Space-based optical observation high-orbit space debris short-arc initial orbit determination method and system

Abstract

The present application provides a kind of space debris short arc initial orbit determination method and system for space-based optical observation high orbit, comprising: step S1: the angle measuring information of the same unidentified space debris imaging by space-based optical observation platform is obtained;Step S2: according to the observation ability of space-based optical observation platform, observation data is obtained, and the upper limit and lower limit of the distance of high-orbit space debris from space-based observation platform are set;Step S3: according to the observation data, the upper limit and lower limit of the actual observation distance corresponding to the observation arc segment are calculated;Step S4: within the upper limit and lower limit of the actual observation distance, a plurality of groups of particles are randomly initialized;Step S5: the loss function corresponding to each group of particles is calculated;Step S6: each group of particles is updated, and the loss function corresponding to the updated particle is calculated, and each optimal particle and global optimal particle are recorded;Step S7: repeat step S6 until the exit loop condition is met.The present application is simple to implement, and can improve the success rate of space debris short arc initial orbit determination for high orbit.

Description

Technical Field

[0001] This invention relates to the field of orbit determination technology, specifically to a method and system for determining the initial orbit of a short arc of high-orbit space debris observed by space-based optical observation. Background Technology

[0002] Since the launch of the first artificial satellite, space debris in Earth's orbit has been increasing. The presence of space debris poses a serious threat to spacecraft operating normally in orbit, necessitating monitoring of their orbits. Currently, space debris monitoring primarily relies on ground-based equipment, such as ground-based astronomical telescopes and ground-based radar. However, ground-based equipment is affected by geographical location, has periods of invisibility, and its observations are influenced by the Earth's atmosphere. In contrast, space-based observation can effectively improve observation conditions, especially for observing high-orbit space debris. Optical cameras, due to their ease of achieving low power consumption, high resolution, and wide field-of-view coverage, have important applications in the field of space debris monitoring.

[0003] Space-based optical cameras can only acquire relative angular measurement information of the target in a single image capture. For initial orbit determination based solely on angular measurement data, several methods exist, including the Gauss method, the Laplace method, the constrained domain method, and the dual-distance search method. Reference 1 (Liu Lin, Initial Orbit Calculation Method Considering Earth's Oblateness Perturbation, Acta Astronomica Sinica, 2003, Vol. 44, No. 2) presents a Laplace initial orbit determination method considering oblateness perturbation. Reference 2 (Liu Xiangchun, Research on Space Debris Orbit Determination Method Based on Space-Based Photographic Tracking, 2009, National University of Defense Technology, Master's Thesis) presents a Laplace initial orbit calculation method. Reference 3 (Liu Lei, Research on Initial Orbit Determination of Space Target Direction Finding Based on Space-Based Surveillance, 2010, National University of Defense Technology, Doctoral Dissertation) focuses on the application and corresponding improvements of the dual-distance iteration method, the Gauss method, and the Laplace method in space-based direction finding initial orbit determination. Reference 4 (Wang Xueying, A method for positioning space-based optical GEO targets and geometric evaluation of initial orbit algorithm observations, Aerospace Control, 2012, Vol. 30, No. 2) uses the generalized Laplace initial orbit algorithm to process multiple observation arcs of space-based optical multi-platforms to locate targets in the GEO region. Reference 5 (Zhang Pin, A method for determining the initial orbit of space targets using only angle observations, 2017, Wuhan University, Master's Thesis) studies the application effectiveness of the Gauss method, Gooding method, and dual-distance search numerical method in space-based optical observation systems. Reference 6 (Huang Pu, A method for calculating the initial orbit of low-orbit satellites to high-orbit satellites using only angle measurement, Flight Mechanics, 2020, Vol. 38, No. 1) establishes an extended Laplace dynamic model to solve for the initial orbit. Reference 7 (Zhao Kexin, Initial Orbit Determination Problem and Method for Space-Based Optical Space Target Monitoring, Acta Aeronautica Sinica, 2022, Vol. 44, No. 1) addresses the phenomenon that traditional Laplace-type initial orbit determination methods converge to the observation platform's orbit, providing a mathematical representation of trivial solutions and improving the original Laplace octet equation into a septet equation. Reference 8 (Zhao Kexin, A New Method for Space-Based Initial Orbit Determination Using 3rd Azimuth Observation, Acta Astronomica Sinica, 2022, Vol. 63, No. 5) derives the analytical form of the slant range condition equation based on the improved Gauss equations, and uses orbital energy constraints to eliminate singularities in the equation system during the solution process. References 9 (Li Xinran, A Shortest Arc Orbit Determination Method Based on Evolutionary Computation, Doctoral Dissertation, University of Science and Technology of China, 2018) and 10 (Li Xinran, A Shortest Arc Orbit Determination Based on Particle Swarm Optimization, Journal of Aircraft Measurement and Control, 2015, Vol. 34, No. 6) studied the shortest arc orbit determination problem from an evolutionary perspective, constructed a 3-parameter (a, e, and M in Kepler roots) optimization model, and implemented algorithms based on three different evolutionary mechanisms: genetic algorithm, particle swarm optimization algorithm, and differential evolution algorithm.Reference 11 (Song Kezhen, A method for determining extremely short arc space-based orbits based on genetic algorithm, Spacecraft Engineering, 2019, Vol. 28, No. 5) optimizes the solution of the six parameters a, e, M and i, Ω, ω in two steps based on the genetic algorithm. Reference 12 (Chen Long, Non-cooperative common-view observation and initial orbit determination of LEO space targets, Acta Optica Sinica, Vol. 41, No. 19) presents a method for determining the initial orbit of the same target using both ground-based optical and laser observations. When the observation data comes from different stations and includes laser observation data, the constraint on the target is strong, thus obtaining a high-precision initial orbit determination result. However, this method is not well applicable to short arc data from space-based observations. Reference 13 (Du Xiaoning, Spacecraft Initial Orbit Optimization Model Based on Particle Swarm Optimization Algorithm, Journal of Harbin Institute of Technology, Vol. 43, No. 5) proposes a spacecraft initial orbit optimization model based on particle swarm optimization algorithm. This model is oriented towards the measurement and control accuracy of telemetry and control equipment, multiple sets of orbital elements, system objective equations and particle swarm optimization algorithm. It is not applicable to angle-only data for short arc segments.

