, and the spatial position of the target at each observation time is solved by least squares to form a discrete position sequence. Observation points are selected from the beginning and end of the discrete position sequence to form a set of starting positions and a set of ending positions. These are then combined in pairs to form multiple sets of positions. A Lambert problem based on a two-body orbit is constructed and the orbital parameters are solved to obtain a set of candidate orbit solutions. Constraints are applied to the candidate orbits and the root mean square of the observation residuals is used as an evaluation index to select the optimal initial orbit. Based on the position and velocity information of the optimal initial orbit, the near-Earth space orbit region to which the target belongs is determined, and dynamic model parameters matching the determined orbit region are configured. The observation equations for orbit refinement are constructed, and all angle measurement data under the cooperative observation conditions are used as observations. The initial state is iteratively corrected under the least squares criterion until the convergence condition is met, and the refined orbit state is obtained.

[0007] As a further technical solution, a discrete position sequence is formed, including: constructing a line-of-sight direction unit vector based on the right ascension and declination angle observations obtained from each observation platform; using the spatial position of each observation platform in the TOD coordinate system and the line-of-sight direction unit vector, eliminating unknown distance parameters through vector collinearity constraints, and deriving a linear observation equation about the target position; superimposing the linear observation equations of multiple platforms at the same time to form an overdetermined system of equations, and using least squares to solve for the optimal estimate of the target's spatial position at that time; and repeating the steps of constructing the line-of-sight direction unit vector based on the angle observations, deriving the linear observation equations, superimposing the system of equations, and using least squares to solve for multiple collaborative observation times to construct a discrete trajectory sequence of the target.

[0008] As a further technical solution, the optimal initial orbit is selected by: selecting observation points from the first and last quarter portions of the arc segment to form a set of starting and ending positions respectively; combining the points in the starting and ending positions in pairs to form multiple position pairs; for each position pair, using the Gooding method to solve the Lambert problem based on the two-body orbit to obtain the six root numbers of candidate orbits; applying constraints to the candidate orbits to obtain a set of candidate orbit solutions; performing orbit propagation on each candidate orbit solution, calculating the root mean square of the observation residuals between the predicted and actual positions at all observation points, and selecting the candidate orbit solution with the smallest root mean square as the optimal initial orbit.

[0009] As a further technical solution, the refined orbital state is obtained by: assuming that the target motion satisfies the dynamic equation, and the state vector includes position and velocity; using all angle measurement data under multi-satellite collaborative observation conditions as observations, constructing an observation equation with the initial state of the target as the variable, and defining the loss function as the sum of squares of the observation residuals; performing first-order linearization on the observation equation at the initial estimate to obtain the linearized residual expression; using the iterative least squares method to solve the state correction and update the initial state estimate, repeating the iteration until the magnitude of the correction is less than the preset convergence threshold.

[0010] As a further technical solution, during the initial orbit refinement process, collaborative observation data from two or more space-based platforms are introduced, and the observation equations of each platform are superimposed to construct an observation matrix.

[0011] As a further technical solution, the coefficient matrix in the linear observation equation is an antisymmetric matrix sub-block corresponding to the cross product operation constructed using the line-of-sight direction vector, and the constant term is composed of the cross product result of the line-of-sight direction vector and the position of the observation platform.

[0012] As a further technical solution, the observation matrix in the iterative least squares consists of a product of two parts: the first part is the partial derivative of the observation model with respect to the instantaneous state vector of the target, and the second part is the partial derivative of the instantaneous state vector with respect to the initial state vector. The second part is calculated through the state transition matrix of the dynamic equation.

[0013] According to one aspect of the present invention, an electronic device is provided, including a processor and a memory, the memory storing a computer program, wherein the processor executes the computer program to implement the method described herein.

[0014] According to one aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the method described thereon.

