Space debris angle-measurement-only short arc rapid initial orbit determination method and system

Abstract

The invention provides a space debris angle-measurement-only short-arc rapid initial orbit determination method and a space debris angle-measurement-only short-arc rapid initial orbit determination system. The method comprises the following steps: S1, acquiring space debris angle-only segmental arc observation data; and S2, performing polynomial fitting on the observation data. And S3, calculating the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint moment of the arc section. And S4, calculating the change rate of the pointing vector at the midpoint moment of the arc section. And S5, determining the distance at the midpoint moment of the arc section and the initial value of the distance change rate. And S6, calculating an objective function corresponding to the initial value. Step S7, if the target function does not reach the convergence condition, calculating a target function gradient corresponding to the current distance and the distance variation rate, updating the current distance and the distance variation rate, and executing steps S6 to S7; and if the target function reaches the convergence condition, calculating the corresponding position and speed. The implementation process is simple and easy to implement, and the method can be effectively applied to the space debris angle-only short arc initial orbit.

Description

Technical Field

[0001] The present invention relates to the technical field of space situation awareness. Specifically, it relates to a method and system for quickly determining the initial orbit of space debris with only angle measurement and short arc. Background Art

[0002] Currently, space debris monitoring equipment mainly relies on ground-based monitoring equipment. Among them, the ground-based astronomical telescope system has long occupied an important position and been widely used in the field of space debris monitoring due to its advantages of low energy consumption and high spatial resolution. However, ground-based observations are restricted by geography. In recent years, various countries have actively developed space-based space debris monitoring equipment, and the space-based optical telescope system is a typical representative among them. Passive optical telescope systems have a common problem, that is, they cannot obtain ranging information. Therefore, in many scenarios, such as during the process of determining a new target, for the situation where only angle measurement observations of a short arc can be obtained, it is necessary to perform an initial orbit determination operation based on only angle measurement information.

[0003] Initial orbit determination refers to determining the initial orbit information of a target based on an observation short arc data without other prior information about the space debris. However, generally, the orbit information determined in this way has a large error and can only be used as the initial value for subsequent orbit improvement of the target, rather than directly outputting it as the orbit information of the space debris. At the same time, initial orbit information is also often used when correlating arc segments of multi-type observation data without prior information. There are obvious differences between initial orbit determination and precise orbit determination. The input of initial orbit determination is usually a short arc and there is no prior orbit information; while precise orbit determination, also known as orbit improvement, generally requires continuous long-duration continuous observation data or long-duration discrete observation data, and there must be initial orbit information in advance as the improvement initial value.

[0004] For the initial orbit determination of only angle measurement observation data, there are mainly the following types of methods currently: Gauss method, Laplace method, Gooding method, admissible region method, double-ρ / double-r method, etc.

[0005] Laplace method: Document 1 (Liu Lin, Initial orbit calculation method considering the perturbation of the Earth's oblateness, Acta Astronomica Sinica, 2003, Vol. 44, No. 2) presented the Laplace initial orbit determination method considering oblateness perturbation. Document 2 (Liu Xiangchun, Research on the orbit determination method of space debris by space-based photographic tracking, Master's thesis, 2009) applied the Laplace initial orbit calculation to space-based angle-only observation data. Patent 1 (A method for determining the initial orbit of a low-Earth target satellite based on space-based satellite angle measurement data, Patent No. CN103927289A) disclosed a method for determining the initial orbit of a low-Earth target satellite based on space-based satellite angle measurement data. On the basis of the traditional Laplace method, additional constraint shielding false solutions were added to the conditional equation to form a conditional equation with constraints for iteration.

[0006] Feasible region method: Document 3 (Liu Xin, Initial orbit determination of small celestial bodies based on intelligent optimization algorithms, Acta Astronomica Sinica, 2023, Vol. 64, No. 4) applied the particle swarm algorithm to double-distance search and feasible region methods respectively.