[0004] The invention patent with publication number CN103927289A discloses a method for determining the initial orbit of a low-Earth orbit target satellite based on space-based satellite angle measurement data. This method uses the angle measurement data of a high-speed moving low-Earth orbit target satellite relative to a low-Earth orbit observation satellite to obtain the conditional equation of the observation line vector. Based on the traditional Laplace method, certain constraints are added to form a conditional equation containing constraints for iteration.

[0005] The invention patent with publication number CN115828037A discloses a method and system for determining the initial orbit of space debris on a space-based optical monitoring platform. Based on the search of the distance between the start and end points of the arc segment, an optimization model is constructed, and the optimal solution is calculated by performing multiple sets of initialization and iteration on the distance between the start and end points.

[0006] Determining the initial short-arc orbit of space debris is challenging due to insufficient geometric constraints and the existence of trivial solutions. To further improve the success rate of determining the initial short-arc orbit of high-orbit space debris, this invention proposes a novel solution model tailored to the orbital characteristics of high-orbit space debris. This model combines quantum particle swarm optimization (QPSO) with a two-dimensional solution space defined by distance and the rate of change of distance to achieve optimal solution. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method and system for determining the initial short-arc orbit of high-orbit space debris in space-based optical observation.

[0008] According to the present invention, a method and system for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation are provided, the scheme of which is as follows:

[0009] Firstly, a method for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation is provided, the method comprising:

[0010] Step S1: Obtain angular measurement information of the image of the same unidentified space debris from the space-based optical observation platform;

[0011] Step S2: Based on the observation capabilities of the space-based optical observation platform, acquire observation data and set the upper and lower limits of the distance between high-orbit space debris and the space-based observation platform;

[0012] Step S3: Based on the observation data, calculate the upper and lower limits of the actual observation distance for the corresponding arc segment in this observation;

[0013] Step S4: Within the upper and lower limits of the actual observation distance, randomly initialize multiple sets of particles;

[0014] Step S5: Calculate the loss function for each group of particles;

[0015] Step S6: Update each group of particles, calculate the loss function corresponding to the updated particles, and record the best particle in each group and the global best particle.

[0016] Step S7: Repeat step S6 until the loop exit condition is met.

[0017] Preferably, the lower limit of the observation distance corresponding to the space-based optical observation platform in step S2 is L. min In step S3, the lower limit ρ of the actual observation distance corresponding to this arc segment min =L min .

[0018] Preferably, the upper limit of the observation distance corresponding to the space-based optical observation platform in step S2 is L. max The lower limit is L min In step S3, the upper limit of the observation distance ρ corresponds to this time. max The calculation is as follows:

[0019] Step S3.1: Let the distance between the space debris and the observation platform be ρ = L. max Calculate the location of the space debris :

[0020]

[0021] in, This is the position vector of the space-based optical observation platform itself. The pointing vector of the space debris relative to the space-based optical observation platform is calculated from right ascension and declination;

[0022] Step S3.2: Calculate the composite velocity vector Its definition is:

[0023]

[0024] in, This is the velocity vector of the space-based optical observation platform itself. It is a vector pointing to change.

[0025] Step S3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max If the calculation is complete, proceed to step S3.4; otherwise, proceed to step S3.4.

[0026]

[0027] in, Representing vectors with vector The inner product, Representing vectors Inner product with itself; μ e It is the gravitational constant;

[0028] Step S3.4: Use the bisection method to find L min ~L max Within the range, the value of the distance ρ corresponding to the zero point in formula 3) is ρ. max .

[0029] Preferably, in step S3.2, the direction of the change vector is... The calculation is performed using the difference approximation of the observed data, i.e.

