Method and system for determining space-based optical observation high-orbit space debris short arc initial orbit

Abstract

The invention provides a space-based optical observation high-orbit space debris short arc initial orbit determination method and system. The method comprises the steps that S1, angle measurement information of imaging of the same unidentified space debris by a space-based optical observation platform is acquired; s2, acquiring observation data according to the observation capability of the space-based optical observation platform, and setting the upper limit and the lower limit of the distance between the high-orbit space debris and the space-based optical observation platform; s3, calculating an actual observation distance upper limit and an actual observation distance lower limit corresponding to the current observation arc section according to the observation data; s4, randomly initializing a plurality of groups of particles within the upper limit and lower limit range of the actual observation distance; s5, calculating a loss function corresponding to each group of particles; s6, updating each group of particles, calculating a loss function corresponding to the updated particles, and recording each group of optimal particles and global optimal particles; and step S7, repeating the step S6 until the cycle quitting condition is met. The method is easy to implement, and the success rate of determining the high-orbit space debris short arc initial orbit can be increased.

Description

Technical Field

[0001] The present invention relates to the field of orbit determination technology, and in particular to a method and system for determining the short arc initial orbit of high-orbit space debris by space-based optical observation. Background Art

[0002] Since the launch of the first artificial satellite, the number of space debris in the Earth's orbit has increased. The existence of space debris poses a serious threat to the normal operation of spacecraft in orbit, and its orbit needs to be monitored. At present, space debris monitoring mainly relies on ground-based equipment, such as ground-based astronomical telescopes and ground-based radars. Ground-based equipment is affected by the region, there is a certain period of invisibility, and observations will be affected by the Earth's atmosphere. In contrast, space-based observations can effectively improve observation conditions, especially for the observation of high-orbit space debris. Optical cameras have important applications in the field of space debris monitoring due to their low energy consumption, high resolution, and high field of view coverage.

[0003] In a single shot, a space-based optical camera can only obtain the relative angle measurement information of the target. There are several types of initial orbit determination for angle measurement observation data: Gauss method, Laplace method, constraint domain method, double distance search method, etc. Reference 1 (Liu Lin, Initial orbit calculation method considering the influence of the earth's flattening perturbation, Acta Astronomica Sinica, 2003, Vol. 44, No. 2) gives the Laplace initial orbit determination method considering the flattening perturbation. Reference 2 (Liu Xiangchun, Research on orbit determination method for space debris tracking by space-based photography, 2009, National University of Defense Technology, Master's degree thesis) gives the Laplace initial orbit calculation method. Reference 3 (Liu Lei, Research on initial orbit determination of space target direction finding based on space-based monitoring, 2010, National University of Defense Technology, Doctoral degree thesis) focuses on the application of double distance iteration method, Gauss method and Laplace method in space-based direction finding initial orbit determination and corresponding improvements. Reference 4 (Wang Xueying, A method for positioning space-based optical GEO targets and evaluation of initial orbit algorithm observation geometry, Aerospace Control, 2012, Vol. 30, No. 2) uses the generalized Laplace initial orbit algorithm to process the multi-observation arc segments 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 observation values, 2017, Wuhan University, Master's thesis) studies the application efficiency 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 a low-orbit satellite for a high-orbit satellite using only angle measurement, Flight Mechanics, 2020, Vol. 38, No. 1) establishes an extended Laplace dynamics model to solve the initial orbit. Reference 7 (Zhao Kexin, Problems and methods of initial orbit determination for space-based optical space target monitoring, Acta Aeronautica Sinica, 2022, Vol. 44, No. 1) gives a mathematical representation of the trivial solution to the phenomenon that the traditional Laplace type initial orbit determination method converges to the observation platform orbit, and improves the original Laplace octave equation to a septave equation for solution. Reference 8 (Zhao Kexin, A new method for space-based initial orbit determination using 3-dimensional azimuth observation, Acta Astronomica Sinica, 2022, Vol. 63, No. 5) Based on the improved Gauss equation, the analytical form of the slant range condition equation is derived, and the orbital energy constraint is used to eliminate the singularities of the equation group in the solution. Reference 9 (Li Xinran, Extremely short arc orbit determination method based on evolutionary computation, 2018, University of Science and Technology of China, doctoral dissertation) and Reference 10 (Li Xinran, Extremely short arc orbit determination based on particle swarm algorithm, Journal of Spacecraft Measurement and Control, 2015, Vol. 34, No. 6) studied the extremely short arc orbit determination problem from an evolutionary perspective, constructed a three-parameter (a, e, M in Kepler roots) optimization model, and implemented algorithms based on three different evolutionary mechanisms: genetic algorithm, particle swarm algorithm, and differential evolution algorithm.Reference 11 (Song Kezhen, Extremely short arc segment space-based orbit determination method based on genetic algorithm, Spacecraft Engineering, 2019, Vol. 28, No. 5) divides the six parameters a, e, M and i, Ω, ω into two steps for optimization and solution based on 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) gives a method for initial orbit determination of the same target for ground-based optical and laser observations. When the observation data comes from different stations and contains laser observation data, the intensive constraints on the target are stronger, so a higher-precision initial orbit determination result can be obtained. However, the short arc data of space-based observations are not well suited to this method. Reference 13 (Du Xiaoning, Spacecraft Initial Orbit Optimization Model Based on Particle Swarm Algorithm, Journal of Harbin Institute of Technology, Vol. 43, No. 5) proposes a spacecraft initial orbit optimization model based on particle swarm algorithm. This model is oriented to the measurement and control accuracy of measurement and control equipment, multiple sets of orbital roots, system objective equations and particle swarm algorithm, and is not applicable to short arc segments with only angle measurement data.