[0007] Double-distance search method (double-ρ / double-r): Document 4 (Zhang Pin, Initial orbit determination method of low-Earth space debris using distance search, Spacecraft Engineering, 2017, Vol. 26, No. 2) presented a double-distance search method. By searching the distance information at two moments, the initial orbit determination problem of pure angle was transformed into the initial orbit determination problem based on two position vectors. Document 5 (Zhang Pin, A method for determining the initial orbit of a space target using only angle observations, Master's thesis, Wuhan University, 2017) studied the application effectiveness of the Gauss method, Gooding method, and double-distance search numerical method in a space-based optical observation system. Document 6 (Liu Lei, Research on the initial orbit determination of space targets by space-based surveillance direction finding, Doctoral thesis, 2010) studied the application and corresponding improvements of the double-distance search numerical method, Gauss method, and Laplace method in the initial orbit determination of space-based direction finding. Patent 2 (Method and system process for determining the initial orbit of space debris on a space-based optical monitoring platform, Patent Publication No. CN115828037A) constructed an optimization model of the double-distance search numerical method and performed optimal solution calculations through multiple groups of initializations and iterations of the distances at the starting and ending points.

[0008] In addition, some studies have improved and explored the initial orbit determination method from different perspectives: Reference 7 (Huang Pu, Angle-only Initial Orbit Calculation Method for Low-Earth Orbit Satellites to High-Earth Orbit Satellites, Flight Dynamics, 2020, Vol. 38, No. 1) established an extended Laplace dynamics model for angle-only initial orbit calculation. Reference 8 (Wang Xueying, A Space-Based Optical GEO Target Positioning Method and Observation Geometry Evaluation of Initial Orbit Algorithm, Aerospace Control, 2012, Vol. 30, No. 2) used the generalized Laplace algorithm to calculate the initial orbit for multi-platform and multi-observation arcs of space-based optics. Reference 9 (Zhao Kexin, Initial Orbit Determination Problem and Method for Space-Based Optical Space Target Monitoring, Acta Aeronautica et Astronautica Sinica, 2022, Vol. 44, No. 1) gave the mathematical representation of the trivial solution and improved the original Laplace octic equation to a septic equation for solution. Reference 10 (Zhao Kexin, A New Method for Space-Based Initial Orbit Determination Using 3 Azimuth Observations, Acta Astronomica Sinica, 2022, Vol. 63, No. 5) derived the analytical form of the slant range condition equation based on the improved Gauss equation and eliminated the singularities of the equations in the solution using orbit energy constraints. Reference 11 (Cui Wen, Initial Orbit Determination Method for Geostationary Orbit Targets Based on Optical Data, Mechanics in Engineering, August 2023, Vol. 45, No. 4) adopted the method of traversing and searching the semi-major axis of the orbit, introduced more reasonable prior information of pseudo-range measurement values, and proposed an initial orbit determination method for geostationary orbit targets based on astronomical angle measurement data, with the success rate of initial orbit determination being better than 95%. Reference 12 (Li Xinran, Orbit Determination Method for Extremely Short Arcs Based on Evolutionary Computation, 2018, University of Science and Technology of China, Doctoral Dissertation) and Reference 13 (Li Xinran, Orbit Determination for Extremely Short Arcs Based on Particle Swarm Algorithm, Journal of Spacecraft TT&C Technology, 2015, Vol. 34, No. 6) studied the problem of orbit determination for extremely short arcs from an evolutionary perspective, constructed a 3D (a, e, M in Keplerian elements) optimization model, and implemented algorithms based on three different evolutionary mechanisms: genetic algorithm, particle swarm algorithm, and differential evolution algorithm. Reference 14 (Song Kezhen, Space-Based Orbit Determination Method for Extremely Short Arcs Based on Genetic Algorithm, Spacecraft Engineering, 2019, Vol. 28, No. 5) divided the 6 orbit parameters to be estimated into two 3D optimization problems (a, e, M and i, Ω, ω) for solution based on the genetic algorithm.

[0009] To sum up, aiming at the difficulty in simultaneously considering the solution success rate and solution speed that commonly exist in the existing methods, it has become a crucial task to be urgently solved at present to study a method and system for quickly determining the initial orbit of space debris with only angle measurement and short arcs. Summary of the Invention

[0010] Aiming at the defects in the prior art, the purpose of the present invention is to provide a method and system for quickly determining the initial orbit of space debris with only angle measurement and short arcs.