[0030]

[0031] Where Δt is the time interval, calculated by taking two observations that are adjacent in time within an observation arc segment.

[0032] Preferably, the particle initialization in step S4 includes:

[0033] Step S4.1: Set the number of groups N;

[0034] Step S4.2: For the i-th particle in the group, i = 1, 2, ..., N, the distance range ρ obtained in step S3 is... min ~ρ max A value ρ is randomly generated inside. i ;

[0035] Step S4.3: Calculate the position ρ i The corresponding rate of change of distance dρ i / dt upper limit and lower limit

[0036] Step S4.4: Within the range of distance change rate A value is randomly generated inside.

[0037] Preferably, the distance change rate dρ in step S4.3 i / dt upper limit and lower limit The calculation method is as follows:

[0038]

[0039] Where, μ e r is the gravitational constant; r is the position vector. The size, i.e., the modulus,

[0040] Preferably, the loss function f corresponding to the particle in step S5 is set to

[0041]

[0042] Where M represents the number of samples within a short arc segment of space-based optical observation, i.e., the number of samples within a short arc segment. Let j be the measured value of the pointing vector at the j-th sampling point. For ρ, The estimated pointing vector value of the orbital position deduced from the determined orbit relative to the measured position of the space-based optical observation platform. This represents the inner product operation of two vectors, where arccos is the inverse cosine function, and e is the product of ρ, The eccentricity corresponding to a given trajectory, where α is the weighting coefficient;

[0043] If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned the value π+α.

[0044] Preferably, the loop exit condition in step S7 includes:

[0045] The maximum number of iterations has been reached;

[0046] Or the loss function value corresponding to the current global optimal position is less than the set threshold.

[0047] Secondly, a space-based optical observation system for determining the initial short-arc orbit of high-orbit space debris is provided, the system comprising:

[0048] Module M1: Acquires angular measurement information from the space-based optical observation platform for imaging the same unidentified space debris;

[0049] Module M2: Based on the observation capabilities of the space-based optical observation platform, acquire observation data and set the upper and lower limits of the distance between high-orbit space debris and the space-based observation platform;

[0050] Module M3: Based on the observation data, calculate the upper and lower limits of the actual observation distance for the corresponding arc segment in this observation.

[0051] Module M4: Randomly initializes multiple sets of particles within the upper and lower limits of the actual observation distance;

[0052] Module M5: Calculates the loss function for each group of particles;

[0053] Module M6: Updates each group of particles, calculates the loss function corresponding to the updated particles, and records the best particle in each group and the global best particle;

[0054] Module M7: Repeat module M6 until the exit loop condition is met.

[0055] Preferably, the lower limit of the observation distance corresponding to the space-based optical observation platform in module M2 is L. min In module M3, the lower limit ρ of the actual observation distance corresponding to this arc segment min =L min ;

[0056] The upper limit of the observation distance corresponding to the space-based optical observation platform in module M2 is L. max The lower limit is L min In module M3, the upper limit ρ corresponding to the current observation distance is... max The calculation is as follows:

[0057] Module M3.1: Let the distance ρ = L between the space debris and the observation platform. max Calculate the location of the space debris

[0058]

[0059] in, This is the position vector of the space-based optical observation platform itself. The pointing vector of the space debris relative to the space-based optical observation platform is calculated from right ascension and declination;

[0060] Module M3.2: Calculate the composite velocity vector Its definition is:

[0061]

[0062] in, This is the velocity vector of the space-based optical observation platform itself. It is a vector pointing to change.

[0063] Module M3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max If the calculation is complete, then proceed to module M3.4.

[0064]

[0065] in, Representing vectors with vector The inner product, Representing vectors Inner product with itself; μ e It is the gravitational constant;

[0066] Module M3.4: Using the binary search method in L min ~L max Within the range, the value of the distance ρ corresponding to the zero point in formula 3) is ρ. max ;

[0067] The pointing change vector in module M3.2 The calculation is performed using the difference approximation of the observed data, i.e.

[0068]

[0069] Where Δt is the time interval, calculated by taking two observations that are adjacent in time within an observation arc segment;

[0070] Particle initialization in module M4 includes:

[0071] Module M4.1: Set the number of groups N;

[0072] Module M4.2: For the i-th particle in the group, i = 1, 2, ..., N, the distance range ρ obtained in Module M3 is... min ~ρ max A value ρ is randomly generated inside. i ;

[0073] Module M4.3: Calculate position ρ i The corresponding rate of change of distance dρ i / dt upper limit and lower limit

[0074] Module M4.4: In the range of distance change rate A value is randomly generated inside.