[0015] According to one aspect of the present invention, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the method described herein.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention addresses the challenges of determining unknown targets under space-based dual / multi-satellite collaborative observation conditions. Utilizing multi-platform optical angle-only data, it forms a discrete position sequence through line-of-sight convergence. Combining this with the Gooding initial orbit determination method based on the Lambert problem at both ends, and using orbital physical constraints and residual evaluation to screen for the optimal initial orbit, it constructs observation equations based on a near-Earth space dynamics model and refines them using least-squares iterative methods. This effectively solves the problems of ill-conditioned initial orbit determination, numerous trivial solutions, and sensitivity to measurement errors in ultra-short arc segments (arc length less than 1% of the target orbit period). This invention fully leverages the spatial geometric complementarity of multi-satellite collaborative observations, using all available space-based optical angle-only data for orbit calculation, significantly enhancing the constraint capability of the orbit solution and thus greatly improving the accuracy and stability of orbit determination. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the space-based dual-multi-satellite collaborative observation method for ultra-short arc precision orbit determination of unknown targets provided in an embodiment of the present invention.

[0019] Figure 2 This diagram illustrates the impact of different collaborative observation conditions on orbit determination and orbit prediction accuracy, as provided in the embodiments of the present invention. Detailed Implementation

[0020] To address the shortcomings of existing technologies, research on determining the ultra-short arc orbits of unknown targets in dual / multi-satellite collaborative observation scenarios is of great significance. On one hand, such methods need to be universally applicable to targets with different orbital types; on the other hand, after obtaining coarse initial orbit information, orbit refinement can be performed by combining all space-based observation data to improve orbit determination accuracy. Furthermore, by rationally configuring space-based observation platforms (such as deploying observation satellites at different orbital altitudes), the target observation arc length can be significantly increased, thereby further improving the stability and accuracy of initial orbit parameter calculation for unknown targets.

[0021] Therefore, this invention provides a method for precise orbit determination of an unknown target using ultra-short arcs through space-based dual-multi-satellite collaborative observation, comprising:

[0022] The first step is to obtain the discrete position information of the target under dual / multi-satellite collaborative observation conditions.

[0023] S1.1 Under the condition of collaborative observation of the same unknown target by two or more space-based optical observation platforms, obtain the spatial position of each observation platform at the same time in the TOD (True of Date, TOD) coordinate system. and angular observation (right ascension) Declination ), , This represents the number of angle observations.

[0024] Construct a unit vector for the direction of the observation line of sight based on optical angle measurement observation information: .

[0025] Since the observation only provides angle information and not distance information, the location of the observed target at the observation time is... The following geometric relationship must be satisfied: , in, This represents the distance between the observation platform and the observation target. Since this is an angle-only observation, the distance is unknown, so this unknown distance parameter is used to eliminate it. The cross product relationship between vectors can be constructed using the collinearity constraint: .

[0026] S1.2, Expanding and rearranging formula (3), we can obtain the linear observation equation regarding the target location information: , Among them, matrix By line of sight vector The construction, in essence, is a sub-block of the antisymmetric matrix corresponding to the cross product operation; vector Depend on With platform location The cross product of these terms constitutes the constant term representing the observation constraint.

[0027] S1.3 For N observation platforms, the observation equations of each platform can be superimposed to construct an overall linear system: Since this system typically consists of an overdetermined system of equations, the least squares method is used to solve for the target position, and the solution is: , This allows us to obtain the optimal estimate of the target's spatial position at the current observation time. Furthermore, by repeating the above process for the observation times of multiple coordinated observations, we can construct a discrete trajectory sequence of the target and provide initial input for subsequent initial trajectory determination.

[0028] The second step is to obtain the discrete position sequence of the target under multi-satellite collaborative observation conditions. Afterwards, the initial track determination was carried out. , , Both represent the observation time.

[0029] S2.1 To improve the stability of initial orbit determination under short or ultra-short arc conditions (arc segment duration less than 1% of the target orbital motion period), several observation points are selected from the first and last quarters of the arc segment to form a set of initial positions and a set of final positions. These are then combined in pairs to form multiple sets of positions, thus constructing the classic Lambert problem based on two-body orbits. That is, given the geocentric position and flight time of the target at the start and end times, the target's flight trajectory parameters are determined.

[0030] For any combination and The orbital parameters are solved using the Gooding method: ,in, The orbital number is six. .