[0011] A method for quickly determining the initial orbit of space debris with only angle measurement in a short arc according to the present invention includes the following steps:

[0012] Step S1: Obtain the observation data of the space debris with only angle measurement in the arc segment;

[0013] Step S2: Perform polynomial fitting on the observation data;

[0014] Step S3: Based on the polynomial fitting, calculate the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial sphere coordinate system at the midpoint time of the arc segment;

[0015] Step S4: Based on the polynomial fitting, calculate the change rate of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial sphere coordinate system at the midpoint time of the arc segment;

[0016] Step S5: Set the initial values of the distance and the distance change rate at the midpoint time of the arc segment, and assign them to the current distance and the distance change rate respectively;

[0017] Step S6: Based on the pointing vector and the change rate of the pointing vector, calculate the objective function corresponding to the current distance and the distance change rate;

[0018] Step S7: Determine whether the objective function reaches the convergence condition. If it does not reach the convergence condition, calculate the gradient of the objective function corresponding to the current distance and the distance change rate, and use the gradient-based optimization algorithm to update the current distance and the distance change rate, and repeat steps S6 to S7; if it reaches the convergence condition, end the calculation, and calculate the corresponding position and velocity according to the current distance and the distance change rate.

[0019] Preferably, in step S1, the observation data includes the time t i at multiple sampling times, the position of the observation station in the J2000 geocentric celestial sphere coordinate system the velocity of the observation station the right ascension α of the space debris relative to the observation station i and the declination δ i , where the subscript i ranges from 1, 2,..., M, and M is the total number of sampling points of the observation data.

[0020] Preferably, in step S2, for the right ascension α i and the declination δ i in the observation data, perform polynomial fitting on the time t i respectively, and calculate the right ascension α m corresponding to the midpoint t m of the arc segment, the declination δ m and the right ascension change rate the declination change rate When the total number of sampling points M of the observed data is less than 30, a quadratic polynomial is used for fitting. When the number of sampling points reaches 30 or more, a cubic polynomial is used for fitting.

[0021] Preferably, in step S3, the midpoint t of the arc segment m The pointing vector corresponding to the moment is calculated from the right ascension and declination obtained by fitting. The calculation formula is as follows:

[0022]

[0023] In step S4, calculate the midpoint t of the arc segment m At the moment, the rate of change of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial sphere coordinate system

[0024]

[0025] Preferably, step S6 includes the following sub-steps:

[0026] Step S6.1, calculate the position m At the moment t of the midpoint, guess the position of the orbit and velocity

[0027]

[0028] Step S6.2, according to the position and velocity at the midpoint moment, recursively calculate the position values of the guessed orbit at all observation moments, and calculate the pointing vector of the guessed orbit relative to the observation station at the moment

[0029] Step S6.3, calculate the eccentricity, distance constraint function, and distance rate constraint function corresponding to the guessed orbit.

[0030] Step S6.5, calculate the objective function

[0031] Preferably, in step S6.3, according to the observed distance ρ m and the distance rate calculate the eccentricity e m , the formula is:

[0032]

[0033] Among them, μ is the geocentric gravitational constant, μ = 3.986004418×10 14 m 3 / s 2 . The scalar r m represents the modulus of the position The scalar v m represents the velocity Modulus value;

[0034] If the upper and lower limits of the observation distance are ρ max , ρ min respectively, and the upper and lower limits of the distance rate are then the distance constraint function g(ρ m ), and the distance rate constraint function are calculated as follows

[0035]

[0036] Preferably, in step S6.5, the calculation formula of the objective function is:

[0037]

[0038] wherein, represents the pointing vector of the guessed orbit uniquely determined by the six parameters of the observation distance ρ m , the distance rate right ascension α m , declination δ m , right ascension rate declination rate relative to the observation station at time t i . represents the pointing vector relative to the observation station at time t i calculated from the right ascension α i and declination δ i of the space debris relative to the observation station in step S1. represents the inner product calculation of two vectors. c1, c2, and c3 respectively represent the eccentricity constraint coefficient, distance constraint coefficient, and distance rate constraint coefficient. e m represents the eccentricity corresponding to the guessed orbit, g(ρ m ) is the distance constraint function, is the distance rate constraint function. The unit of the observation distance ρ m is: Earth radius (6378.137 km). The unit of time is: hour, that is, the unit of the distance rate is: Earth radius / hour.