[0004] The invention patent with publication number CN103927289A discloses a method for determining the initial orbit of a low-orbit target satellite based on the angle measurement data of a space-based satellite. This method uses the angle measurement data of a high-speed moving low-orbit target satellite relative to a low-orbit observation satellite to obtain the conditional equation of the observation line of sight vector. Certain constraints are added to the traditional Laplace method 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 for a space-based optical monitoring platform. Based on the search for the distance between the starting point and the end point of the arc segment, an optimization model is constructed, and the optimal solution is calculated by initializing and iterating multiple groups of distances between the starting point and the end point.

[0006] The determination of the initial orbit of short arc of space debris is difficult to solve due to insufficient geometric constraints on the one hand and the existence of trivial solutions on the other hand. In order to further improve the success rate of the initial orbit determination of short arc of high-orbit space debris, this paper proposes a new solution model based on the orbit characteristics of high-orbit space debris, and combines the quantum particle swarm optimization algorithm to perform the optimal solution in the two-dimensional solution space composed of distance and distance change rate. Summary of the invention

[0007] In view of the defects in the prior art, the present invention provides a method and system for determining the initial orbit of a short arc of high-orbit space debris by space-based optical observation.

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

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

[0010] Step S1: obtaining the angle measurement information of the space-based optical observation platform imaging the same unidentified space debris;

[0011] Step S2: According to the observation capability of the space-based optical observation platform, the observation data is obtained, and the upper and lower limits of the distance between the high-orbit space debris and the space-based observation platform are set;

[0012] Step S3: Calculate the upper and lower limits of the actual observation distance corresponding to the current observation arc segment according to the observation data;

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

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

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

[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 , the lower limit of the actual observation distance corresponding to this arc segment in step S3 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 , corresponding to the upper limit of the observation distance ρ in step S3 max The calculation is as follows:

[0019] Step S3.1: Let the distance of the space debris from the observation platform be ρ = L max , calculate the position corresponding to the space debris :

[0020]

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

[0022] Step S3.2: Calculate the velocity composite vector It is defined as:

[0023]

[0024] in, is the velocity vector of the space-based optical observation platform itself, is the direction change vector;

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

[0026]

[0027] in, Representation vector With vector The inner product of Representation vector The inner product with itself; μ e is the gravitational constant;

[0028] Step S3.4: Use the binary search method to find the min ~L max Solve the value of the distance ρ corresponding to the zero point of formula 3) within the range, which is ρ max .