[0075] The distance change rate dρ in module M4.3 i / dt upper limit and lower limit The calculation method is as follows:

[0076]

[0077] Where, μ e r is the gravitational constant; r is the position vector. The size, i.e., the modulus,

[0078] The loss function f corresponding to the particles in module M5 is set as follows:

[0079]

[0080] Where M represents the number of samples within a short arc segment of space-based optical observation, i.e., the number of samples within a short arc segment. Let j be the measured value of the pointing vector at the j-th sampling point. For by ρ The estimated pointing vector value of the orbital position deduced from the determined orbit relative to the measured position of the space-based optical observation platform. This represents the inner product operation of two vectors, where arccos is the inverse cosine function, and e is the product of ρ, The eccentricity corresponding to a given trajectory, where α is the weighting coefficient;

[0081] If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned the value π+α;

[0082] The loop exit conditions in module M7 include:

[0083] The maximum number of iterations has been reached;

[0084] Or the loss function value corresponding to the current global optimal position is less than the set threshold.

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] 1. This invention addresses the problems of insufficient geometric constraints and the existence of trivial solutions in determining the initial short-arc orbit of high-orbit space debris in space-based optical observations. It constructs a new solution model that incorporates constraints on orbital eccentricity and introduces constraints on observation distance and orbit rationality in the optimization process, thereby significantly improving the success rate of determining the initial short-arc orbit of high-orbit space debris.

[0087] 2. The method of the present invention is reasonable, simple to calculate, and easy to implement. It can be effectively applied to the determination of the initial short arc trajectory of high-orbit space debris under space-based angular measurement data only.

[0088] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

[0089] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0090] Figure 1 This is a flowchart of the present invention;

[0091] Figures 2a to 2k Determine the particle changes during the iterative process for an initial trajectory of a short arc segment;

[0092] Figures 3a to 3k Determine the changes of the optimal particle and the global optimal particle in each group during the iterative process for an initial trajectory of a short arc segment;

[0093] Figures 4a-4b The results show the positional error within the observation arcs used to determine the initial trajectory of 7232 short arcs;

[0094] Figures 5a-5b The results show the relative error of the semi-major axis of the track for initial track determination of 7232 short arc segments. Detailed Implementation

[0095] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0096] This invention provides a method for determining the initial orbit of a short arc of high-orbit space debris in space-based optical observations, referring to... Figure 1 As shown, the method specifically includes the following:

[0097] Step S1: Obtain the angular measurement information of the image of the same unidentified space debris by the space-based optical observation platform, including the imaging time, the position and velocity of the space-based optical observation platform in the epoch geocentric celestial coordinate system, and the pointing information (right ascension and declination) of the space debris relative to the space-based optical observation platform in the epoch geocentric celestial coordinate system.

[0098] Step S2: Based on the observation capabilities of the space-based optical observation platform, acquire observation data and set the upper and lower limits of the distance between high-orbit space debris and the space-based observation platform.

[0099] In step S2, the lower limit of the observation distance corresponding to the space-based optical observation platform is L. min In step S3, the lower limit ρ of the actual observation distance corresponding to this arc segment min =L min .

[0100] Step S3: Based on the observation data, calculate the upper and lower limits of the actual observation distance for the corresponding arc segment in this observation.

[0101] Specifically, the upper limit of the observation distance corresponding to the China-space-based optical observation platform is L. max The lower limit is L min In this step, the upper limit of the observation distance ρ corresponds to. max The calculation is as follows:

[0102] Step S3.1: Let the distance between the space debris and the observation platform be ρ = L. max Calculate the location of the space debris :

[0103]

[0104] in, This is the position vector of the space-based optical observation platform itself. The pointing vector (unit vector) of the space debris relative to the space-based optical observation platform is calculated from right ascension and declination;

[0105] Step S3.2: Calculate the composite velocity vector Its definition is:

[0106]

[0107] in, This is the velocity vector of the space-based optical observation platform itself. It is a vector pointing to change.

[0108] Pointing to the changing vector The calculation is performed using the difference approximation of the observed data, i.e.

[0109]

[0110] Where Δt is the time interval, calculated by taking two observations that are adjacent in time within an observation arc segment.

[0111] Step S3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max If the calculation is complete, proceed to step S3.4; otherwise, proceed to step S3.4.

[0112]

[0113] in, Representing vectors with vector The inner product, Representing vectors Inner product with itself; μ e μ is the gravitational constant of the Earth's core. e =3.986004418×10 14 m 3 / s 2 .

[0114] Step S3.4: Use the bisection method to find L min ~L max Within the range, the value of the distance ρ corresponding to the zero point in formula 3) is ρ. max .

[0115] Step S4: Within the upper and lower limits of the actual observation distance, randomly initialize multiple sets of particles.

[0116] Particle initialization includes:

[0117] Step S4.1: Set the number of groups N;

[0118] Step S4.2: For the i-th particle in the group, i = 1, 2, ..., N, the distance range ρ obtained in step S3 is... min ~ρ max A value ρ is randomly generated inside. i ;

[0119] Step S4.3: Calculate the position ρ i The corresponding rate of change of distance dρ i / dt upper limit and lower limit

[0120] Distance change rate dρ i / dt upper limit and lower limit The calculation method is as follows:

[0121]

[0122] Where, μ e r is the gravitational constant; r is the position vector. The size, i.e., the modulus,

[0123] Step S4.4: Within the range of distance change rate A value is randomly generated inside.

[0124] Step S5: Calculate the loss function for each group of particles.