[0031] S2.2 To ensure the rationality of the orbital solutions, constraints are imposed on the candidate orbits (such as limiting the eccentricity range), thus obtaining a set of candidate orbital solutions. To further determine the optimal orbit from the candidate orbital solutions, the observed-minus-computed (OC) residual is introduced as an evaluation metric. For any candidate orbital solution, orbital propagation is performed to obtain the predicted position. And compare it with the observed position to construct the initial orbit determination residual statistics: , Where N is the number of observation points. Finally, the candidate orbit solution corresponding to the smallest RMS value is selected as the optimal orbit solution and output.

[0032] The third step is to configure a high-fidelity orbit perturbation model.

[0033] S3.1 Based on the target's initial orbital position and velocity information obtained from the above dual / multi-satellite collaborative observations, determine the near-Earth space orbital region to which the target belongs.

[0034] S3.2, Configure appropriate dynamic model parameters based on the target's orbital altitude and operational characteristics. For near-Earth space targets, the main perturbation models include: the Earth's non-spherical gravitational field model (usually requiring higher orders, such as J2 terms and higher-order gravity terms), the atmospheric drag model (the LEO region is the main perturbation term), the solar radiation pressure model, the gravity of a third celestial body (mainly considering the gravity of the Sun and Moon), and the effects of Earth's rotation and polar motion.

[0035] The fourth step is to refine the initial orbit using iterative least squares estimation.

[0036] S4.1 First, construct the observation equations for orbit refinement. Assume the target motion satisfies the dynamic equations. , where the state vector Given an initial state Within the single-arc observation time interval, all angular measurement data under multi-satellite collaborative observation conditions are used as observations. Based on the orbital dynamics equations, the initial orbital state is improved, and the observation equations are expressed as follows: , in, , is the observation vector; These are theoretical observations calculated based on the observation model, representing the instantaneous state of the target. The function; This represents the difference between the theoretical value and the actual observed value caused by measurement error, and is usually considered to be a Gaussian white noise distribution.

[0037] Based on orbital propagation, the observations can be further represented as the initial state. Functions: , in, The theoretical observation value calculated based on the observation model represents the initial state of the target. The function.

[0038] S4.2, Under the least squares criterion, the optimal estimation of the target's initial state is achieved by minimizing the observation loss. The loss function is expressed as: , in, This represents the difference between the actual observed value and the theoretical observed value, i.e., the observation residual.

[0039] Due to the nonlinear characteristics of the observation equation, the observation equation at initial values... Performing first-order linearization at the point yields a linear expression for the residuals: .

[0040] S4.3, let , The observation equation can then be written as: , Among them, the observation matrix Defined as: .

[0041] S4.4, the correction is solved using the iterative least squares method: , And update the initial state: , Repeat the iterations until the convergence condition is met. , This is the preset convergence threshold.

[0042] S4.5, the orbit refinement method described above can significantly improve the accuracy of single-arc initial orbit determination. Specifically, based on the initial orbit solution of the Lambert problem for two-body orbits, more observational data from space-based platforms are introduced to participate in the orbit refinement process, fully utilizing the observational geometric constraints of each space-based platform to strengthen the orbit observation matrix. The strength of the orbit is further enhanced to improve the accuracy and stability of orbit determination.

[0043] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0045] like Figure 1 As shown in the figure, the specific implementation process of the space-based dual-multi-satellite collaborative observation method for ultra-short arc precision orbit determination of unknown targets provided in this embodiment of the invention is as follows.

[0046] The first step is to acquire observation data under dual / multi-satellite collaborative observation conditions and process the angle observation data acquired by each observation platform. The space-based optical angle observation error is 4″ (arcseconds). The orbital parameters of the space-based platform and the orbital parameters of the observed target are shown in Table 1. Combining the known positions of the observation platforms, and using the collaborative observation conditions of dual / multi-satellite observation platforms, the spatial position information of the observed target is calculated at the same time using the intersection relationship of multiple lines of sight, forming a position sequence of the target at multiple discrete moments.