[0029] Preferably, the direction change vector in step S3.2 Using the difference approximation of the observed data, that is,

[0030]

[0031] Among them, Δt is the time interval, and two observations that are adjacent in time in an observation arc are taken for calculation.

[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 min ~ρ max A value ρ is randomly generated within i ;

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

[0036] Step S4.4: In the range of distance change rate Generate a random value within

[0037] Preferably, the distance change rate dρ in step S4.3 is i Upper limit of / dt With lower limit The calculation method is:

[0038]

[0039] Among them, μ e is the gravitational constant; r is the position vector The size of, that is, the modulus value,

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

[0041]

[0042] Where M is the number of samples in a short arc segment of space-based optical observation, that is, the number of samples in a short arc segment, is the measured value of the pointing vector of the jth sampling point, Because ρ, The estimated value of the pointing vector of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform, represents the inner product operation of two vectors, arccos is the inverse cosine function, and e is the function of ρ, The eccentricity corresponding to the determined orbit, α is the weight coefficient;

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

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

[0045] The set upper limit of the number of iterations is reached;

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

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

[0048] Module M1: Obtaining the angle measurement information of the space-based optical observation platform imaging the same unidentified space debris;

[0049] Module M2: According to the observation capability of the space-based optical observation platform, obtain 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: Calculate the upper and lower limits of the actual observation distance corresponding to the current observation arc segment based on the observation data;

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

[0052] Module M5: Calculate the loss function corresponding to each group of particles;

[0053] Module M6: Update each group of particles, calculate the loss function corresponding to the updated particles, and record the optimal particles in each group and the global optimal particles;

[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 the module M2 is L min , the lower limit of the actual observation distance of this arc segment in module M3 min =L min ;

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

[0057] Module M3.1: Let the distance of the space debris from the observation platform be ρ = L max , calculate the position corresponding to the space debris

[0058]

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

[0060] Module M3.2: Calculation of velocity resultant vector It is defined as:

[0061]

[0062] in, is the velocity vector of the space-based optical observation platform itself, is the direction change vector;

[0063] Module M3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max , the calculation is completed; otherwise, execute module M3.4;

[0064]

[0065] in, Representation vector With vector The inner product of Representation vector The inner product with itself; μ e is the gravitational constant;

[0066] Module M3.4: Using dichotomy in L min ~L max Solve the value of the distance ρ corresponding to the zero point of formula 3) within the range, which is ρ max ;

[0067] The module M3.2 points to the change vector Using the difference approximation of the observed data, that is,

[0068]

[0069] Among them, Δt is the time interval, and two observations adjacent in time in an observation arc are taken for calculation;

[0070] The particle initialization in the 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 min ~ρ max A value ρ is randomly generated within i ;

[0073] Module M4.3: Calculating position ρ i The corresponding distance change rate dρ i Upper limit of / dt With lower limit

[0074] Module M4.4: In the range of distance change rate Generate a random value within

[0075] The distance change rate dρ in the module M4.3 i Upper limit of / dt With lower limit The calculation method is:

[0076]

[0077] Among them, μ e is the gravitational constant; r is the position vector The size of, that is, the modulus value,

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

[0079]

[0080] Where M is the number of samples in a short arc segment of space-based optical observation, that is, the number of samples in a short arc segment, is the measured value of the pointing vector of the jth sampling point, Because The estimated value of the pointing vector of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform, represents the inner product operation of two vectors, arccos is the inverse cosine function, and e is the function of ρ, The eccentricity corresponding to the determined orbit, α is the weight coefficient;

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

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

[0083] The set upper limit of the number of iterations is 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. Aiming at the problems of insufficient geometric constraints and trivial solutions in the initial orbit determination of short arcs of high-orbit space debris by space-based optical observation, the present invention constructs a new solution model, in which the constraint of orbit eccentricity is added, and the constraints of observation distance and orbit rationality are introduced in the optimization process, which greatly improves the success rate of the initial orbit determination of short arcs 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 orbit of high-orbit space debris under the space-based angle measurement data only.