[0125] The loss function f corresponding to the particle in step S5 is set as follows:

[0126]

[0127] Where M represents the number of samples within a short arc segment of space-based optical observation, i.e., the number of samples within a short arc segment. Let j be the measured value of the pointing vector at the j-th sampling point. For ρ, The estimated pointing vector value of the orbital position deduced from the determined orbit relative to the measured position of the space-based optical observation platform. This represents the inner product operation of two vectors, where arccos is the inverse cosine function, and e is the product of ρ, The eccentricity corresponding to a given orbit, where α is the weighting coefficient.

[0128] The value of the weighting coefficient α in the loss function is determined based on the angle measurement accuracy of the space-based optical observation. For a space-based optical observation platform with an angle measurement accuracy of δ (unit: rad), α can be δ / 2000.

[0129] If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned the value π+α.

[0130] Step S6: Use the Quantum Particle Swarm Optimization (QPSO) algorithm to update each group of particles, calculate the loss function corresponding to the updated particles, and record the best particle in each group and the global best particle.

[0131] Step S7: Repeat step S6 until the loop exit condition is met.

[0132] The conditions for exiting the loop include: (1) reaching the set upper limit of the number of iterations; (2) the loss function value corresponding to the current global optimal position is less than the set threshold. Meeting either one of these conditions is sufficient.

[0133] This invention also provides a system for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation. This system can be implemented by executing the steps of the method for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation. That is, those skilled in the art can understand the method for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation as a preferred embodiment of the system. Specifically, the system includes the following:

[0134] Module M1: Acquires angular measurement information of the image of the same unidentified space debris by the space-based optical observation platform, including the imaging time, the position and velocity of the space-based optical observation platform in the epoch geocentric celestial coordinate system, and the pointing information (right ascension and declination) of the space debris relative to the space-based optical observation platform in the epoch geocentric celestial coordinate system.

[0135] Module M2: Based on the observation capabilities of the space-based optical observation platform, acquire observation data and set the upper and lower limits of the distance between high-orbit space debris and the space-based observation platform.

[0136] The lower limit of the observation distance for the space-based optical observation platform in module M2 is L. min In module M3, the lower limit ρ of the actual observation distance corresponding to this arc segment min =L min .

[0137] Module M3: Based on the observation data, calculate the upper and lower limits of the actual observation distance for the corresponding arc segment in this observation.

[0138] Specifically, the upper limit of the observation distance corresponding to the China-space-based optical observation platform is L. max The lower limit is L min The upper limit ρ of the current observation distance in this module max The calculation is as follows:

[0139] Module M3.1: Let the distance ρ = L between the space debris and the observation platform. max Calculate the location of the space debris :

[0140]

[0141] in, This is the position vector of the space-based optical observation platform itself. The pointing vector (unit vector) of the space debris relative to the space-based optical observation platform is calculated from right ascension and declination;

[0142] Module M3.2: Calculate the composite velocity vector Its definition is:

[0143]

[0144] in, This is the velocity vector of the space-based optical observation platform itself. It is a vector pointing to change.

[0145] Pointing to the changing vector The calculation is performed using the difference approximation of the observed data, i.e.

[0146]

[0147] Where Δt is the time interval, calculated by taking two observations that are adjacent in time within an observation arc segment.

[0148] Module M3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max If the calculation is complete, then proceed to module M3.4.

[0149]

[0150] in, Representing vectors with vector The inner product, Representing vectors Inner product with itself; μ e μ is the gravitational constant of the Earth's core. e =3.986004418×10 14 m 3 / s 2 .

[0151] Module M3.4: Using the binary search method in L min ~L max Within the range, the value of the distance ρ corresponding to the zero point in formula 3) is ρ. max .

[0152] Module M4: Randomly initializes multiple sets of particles within the upper and lower limits of the actual observation distance.

[0153] Particle initialization includes:

[0154] Module M4.1: Set the number of groups N;

[0155] Module M4.2: For the i-th particle in the group, i = 1, 2, ..., N, the distance range ρ obtained in Module M3 is... min ~ρ max A value ρ is randomly generated inside. i ;

[0156] Module M4.3: Calculate position ρ i The corresponding rate of change of distance dρ i / dt upper limit and lower limit

[0157] Distance change rate dρ i / dt upper limit and lower limit The calculation method is as follows:

[0158]

[0159] Where, μ e r is the gravitational constant; r is the position vector. The size, i.e., the modulus,

[0160] Module M4.4: In the range of distance change rate A value is randomly generated inside.

[0161] Module M5: Calculates the loss function for each group of particles.

[0162] The loss function f for the particles in module M5 is set as follows:

[0163]

[0164] Where M represents the number of samples within a short arc segment of space-based optical observation, i.e., the number of samples within a short arc segment. For the j-th

[0165] The measured value of the pointing vector at each sampling point. For ρ, The estimated pointing vector value of the orbital position deduced from the determined orbit relative to the measured position of the space-based optical observation platform. This represents the inner product operation of two vectors, where arccos is the inverse cosine function, and e is the product of ρ, The eccentricity corresponding to a given orbit, where α is the weighting coefficient.