[0047] Table 1. Parameters of the orbits of the space-based platform and the target. .

[0048] The second step involves selecting several observation points at the beginning and end of the collaborative observation arc to construct multiple sets of observation point combinations. For each set of observation points, the initial orbital parameters of the target are calculated using the two-point orbit determination method, and reasonable physical constraints (such as orbital eccentricity range limitations) are applied to the calculation results to obtain multiple candidate initial orbital solutions. Subsequently, each candidate orbit is propagated and compared with the observation data. The optimal initial orbital solution is selected through error evaluation indicators and used as the initial value for subsequent orbital refinement. The initial orbital determination results are shown in Tables 2 and 3. In the tables, "Observation Platform 1–2" represents the initial orbit determined by the observation data obtained by Platform 1 and Platform 2 under collaborative observation conditions, and the rest are similar.

[0049] Table 2 Initial orbit determination results from collaborative observations across different platforms over 20 seconds .

[0050] Table 3. Initial orbit determination results of 30s from collaborative observations across different platforms .

[0051] The third step involves refining the orbit based on the initial trajectory. A corresponding dynamic model is established according to the near-Earth space orbit region where the target is located.

[0052] The fourth step involves constructing observation equations by combining the state information within the observed arc segment. The initial state is iteratively corrected using the least squares method, continuously reducing the residual between the observed values ​​and the model predictions until the convergence condition is met, thus obtaining the refined orbit state. All observation data from more platforms are incorporated into the refinement process to further improve the accuracy and stability of orbit determination. After successful single-arc orbit determination, a 120-second prediction is made, and the accuracy of orbit determination and prediction is evaluated using the reference orbit of the observed target. The results are shown in Tables 4 and 5.

[0053] Table 4. Accuracy of orbit determination under 20s conditions of collaborative observation. .

[0054] Table 5. Accuracy of orbit determination under 30s collaborative observation conditions. .

[0055] The number of arc segments represents the number of collaborative observation platforms involved in orbit determination (1 indicates a set of collaborative observation data formed by two observation platforms, and so on). The results in the table show that, under different collaborative observation arc lengths, the orbit determination and prediction accuracy corresponding to a 30-s collaborative observation arc length is generally better than that of a 20-s collaborative observation arc length. As the number of observation platforms increases, both orbit determination and prediction accuracy show an improving trend; however, when the number of platforms reaches a certain scale, the improvement in accuracy tends to saturate, and further increasing the number of observation platforms no longer significantly improves accuracy. Figure 2 The trend curves of relevant accuracy indices as a function of the number of platforms are presented under the condition of a 30s arc length for collaborative observation. It is clear from the figure that when the number of platforms is small, increasing the number of observation platforms effectively enhances the geometric constraints of the observation, thereby significantly improving orbit determination and prediction accuracy; the accuracy improvement is quite significant. However, when the number of platforms increases to a certain extent, the curves gradually flatten out, consistent with the analysis results in the table.

[0056] Based on the same inventive concept as the foregoing method embodiments, this embodiment of the invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program. When the processor executes the computer program, it performs the following steps:

[0057] Step S1: Utilize collaborative observation data from two or more space-based optical observation platforms on the same unknown target to obtain the spatial position and angle observations of each platform, construct a unit vector of the line of sight direction, construct a linear observation equation using vector collinearity constraints, and solve for the spatial position of the target at each observation time using least squares to form a discrete position sequence.

[0058] Step S2: Select observation points from the beginning and end of the discrete position sequence to form a set of starting positions and a set of ending positions, combine them in pairs to form multiple sets of positions, construct a Lambert problem based on a two-body orbit and solve the orbit parameters to obtain a set of candidate orbit solutions, apply constraints to the candidate orbits and use the root mean square of the observation residuals as an evaluation index to select the optimal initial orbit.

[0059] Step S3: Determine the near-Earth space orbit region to which the target belongs based on the position and velocity information of the optimal initial orbit, and configure the dynamic model parameters that match the determined orbit region.