[0088] Other beneficial effects of the present invention will be explained in the specific implementation manner through the introduction of specific technical features and technical solutions. Through the introduction of these technical features and technical solutions, those skilled in the art should be able to understand the beneficial technical effects brought about by the technical features and technical solutions. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0090] Figure 1 is a flow chart of the present invention;

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

[0092] Figure 3a to Figure 3k Determine the changes of each group of optimal particles and the global optimal particles during the iteration process for the initial trajectory of a short arc segment;

[0093] Figure 4a to Figure 4b The position error results within the observed arcs for initial orbit determination of 7232 short arcs;

[0094] Figure 5a to Figure 5b The relative error results of the orbit semi-major axis for the initial orbit determination of 7232 short arc segments. DETAILED DESCRIPTION

[0095] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0096] The embodiment of the present invention provides a method for determining the initial orbit of a short arc of high-orbit space debris by space-based optical observation, referring to Figure 1 As shown, the method specifically includes the following contents:

[0097] Step S1: Obtaining the angular measurement information of the space-based optical observation platform imaging the same unidentified space debris, 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: According to the observation capability of the space-based optical observation platform, observation data is obtained, and the upper and lower limits of the distance between the high-orbit space debris and the space-based observation platform are set.

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

[0100] Step S3: Calculate the upper and lower limits of the actual observation distance corresponding to the current observation arc segment based on the observation data.

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

[0102] Step S3.1: Let the distance of the space debris from the observation platform be ρ = L max , calculate the position corresponding to the space debris :

[0103]

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

[0105] Step S3.2: Calculate the velocity composite vector It is defined as:

[0106]

[0107] in, is the velocity vector of the space-based optical observation platform itself, is the direction change vector;

[0108] Pointing change vector Using the difference approximation of the observed data, that is,

[0109]

[0110] Among them, Δt is the time interval, and two observations that are adjacent in time in an observation arc are taken for calculation.

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

[0112]

[0113] in, Representation vector With vector The inner product of Representation vector The inner product with itself; μ e is the gravitational constant, μ e =3.986004418×10 14 m 3 / s 2 .

[0114] Step S3.4: Use the binary search method to find the min ~L max Solve the value of the distance ρ corresponding to the zero point of formula 3) within the range, which is ρ max .

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

[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 min ~ρ max A value ρ is randomly generated within i ;

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

[0120] Distance change rate dρ i Upper limit of / dt With lower limit The calculation method is:

[0121]

[0122] Among them, μ e is the gravitational constant; r is the position vector The size of, that is, the modulus value,

[0123] Step S4.4: In the range of distance change rate Generate a random value within

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

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

[0126]

[0127] Where M is the number of samples in a short arc segment of space-based optical observation, that is, the number of samples in a short arc segment, is the measured value of the pointing vector of the jth sampling point, Because ρ, The estimated value of the pointing vector of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform, represents the inner product operation of two vectors, arccos is the inverse cosine function, and e is the function of ρ, The eccentricity corresponding to the determined orbit, α is the weight coefficient.

[0128] The value of the weight coefficient α in the loss function is determined according to the angular measurement accuracy of space-based optical observations. For a space-based optical observation platform with an angular measurement accuracy of δ (unit: rad), α can be taken as δ / 2000.

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

[0130] Step S6: Using the quantum particle swarm optimization (QPSO) algorithm, update each group of particles, calculate the loss function corresponding to the updated particles, and record the optimal particles in each group and the global optimal particle;

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

[0132] The exit conditions include: (1) reaching the 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. Either of the two conditions can be satisfied.