[0166] The value of the weighting coefficient α in the loss function is determined based on the angle measurement accuracy of the space-based optical observation. For a space-based optical observation platform with an angle measurement accuracy of δ (unit: rad), α can be δ / 2000.

[0167] If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned the value π+α.

[0168] Module M6: Utilizes the Quantum Particle Swarm Optimization (QPSO) algorithm to update each group of particles, calculates the loss function corresponding to the updated particles, and records the best particle in each group and the globally best particle.

[0169] Module M7: Repeat module M6 until the exit loop condition is met.

[0170] The conditions for exiting the loop include: (1) reaching the set upper limit of the number of iterations; (2) the loss function value corresponding to the current global optimal position is less than the set threshold. Meeting either one of these conditions is sufficient.

[0171] The present invention will now be described in more detail.

[0172] This invention provides a method for determining the initial short-arc trajectory of high-orbit space debris using space-based optical observation. For angular measurement information obtained from imaging the same unidentified space debris by a space-based optical observation platform, the method includes the imaging time, the position and velocity of the space-based optical observation platform in the epoch geocentric celestial coordinate system, and the pointing information (right ascension and declination) of the space debris relative to the space-based optical observation platform in the epoch geocentric celestial coordinate system. From this pointing information, the pointing vector (unit vector) of the space debris relative to the space-based optical observation platform can be calculated.

[0173] Location corresponding to space debris and speed satisfy

[0174]

[0175] in, Let ρ be the position and velocity vectors of the space-based optical observation platform, ρ be the distance between the space debris and the observation platform, and dρ / dt be the rate of change of distance. This is the direction of the changing vector. For angle-only data, ρ and dρ / dt are both unknown. It was not measured directly, but it can be determined based on the pointing vector sampled at multiple time points. Perform difference approximation, i.e.

[0176]

[0177] Δt is the time interval, which is generally calculated using two observations that are adjacent in time within an observation arc segment.

[0178] The unknowns ρ and dρ / dt can be further constrained based on the performance of the space-based optical observation platform and orbital constraints. Because the imaging characteristics of very close targets differ significantly on the space-based optical observation platform, there is a lower limit to the distance of space debris observation data generated by space-based optics. Simultaneously, based on the observation capabilities of the space-based optical observation platform, space debris that is too distant cannot be imaged or detected, thus there is an upper limit L in terms of distance. max The upper and lower distance limits here will be adaptively updated when applied to specific observation arc segments, meaning that the upper and lower limits here can be wider within an appropriate range.

[0179] Based on the geocentric two-body energy constraint, the actual observation distance range corresponding to the current observation arc segment can be calculated.

[0180]

[0181] Where r and v represent position vectors and velocity vector The size (i.e., the modulus), μ eμ is the gravitational constant of the Earth's core. e =3.986004418×10 14 m 3 / s 2 .

[0182] Formula 7 defines the velocity composition vector.

[0183]

[0184] Therefore, according to Formula 8, the upper limit of the distance ρ corresponding to this observation can be calculated. max And the rate of change corresponding to a certain distance ρ. The upper and lower limits. In the limit state, it satisfies Formula 8 and takes the extreme value 0, that is, at the limit, we have

[0185]

[0186] in, Representing vectors with vector The inner product, Representing vectors The inner product with itself. A reasonable ρ, Should meet

[0187]

[0188] If the current distance ρ = L max If formula 3 can be satisfied, then ρ max =L max The bisection method can be used to calculate L min ~L max The value of the distance ρ corresponding to the zero point in the range formula (3) is ρ. max .

[0189] Furthermore, for a distance ρ that satisfies Formula 3, the rate of change of distance dρ i / dt upper limit and lower limit satisfy

[0190]

[0191] After determining the above distance constraints, considering the orbital characteristics of high-orbit space debris, its orbital eccentricity is generally small, while the geometric constraints of short arcs observed by space-based observation are insufficient, and there may be many orbits close to the actual measured values. Therefore, based on the orbital characteristics of high-orbit space debris, this invention further constrains the optimization solution model by adding a factor of orbital eccentricity and adjusting it through certain weighting coefficients.

[0192] The loss function f is set as follows

[0193]

[0194] Where M represents the number of samples within a short arc segment of space-based optical observation, i.e., the number of samples within a short arc segment. Let j be the measured value of the pointing vector at the j-th sampling point. For ρ, The estimated pointing vector value of the orbital position deduced from the determined orbit relative to the measured position of the space-based optical observation platform. This represents the inner product operation of two vectors, where arccos is the inverse cosine function, and e is the product of ρ, The eccentricity corresponding to the determined orbit is α, which is a weighting coefficient. Modifying the weighting coefficient can adjust the contribution of the orbit eccentricity constraint to the final result. The value of the weighting coefficient α in the loss function is determined based on the angular measurement accuracy of the space-based optical observation. For a space-based optical observation platform with an angular measurement accuracy of δ (unit: rad), α can be taken as δ / 2000. If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned the value π+α.