[0060] Step S4: Construct the observation equations for orbit refinement, using all angle measurement data under the cooperative observation conditions as observations, and iteratively correct the initial state under the least squares criterion until the convergence condition is met, to obtain the refined orbit state.

[0061] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), or an application-specific integrated circuit (ASIC). The memory can be a read-only memory (ROM), a random access memory (RAM), flash memory, or a hard disk, etc.

[0062] In practical applications, this electronic device can be integrated into the ground data processing system of a space-based observation platform or deployed in the satellite's on-orbit computing unit for real-time or near-real-time processing of multi-satellite collaborative observation data.

[0063] Based on the same inventive concept as the foregoing method embodiments, this embodiment of the invention also provides a computer-readable storage medium storing a computer program thereon. When the program is executed by a processor, it implements all the steps of the above-described method for precise orbit determination of an unknown target using a dual-satellite collaborative observation system.

[0064] The storage media include, but are not limited to, USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0065] In a specific application scenario, ground operators insert a USB flash drive or CD containing the computer program into the ground station computer. After the computer loads the program, it automatically reads the collaborative angle measurement data transmitted from the space-based optical observation platform, performs orbit determination calculations, and outputs the target orbit parameters.

[0066] Based on the same inventive concept as the foregoing method embodiments, this invention also provides a computer program product, including a computer program. When executed by a processor, the computer program implements all the steps of the aforementioned method for precise orbit determination of an unknown target using a dual-satellite collaborative observation system.

[0067] The computer program product may be provided in the form of a software package, an application (APP), or firmware. Users can obtain the computer program product by downloading it from a network or through physical media, and install and run it on a general-purpose computer, server, or embedded device.

[0068] In one embodiment, the computer program product is deployed on a cloud service platform. The space-based observation platform uploads real-time angle measurement data to the cloud server. After the cloud server loads the computer program product, it automatically performs orbit determination calculations and pushes the refined orbit status to the user terminal in real time.

[0069] In summary, the present invention targets low-Earth orbit targets by using multi-platform space-based optical observation equipment to acquire target observation data, thereby determining the initial orbit of unknown targets, obtaining their prior coarse orbit parameters, and refining the orbit based on the orbit dynamics model, thus improving the accuracy of orbit determination.

[0070] This invention deploys two or more space-based optical observation platforms in near-Earth space. During the observation period, through reasonable observation scheduling and the setting of the line-of-sight directions of the optical telescopes, it ensures that at least two observation optical platforms can conduct collaborative observations of the same target, recording the target's angular observation data sequence (generally right ascension and declination observation values) at a certain observation frequency. Based on the geometric relationship of multi-satellite collaborative observation, the line-of-sight directions are constructed and spatial geometry is restored. By converging the directions of multiple lines of sight at the same observation time, the spatial position information of the target at each observation time is calculated, thus forming a discrete position sequence of the target. On this basis, the Gooding initial orbit determination method based on the Lambert problem at the first and last points is used to obtain the initial orbit parameters of the observed target, and the optimal initial orbit solution is selected by combining orbital physical constraints and initial orbit determination residual evaluation indicators. Subsequently, based on the dynamic characteristics of the near-Earth space target, an orbital dynamic model under conservative and non-conservative force constraints is established, observation equations are constructed, and the initial orbit parameters are iteratively corrected using the least squares method to achieve orbit refinement under perturbation conditions. During the orbit refinement process, all available space-based optical angle measurement data are used to calculate the orbit. The complementarity of multi-satellite observation information in various spatial geometries is utilized to effectively enhance the constraint capability of the orbit solution, thereby further improving the accuracy and stability of the orbit determination.