[0133] The present invention also provides a system for determining the initial short arc orbit of high-orbit space debris by space-based optical observation. The system can be implemented by executing the process steps of the method for determining the initial short arc orbit of high-orbit space debris by 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 by space-based optical observation as a preferred implementation of the system for determining the initial short arc orbit of high-orbit space debris by space-based optical observation. The system specifically includes the following contents:

[0134] Module M1: Obtain the angular measurement information of the space-based optical observation platform imaging the same unidentified space debris, 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: According to the observation capability of the space-based optical observation platform, the observation data is obtained and the upper and lower limits of the distance between the high-orbit space debris and the space-based observation platform are set.

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

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

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

[0139] Module M3.1: Let the distance of the space debris from the observation platform be ρ = L max , calculate the position corresponding to the space debris :

[0140]

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

[0142] Module M3.2: Calculation of velocity resultant vector It is defined as:

[0143]

[0144] in, is the velocity vector of the space-based optical observation platform itself, is the direction change vector;

[0145] Pointing change vector Using the difference approximation of the observed data, that is,

[0146]

[0147] Among them, Δt is the time interval, and two observations that are adjacent in time in an observation arc are taken for calculation.

[0148] Module M3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max , the calculation is completed; otherwise, execute module M3.4;

[0149]

[0150] in, Representation vector With vector The inner product of Representation vector The inner product with itself; μ e is the gravitational constant, μ e =3.986004418×10 14 m 3 / s 2 .

[0151] Module M3.4: Using dichotomy in L min ~L max Solve the value of the distance ρ corresponding to the zero point of formula 3) within the range, which is ρ max .

[0152] Module M4: Randomly initialize multiple groups 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 min ~ρ max A value ρ is randomly generated within i ;

[0156] Module M4.3: Calculating position ρ i The corresponding distance change rate dρ i Upper limit of / dt With lower limit

[0157] Distance change rate dρ i Upper limit of / dt With lower limit The calculation method is:

[0158]

[0159] Among them, μ e is the gravitational constant; r is the position vector The size of, that is, the modulus value,

[0160] Module M4.4: In the range of distance change rate Generate a random value within

[0161] Module M5: Calculate the loss function corresponding to each group of particles.

[0162] The loss function f corresponding to the particles in module M5 is set as

[0163]

[0164] Where M is the number of samples in a short arc segment of space-based optical observation, that is, the number of samples in a short arc segment, For the jth

[0165] The measured value of the pointing vector of the sampling point, Because ρ, The estimated value of the pointing vector of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform, represents the inner product operation of two vectors, arccos is the inverse cosine function, and e is the function of ρ, The eccentricity corresponding to the determined orbit, α is the weight coefficient.

[0166] The value of the weight coefficient α in the loss function is determined according to the angular measurement accuracy of space-based optical observations. For a space-based optical observation platform with an angular measurement accuracy of δ (unit: rad), α can be taken as δ / 2000.

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

[0168] Module M6: Use the quantum particle swarm (QPSO) algorithm to update each group of particles, calculate the loss function corresponding to the updated particles, and record the optimal particles in each group and the global optimal particles;

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

[0170] The exit conditions include: (1) reaching the 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. Either of the two conditions can be satisfied.

[0171] Next, the present invention will be described in more detail.

[0172] The present invention provides a method for determining the initial short arc orbit of high-orbit space debris in space-based optical observation. For the angle measurement information of the space-based optical observation platform imaging the same unidentified space debris, the information includes the imaging time, the position and speed 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 in the epoch geocentric celestial coordinate system relative to the space-based optical observation platform. The pointing vector (unit vector) of the space debris relative to the space-based optical observation platform can be calculated from the pointing information.

[0173] The location of space debris and speed satisfy

[0174]

[0175] in, are the position vector and velocity vector of the space-based optical observation platform itself, ρ is the distance of the space debris relative to the observation platform, dρ / dt is the distance change rate, is the direction change vector. For angle measurement data only, ρ and dρ / dt are unknown. It is not directly measured, but can be determined based on the pointing vector sampled at multiple times. Perform a difference approximation, that is

[0176]

[0177] Δt is the time interval, and generally two observations that are adjacent in time in an observation arc are taken for calculation.