[0039] Preferably, in step S7, the calculation formula of the objective function gradient is as follows:

[0040]

[0041] The present invention also provides a space debris angle-only short-arc rapid initial orbit determination system, including:

[0042] Module M1, which acquires the observation data of the angular-only arc segment of space debris;

[0043] Module M2, which performs polynomial fitting on the observation data;

[0044] Module M3, which calculates the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint time of the arc segment based on the polynomial fitting;

[0045] Module M4, which calculates the rate of change of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint time of the arc segment based on the polynomial fitting;

[0046] Module M5, which sets the initial values of the distance and the rate of change of distance at the midpoint time of the arc segment and assigns them to the current distance and the rate of change of distance respectively;

[0047] Module M6, which calculates the objective function corresponding to the current distance and the rate of change of distance based on the pointing vector and the rate of change of the pointing vector;

[0048] Module M7, which determines whether the objective function reaches the convergence condition. If the convergence condition is not reached, it calculates the gradient of the objective function corresponding to the current distance and the rate of change of distance, and updates the current distance and the rate of change of distance using a gradient-based optimization algorithm, and repeats to execute Module M6 to Module M7; if the convergence condition is reached, it ends the calculation, and calculates the corresponding position and velocity based on the current distance and the rate of change of distance.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. Aiming at the problems of non-convergence, easy convergence to trivial solutions, and low solution efficiency that are prone to occur in the process of determining the initial orbit of the angular-only short arc of space debris, the present invention constructs an optimization problem in the distance-rate of change of distance solution space. The objective function involved in this optimization problem comprehensively considers the observed values, the rationality of the orbit, and the constraints of the observation equipment capabilities, ensuring the convergence of the calculation of the initial orbit of the angular-only short arc of space debris while improving the algorithm efficiency.

[0051] 2. The present invention gives a method for calculating the gradient of the objective function and uses a gradient-based iterative solution method. This method has a reasonable design idea, a simple calculation process, and is easy to implement, and can be effectively applied to the initial orbit of the angular-only short arc of space debris. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, objectives, and advantages of the present invention will become more obvious:

[0053] Figure 1 It is a flowchart of a method for determining the initial orbit of the angular-only short arc observation data of space debris in an embodiment of the present invention;

[0054] Figure 2 This is the time-consuming test result of an initial orbit determination method for space debris with only angle measurement short-arc observation data in the embodiments of the present invention;

[0055] Figure 3 This is the semi-major axis deviation of the initial orbit determination result of an initial orbit determination method for space debris with only angle measurement short-arc observation data in the embodiments of the present invention;

[0056] Figure 4 This is the inclination deviation of the initial orbit determination result of an initial orbit determination method for space debris with only angle measurement short-arc observation data in the embodiments of the present invention;

[0057] Figure 5 This is the eccentricity deviation of the initial orbit determination result of an initial orbit determination method for space debris with only angle measurement short-arc observation data in the embodiments of the present invention. Detailed implementation manners

[0058] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several changes and improvements can still be made. These all belong to the protection scope of the present invention.

[0059] The present invention proposes an initial orbit determination method and system for space debris with only angle measurement short-arc observation data. In the solution space composed of distance and distance rate, through an objective function including constraint terms for distance and distance rate, the solution space is further constrained. At the same time, this method calculates the partial derivatives of the objective function and uses a gradient-based solution algorithm to quickly perform iterative solution, so as to effectively improve the algorithm efficiency on the premise of ensuring the convergence of the initial orbit calculation of space debris with only angle measurement short-arc.