[0071] 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 or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for precise orbit determination of an unknown target using ultra-short arcs through space-based dual-multi-satellite collaborative observation, characterized in that... include: By utilizing the collaborative observation data of two or more space-based optical observation platforms on the same unknown target, the spatial position and angle observations of each platform are obtained, a line-of-sight direction unit vector is constructed, a linear observation equation is constructed using vector collinearity constraints, and the spatial position of the target at each observation time is solved by least squares to form a discrete position sequence. Observation points are selected from the beginning and end of the discrete position sequence to form a set of starting positions and a set of ending positions. These are then combined in pairs to form multiple sets of positions. A Lambert problem based on a two-body orbit is constructed and the orbital parameters are solved to obtain a set of candidate orbit solutions. Constraints are applied to the candidate orbits and the root mean square of the observation residuals is used as an evaluation index to select the optimal initial orbit. Based on the position and velocity information of the optimal initial orbit, the near-Earth space orbit region to which the target belongs is determined, and dynamic model parameters matching the determined orbit region are configured. The observation equations for orbit refinement are constructed, and all angle measurement data under the cooperative observation conditions are used as observations. The initial state is iteratively corrected under the least squares criterion until the convergence condition is met, and the refined orbit state is obtained.

2. The method for precise orbit determination of an unknown target using space-based dual-multi-satellite collaborative observation as described in claim 1, characterized in that, The process of forming a discrete position sequence includes: constructing a line-of-sight direction unit vector based on the right ascension and declination angle observations obtained from each observation platform; using the spatial position of each observation platform in the TOD coordinate system and the aforementioned line-of-sight direction unit vector, eliminating unknown distance parameters through vector collinearity constraints, and deriving a linear observation equation about the target position; superimposing the linear observation equations of multiple platforms at the same time to form an overdetermined system of equations, and using least squares to solve for the optimal estimate of the target's spatial position at that time; and repeating the steps of constructing the line-of-sight direction unit vector based on the angle observations, deriving the linear observation equations, superimposing the system of equations, and using least squares to solve for multiple collaborative observation times to construct a discrete trajectory sequence of the target.

3. The method for precise orbit determination of an unknown target using space-based dual-multi-satellite collaborative observation as described in claim 1, characterized in that, The optimal initial orbit is selected by: selecting observation points from the first and last quarter portions of the arc segment to form a set of starting and ending positions; combining the points in the starting and ending positions in pairs to form multiple position pairs; for each position pair, using the Gooding method to solve the Lambert problem based on the two-body orbit to obtain the six root numbers of candidate orbits; applying constraints to the candidate orbits to obtain a set of candidate orbit solutions; performing orbit propagation on each candidate orbit solution, calculating the root mean square of the observation residuals between the predicted and actual positions at all observation points, and selecting the candidate orbit solution with the smallest root mean square as the optimal initial orbit.

4. The method for precise orbit determination of an unknown target using space-based dual-multi-satellite collaborative observation as described in claim 1, characterized in that, The refined orbital state is obtained by: assuming the target motion satisfies the dynamic equations, and the state vector includes position and velocity; using all angle measurement data under multi-satellite collaborative observation conditions as observations, constructing an observation equation with the target's initial state as the variable, and defining the loss function as the sum of squares of the observation residuals; performing first-order linearization on the observation equation at the initial estimate to obtain the linearized residual expression; using the iterative least squares method to solve for the state correction and update the initial state estimate, repeating the iteration until the magnitude of the correction is less than the preset convergence threshold.

5. The method for precise orbit determination of an unknown target using space-based dual-multi-satellite collaborative observation as described in claim 4, characterized in that, During the initial orbit refinement process, collaborative observation data from two or more space-based platforms are introduced, and the observation equations of each platform are superimposed to construct an observation matrix.

6. The method for precise orbit determination of an unknown target using space-based dual-multi-satellite collaborative observation as described in claim 2, characterized in that, The coefficient matrix in the linear observation equation is an antisymmetric matrix sub-block corresponding to the cross product operation constructed using the line-of-sight direction vector, and the constant term is composed of the cross product result of the line-of-sight direction vector and the position of the observation platform.

7. The method for precise orbit determination of an unknown target using space-based dual-multi-satellite collaborative observation as described in claim 4, characterized in that, The observation matrix in the iterative least squares consists of a product of two parts: the first part is the partial derivative of the observation model with respect to the instantaneous state vector of the target, and the second part is the partial derivative of the instantaneous state vector with respect to the initial state vector. The second part is calculated through the state transition matrix of the dynamic equation.

8. An electronic device comprising a processor and a memory, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method of any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

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