[0178] The unknown quantities ρ and dρ / dt can be further constrained according to the performance of the space-based optical observation platform and the orbital constraints. Since the imaging characteristics of too close targets on the space-based optical observation platform are significantly different, there is a lower limit on the distance of the space debris observation data generated by space-based optics. At the same time, according to the observation capabilities of the space-based optical observation platform, space debris that is too far away cannot be imaged and detected, so there is an upper limit on the distance L. max The upper and lower limits of the distance here will be adaptively updated when applied to a specific observation arc segment, that is, the upper and lower limits here can be wider within an appropriate range.

[0179] Further, based on the energy constraints of the geocentric two-body, the actual observation distance range corresponding to this observation arc can be calculated.

[0180]

[0181] Among them, r and v represent the position vector and the velocity vector The size (i.e. modulus value) of μ eis the gravitational constant, μ e =3.986004418×10 14 m 3 / s 2 .

[0182] The velocity composite vector is defined in Formula 7

[0183]

[0184] Then according to formula 8, the upper limit of the distance corresponding to this observation can be calculated max And the rate of change corresponding to a certain distance ρ In the limit state, formula 8 takes the extreme value 0, that is, at the limit there is

[0185]

[0186] in, Representation vector With vector The inner product of Representation vector The inner product of itself. A reasonable ρ, Should meet

[0187]

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

[0189] Furthermore, for the distance ρ that satisfies Formula 3, the distance change rate dρ i Upper limit of / dt With 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, and the geometric constraints of short arcs of space-based observations are insufficient, and there may be more orbits close to the actual measured values. Therefore, based on the orbital characteristics of high-orbit space debris, the present invention further constrains the optimization solution model, adds the factor of orbital eccentricity, and adjusts it through a certain weight coefficient.

[0192] The loss function f is set as

[0193]

[0194] Where M is the number of samples in a short arc segment of space-based optical observation, that is, the number of samples in a short arc segment, is the measured value of the pointing vector of the jth sampling point, Because ρ, The estimated value of the pointing vector of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform, represents the inner product operation of two vectors, arccos is the inverse cosine function, and e is the function of ρ, The eccentricity corresponding to the determined orbit, α is the weight coefficient. Modifying the weight coefficient can adjust the contribution of the orbit eccentricity constraint to the final result. The value of the weight coefficient α in the loss function is determined according to 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 taken as δ / 2000. If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned a value of π+α.

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

[0196] When initializing particles, set the number of groups N, and randomly initialize multiple groups of particles 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 within i Calculate the position ρ i The corresponding distance change rate dρ i Upper limit of / dt With lower limit After that, in the range of distance change rate Generate a random value within Then calculate the loss function value corresponding to each group of particles.

[0197] Use the quantum particle swarm update algorithm to update each group of particles, calculate the loss function corresponding to the updated particles, and record the optimal particles in each group and the global optimal particles. Repeat the iteration until the set upper limit of the number of iterations is reached or the loss function value corresponding to the current global optimal position is less than the set threshold.

[0198] The effectiveness of the method of the present invention is verified by combining simulation data. The position vector of the space-based optical observation platform at UTC time 8Oct2023 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 the observation arc length of 87 seconds, the angle measurement data error is 2", and 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 the present invention, the particle changes during the iteration process are as follows Figure 2a to Figure 2k As shown in the figure, the changes of each group of optimal particles and the global optimal particles are as follows Figure 3a to Figure 3k After 10 iterations, the initial orbit 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 the space-based optical observation platform for observing high-orbit space debris were generated by simulation. The initial orbit determination method of the present invention was performed on each of the 7232 arc segments. The success rate of the initial orbit determination of the arc segment was 100%. The position error and statistical distribution of the observed arc segments were as follows: Figure 4a to Figure 4b The relative error of the semi-major axis of the orbit determination result and the result statistics are shown in Figure 5a to Figure 5b shown.