[0195] Once the loss function and constraints are determined, the quantum particle swarm optimization method can be used to find the optimal solution, which is divided into particle initialization and particle update.

[0196] During particle initialization, the number of groups N is set, and multiple groups of particles are randomly initialized within the upper and lower limits of the observation distance. For the i-th particle in the group (i ranges from 1, 2, ..., N), the distance range ρ obtained in step 3 is... min ~ρ max A value ρ is randomly generated inside. i Calculate the position ρ i The corresponding rate of change of distance dρ i / dt upper limit and lower limit Then, within the range of distance change rate A value is randomly generated inside. Then calculate the loss function value for each group of particles.

[0197] The quantum particle swarm optimization algorithm is used to update each group of particles, and the loss function corresponding to the updated particles is calculated. The best particle in each group and the global best particle are recorded. This process is repeated iteratively until the set upper limit of the number of iterations is reached or the loss function value corresponding to the current global best position is less than the set threshold.

[0198] The effectiveness of the method of this invention is verified below using simulation data. The position vector of the space-based optical observation platform at UTC time 8 Oct 2023 04:00:00.000 is [-1112.378282, -2901.123076, -6517.729755] km, and the velocity vector is [-4.623190, -4.963830, 3.003524] km / s. Within an observation arc of 87 s, the angular measurement data error is 2”. The true values ​​of the position and velocity of the space debris are [-36652.861027, 19113.53058, -8133.468249] km and [-0.967179, -2.497631, -1.515569] km / s, respectively. Using the method of this invention, the particle changes during the iteration process are as follows: Figures 2a to 2k As shown, the changes between the optimal particle in each group and the global optimal particle are as follows: Figures 3a to 3k As shown. After 10 iterations, the initial trajectory calculation results are [-36641.85215378, 19106.63749558, -8132.25032856] km, [-0.96576251, -2.49704634, -1.51536152] km / s.

[0199] Furthermore, 7232 short arc segments formed by high-orbit space debris observations were generated through simulation using a space-based optical observation platform. The initial orbit determination method of this invention was applied to each of the 7232 arc segments, achieving a 100% success rate in initial orbit determination. The positional errors and statistical distribution within the observed arc segments are as follows: Figures 4a-4b As shown. The relative error of the semi-major axis of the trajectory determination results and the statistical results are as follows. Figures 5a-5b As shown.

[0200] This invention provides a method and system for determining the initial short-arc trajectory of high-orbit space debris using space-based optical observations. Addressing the issues of insufficient geometric constraints and the existence of trivial solutions in this method, a novel solution model is constructed. This model incorporates constraints related to orbital eccentricity and introduces constraints on observation distance and orbital rationality during the optimization process, significantly improving the success rate of determining the initial short-arc trajectory of high-orbit space debris. The method is reasonable, computationally simple, and easy to implement, and can be effectively applied to determining the initial short-arc trajectory of high-orbit space debris using only angular measurement data from space-based systems.

[0201] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0202] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation, characterized in that, include: Step S1: Obtain angular measurement information of the image of the same unidentified space debris from the space-based optical observation platform; Step S2: Based on the observation capabilities of the space-based optical observation platform, acquire observation data and set the upper and lower limits of the distance between high-orbit space debris and the space-based observation platform; Step S3: Based on the observation data, calculate the upper and lower limits of the actual observation distance for the corresponding arc segment in this observation; Step S4: Within the upper and lower limits of the actual observation distance, randomly initialize multiple sets of particles; Step S5: Calculate the loss function for each group of particles; Step S6: Update each group of particles, calculate the loss function corresponding to the updated particles, and record the best particle in each group and the global best particle. Step S7: Repeat step S6 until the loop exit condition is met; In step S2, the lower limit of the observation distance corresponding to the space-based optical observation platform is... In step S3, the lower limit of the actual observation distance for this arc segment is... ; The upper limit of the observation distance corresponding to the space-based optical observation platform in step S2 is: The lower limit is Step S3 corresponds to the upper limit of the observation distance for this time. The calculation is as follows: Step S3.1: Set the distance between the space debris and the observation platform. Calculate the location of the space debris : 1） in, This is the position vector of the space-based optical observation platform itself. The pointing vector of the space debris relative to the space-based optical observation platform is calculated from right ascension and declination; Step S3.2: Calculate the composite velocity vector Its definition is: 2） in, This is the velocity vector of the space-based optical observation platform itself. It is a vector pointing to change. Step S3.3: If the current distance If the following constraints are satisfied, then If the calculation is complete, proceed to step S3.4; otherwise, proceed to step S3.