[0200] The embodiment of the present invention provides a method and system for determining the initial orbit of a short arc of high-orbit space debris by space-based optical observation. Aiming at the problems of insufficient geometric constraints and trivial solutions in the initial orbit determination of a short arc of high-orbit space debris by space-based optical observation, a new solution model is constructed. The constraint of orbit eccentricity is added to the model, and the constraints of observation distance and orbit rationality are introduced in the optimization process, which greatly improves the success rate of the initial orbit determination of a short arc of high-orbit space debris. The method of the present invention is reasonable, simple in calculation, and easy to implement, and can be effectively applied to the initial orbit determination of a short arc of high-orbit space debris under space-based angle measurement data only.

[0201] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0202] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for determining the initial short-arc orbit of high-orbit space debris by space-based optical observation, characterized in that: include: Step S1: obtaining the angle measurement information of the space-based optical observation platform imaging the same unidentified space debris; Step S2: According to the observation capability of the space-based optical observation platform, the observation data is obtained, and the upper and lower limits of the distance between the high-orbit space debris and the space-based observation platform are set; Step S3: Calculate the upper and lower limits of the actual observation distance corresponding to the current observation arc segment according to the observation data; Step S4: randomly initialize multiple groups of particles within the upper and lower limits of the actual observation distance; Step S5: Calculate the loss function corresponding to each group of particles; Step S6: Update each group of particles, calculate the loss function corresponding to the updated particles, and record the optimal particles in each group and the global optimal particles; Step S7: Repeat step S6 until the loop exit condition is met.

2. The method for determining the initial short arc orbit of high-orbit space debris by space-based optical observation according to claim 1, characterized in that: The lower limit of the observation distance corresponding to the space-based optical observation platform in step S2 is L min , the lower limit of the actual observation distance corresponding to this arc segment in step S3 min =L min .

3. The method for determining the initial short arc orbit of high-orbit space debris by space-based optical observation according to claim 1, characterized in that: 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 , corresponding to the upper limit of the observation distance ρ in step S3 max The calculation is as follows: Step S3.1: Let the distance of the space debris from the observation platform be ρ = L max , calculate the position corresponding to the space debris in, is the position vector of the space-based optical observation platform itself, is the pointing vector of the space debris relative to the space-based optical observation platform, calculated from the right ascension and declination; Step S3.2: Calculate the velocity composite vector It is defined as: in, is the velocity vector of the space-based optical observation platform itself, is the direction change vector; Step S3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max , the calculation is completed; otherwise, execute step S3.4; in, Representation vector With vector The inner product of Representation vector The inner product with itself; μ e is the gravitational constant; Step S3.4: Use the binary search method to find the min ~L max Solve the value of the distance ρ corresponding to the zero point of formula 3) within the range, which is ρ max .

4. The method for determining the initial short arc orbit of high-orbit space debris by space-based optical observation according to claim 3 is characterized in that: The direction change vector in step S3.2 Using the difference approximation of the observed data, that is, Where Δt is the time interval, and two observations that are adjacent in time in an observation arc are taken for calculation.

5. The method for determining the short arc initial orbit of high-orbit space debris by space-based optical observation according to claim 1, characterized in that: 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 ρ obtained in step S3 min ~ρ max A value ρ is randomly generated within i ; Step S4.3: Calculate position ρ i The corresponding distance change rate dρ i Upper limit of / dt With lower limit Step S4.4: In the range of distance change rate Generate a random value within 6. The method for determining the initial short arc orbit of high-orbit space debris by space-based optical observation according to claim 5, characterized in that: The distance change rate dρ in step S4.3 i Upper limit of / dt With lower limit The calculation method is: Among them, μ e is the gravitational constant; r is the position vector The size of, that is, the modulus value, 7. The method for determining the short arc initial orbit of high-orbit space debris by space-based optical observation according to claim 1, characterized in that: The loss function f corresponding to the particle in step S5 is set as Where M is the number of samples in a short arc segment of space-based optical observation, that is, the number of samples in a short arc segment, is the measured value of the pointing vector of the jth sampling point, Because ρ, The estimated value of the pointing vector of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform, represents the inner product operation of two vectors, arccos is the inverse cosine function, and e is the function of ρ, The eccentricity corresponding to the determined orbit, α is the weight coefficient; If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned a value of π+α.

8. The method for determining the short arc initial orbit of high-orbit space debris by space-based optical observation according to claim 1, characterized in that: The exit loop condition in step S7 includes: The set upper limit of the number of iterations is reached; Or the loss function value corresponding to the current global optimal position is less than the set threshold.

9. A short arc initial orbit determination system for space-based optical observation of high-orbit space debris, characterized in that: include: Module M1: Obtaining the angle measurement information of the space-based optical observation platform imaging the same unidentified space debris; Module M2: According to the observation capability of the space-based optical observation platform, obtain 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: Calculate the upper and lower limits of the actual observation distance corresponding to the current observation arc segment based on the observation data; Module M4: Randomly initialize multiple groups of particles within the upper and lower limits of the actual observation distance; Module M5: Calculate the loss function corresponding to each group of particles; Module M6: Update each group of particles, calculate the loss function corresponding to the updated particles, and record the optimal particles in each group and the global optimal particles; Module M7: Repeat module M6 until the exit loop condition is met.

10. The system for determining the short arc initial orbit of high-orbit space debris by space-based optical observation according to claim 9, characterized in that: The lower limit of the observation distance corresponding to the space-based optical observation platform in the module M2 is L min , the lower limit of the actual observation distance of this arc segment in module M3 min =L min ; The upper limit of the observation distance corresponding to the space-based optical observation platform in the module M2 is L max , the lower limit is L min , module M3 corresponds to the upper limit of this observation distance ρ max The calculation is as follows: Module M3.1: Let the distance of the space debris from the observation platform be ρ = L max , calculate the position corresponding to the space debris in, is the position vector of the space-based optical observation platform itself, is the pointing vector of the space debris relative to the space-based optical observation platform, calculated from the right ascension and declination; Module M3.2: Calculation of velocity resultant vector It is defined as: in, is the velocity vector of the space-based optical observation platform itself, is the direction change vector; Module M3.3: If the current distance ρ = L max If the following constraints are satisfied, then ρ max =L max , the calculation is completed; otherwise, execute module M3.4; in, Representation vector With vector The inner product of Representation vector The inner product with itself; μ e is the gravitational constant; Module M3.4: Using dichotomy in L min ~L max Solve the value of the distance ρ corresponding to the zero point of formula 3) within the range, which is ρ max ; The module M3.2 points to the change vector Using the difference approximation of the observed data, that is, Among them, Δt is the time interval, and two observations adjacent in time in an observation arc are taken for calculation; The particle initialization in the 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 ρ obtained in module M3 min ~ρ max A value ρ is randomly generated within i ; Module M4.3: Calculating position ρ i The corresponding distance change rate dρ i Upper limit of / dt With lower limit Module M4.4: In the range of distance change rate Generate a random value within The distance change rate dρ in the module M4.3 i Upper limit of / dt With lower limit The calculation method is: Among them, μ e is the gravitational constant; r is the position vector The size of, that is, the modulus value, The loss function f corresponding to the particles in the module M5 is set as Where M is the number of samples in a short arc segment of space-based optical observation, that is, the number of samples in a short arc segment, is the measured value of the pointing vector of the jth sampling point, Because ρ, The estimated value of the pointing vector of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform, represents the inner product operation of two vectors, arccos is the inverse cosine function, and e is the function of ρ, The eccentricity corresponding to the determined orbit, α is the weight coefficient; If ρ, If a reasonable trajectory cannot be calculated, the loss function is assigned a value of π+α; The exit loop conditions in the module M7 include: The set upper limit of the number of iterations is reached; Or the loss function value corresponding to the current global optimal position is less than the set threshold.

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