4. 3） in, Representing vectors with vector The inner product, Representing vectors Its inner product with itself; It is the gravitational constant; Step S3.4: Use the bisection method in ~ Solving Formula 3 within the range) Distance corresponding to the zero point The value of is, that is ; In step S3.2, the direction of change vector The calculation is performed using the difference approximation of the observed data, i.e. 4） in, The time interval is calculated by taking two observations that are adjacent in time within an observation arc segment; The particle initialization in step S4 includes: Step S4.1: Set the number of groups N; Step S4.2: For the i-th particle in the group, i=1,2,…,N, the distance range obtained in step S3. ~ A value is randomly generated inside. ; Step S4.3: Calculate the position Corresponding distance change rate upper limit and lower limit ; Step S4.4: Within the range of distance change rate ~ A value is randomly generated inside. ; The rate of change of distance in step S4.3 upper limit and lower limit The calculation method is as follows: 5） in, It is the gravitational constant; Position vector The size, i.e., the modulus, .

2. The method for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation according to claim 1, characterized in that, The loss function corresponding to the particle in step S5 Set as 6） in, This refers to the number of samples within a short arc segment of space-based optical observations, i.e., the number of samples taken within a single short arc segment. For the first The measured value of the pointing vector at each sampling point. For the reason The estimated pointing vector value of the orbital position deduced from the determined orbit relative to the measured position of the space-based optical observation platform. This represents the dot product operation of two vectors. It is an inverse cosine function. For the reason The eccentricity corresponding to a given orbit These are the weighting coefficients; like If a reasonable trajectory cannot be calculated, the loss function is assigned the value of . .

3. The method for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation according to claim 1, characterized in that, The loop exit conditions in step S7 include: The maximum number of iterations has been reached; Or the loss function value corresponding to the current global optimal position is less than the set threshold.

4. A system for determining the initial short-arc orbit of high-orbit space debris using space-based optical observation, characterized in that, include: Module M1: Acquires angular measurement information from the space-based optical observation platform for imaging the same unidentified space debris; Module M2: Based on the observation capabilities of the space-based optical observation platform, acquire observation data and set the upper and lower limits of the distance between high-orbit space debris and the space-based observation platform; Module M3: Based on the observation data, calculate the upper and lower limits of the actual observation distance for the corresponding arc segment in this observation. Module M4: Randomly initializes multiple sets of particles within the upper and lower limits of the actual observation distance; Module M5: Calculates the loss function for each group of particles; Module M6: Updates each group of particles, calculates the loss function corresponding to the updated particles, and records the best particle in each group and the global best particle; Module M7: Repeat module M6 until the exit loop condition is met; The lower limit of the observation distance corresponding to the space-based optical observation platform in module M2 is: The lower limit of the actual observation distance for this arc segment in module M3. ; The upper limit of the observation distance corresponding to the space-based optical observation platform in module M2 is: The lower limit is The upper limit of the observation distance corresponding to this observation is in module M3. The calculation is as follows: Module M3.1: Sets the distance of space debris relative to the observation platform. Calculate the location of the space debris : 1） in, This is the position vector of the space-based optical observation platform itself. The pointing vector of the space debris relative to the space-based optical observation platform is calculated from right ascension and declination; Module M3.2: Calculate the composite velocity vector Its definition is: 2） in, This is the velocity vector of the space-based optical observation platform itself. It is a vector pointing to change. Module M3.3: If the current distance If the following constraints are satisfied, then If the calculation is complete, then proceed to module M3.

4. 3） in, Representing vectors with vector The inner product, Representing vectors Its inner product with itself; It is the gravitational constant; Module M3.4: Using the binary search method in ~ Solving Formula 3 within the range) Distance corresponding to the zero point The value of is, that is ; The pointing change vector in module M3.2 The calculation is performed using the difference approximation of the observed data, i.e. 4） in, The time interval is calculated by taking two observations that are adjacent in time within an observation arc segment; Particle initialization in module M4 includes: Module M4.1: Set the number of groups N; Module M4.2: For the i-th particle in the group, i=1,2,…,N, the distance range obtained in Module M3. ~ A value is randomly generated inside. ; Module M4.3: Calculate Location Corresponding distance change rate upper limit and lower limit ; Module M4.4: In the range of distance change rate ~ A value is randomly generated inside. ; The distance change rate in module M4.3 upper limit and lower limit The calculation method is as follows: 5） in, It is the gravitational constant; Position vector The size, i.e., the modulus, .

5. The space-based optical observation system for determining the initial short-arc orbit of high-orbit space debris according to claim 4, characterized in that, The loss function corresponding to the particles in module M5 Set as 6） in, This refers to the number of samples within a short arc segment of space-based optical observations, i.e., the number of samples taken within a single short arc segment. For the first The measured value of the pointing vector at each sampling point. For the reason The estimated pointing vector value of the orbital position deduced from the determined orbit relative to the measured position of the space-based optical observation platform. This represents the dot product operation of two vectors. It is an inverse cosine function. For the reason The eccentricity corresponding to a given orbit These are the weighting coefficients; like If a reasonable trajectory cannot be calculated, the loss function is assigned the value of . .

6. The space-based optical observation system for determining the initial short-arc orbit of high-orbit space debris according to claim 4, characterized in that, The loop exit conditions in module M7 include: The maximum number of iterations has been reached; Or the loss function value corresponding to the current global optimal position is less than the set threshold.

Images