[0060] Embodiment 1:

[0061] Figure 1 This is the flow chart of an initial orbit determination method for space debris with only angle measurement short-arc observation data in the embodiments of the present invention.

[0062] As Figure 1 shown, this embodiment provides a fast initial orbit determination method for space debris with only angle measurement short-arc, including the following steps:

[0063] Step S1, obtain the observation data of the space debris with only angle measurement arc segment.

[0064] Specifically, the observation data includes the observation time, the right ascension and declination of the space debris relative to the observation station, and the space debris photometric data, etc.

[0065] In this embodiment, in combination with the known position information of the ground station, the following observation data is obtained: the time t at multiple sampling moments i , the position of the observation station in the J2000 geocentric celestial coordinate system the velocity of the observation station and the right ascension α of the space debris relative to the observation station i , declination δ i , where the subscript i ranges from 1, 2,..., M, and M is the total number of sampling points of the observation data.

[0066] Step S2, perform polynomial fitting on the observation data.

[0067] Specifically, since there are measurement errors in all the observation data, for the right ascension α i and declination δ i in the observation data, polynomial fitting is respectively performed on the time t i . Fitting can, to a certain extent, reduce the influence of measurement errors on the observed value at a certain moment, and at the same time, it is also convenient for calculating derivatives. Using the polynomial fitting parameters, calculate the right ascension α m , declination δ m , right ascension rate m declination rate corresponding to the midpoint t

[0068] More specifically, if the total number of sampling points M of the observation data is less than 30, a quadratic polynomial is used for fitting. When the number of sampling points reaches 30 or more, a cubic polynomial is used for fitting.

[0069] Step S3, based on the polynomial fitting, calculate the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint moment of the arc segment.

[0070] Specifically, on the basis of polynomial fitting, calculate the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint t m moment ( i.e., rounded down M / 2), The pointing vector corresponding to the midpoint t m moment is calculated from the right ascension and declination obtained through fitting, rather than the right ascension and declination at the midpoint t m moment in the original observation data. The calculation formula is as follows:

[0071]

[0072] Step S4: Based on polynomial fitting, calculate the rate of change of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint time of the arc segment.

[0073] Specifically, based on polynomial fitting, calculate the midpoint time t m of the arc segment, and the rate of change of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system The formula is as follows:

[0074]

[0075] Step S5: Set the initial values of the distance and the rate of change of distance at the midpoint time of the arc segment, and assign them to the current distance and the rate of change of distance respectively.

[0076] Specifically, the initial values

[0077] Step S6: Based on the pointing vector and the rate of change of the pointing vector, calculate the objective function corresponding to the current distance and the rate of change of distance.

[0078] Specifically, to add reasonable constraints to the problem of determining the initial orbit of a short arc with only angle measurements, construct an optimization problem, and based on the current distance, the rate of change of distance and the right ascension α m , declination δ m , the rate of change of right ascension and the rate of change of declination calculate the objective function corresponding to the guessed orbit

[0079] More specifically, Step S6 includes the following sub-steps:

[0080] Step S6.1: Calculate the position m and velocity of the guessed orbit at the midpoint time t

[0081]

[0082] Step S6.2: According to the position and velocity at the midpoint time, recursively calculate the position values of the guessed orbit at all observation times, and calculate the pointing vector of the guessed orbit relative to the observation station at the time

[0083] Step S6.3: Calculate the eccentricity, distance constraint function, and distance rate constraint function corresponding to the guessed orbit.

[0084] Specifically, according to the observed distance ρ m , the rate of change of distance calculate the eccentricity e m :

[0085]

[0086] Among them, μ is the geocentric gravitational constant, μ = 3.986004418×10 14 m 3 / s 2 ; the scalar r m represents the modulus of the position , and the scalar v m represents the modulus of the velocity .

[0087] If the upper and lower limits of the observation distance are ρ max , ρ min , and the upper and lower limits of the distance change rate are respectively, then the calculation methods of the distance constraint function g(ρ m ) and the distance change rate constraint function are as follows:[[]]

[0088]

[0089] Step S6.5, calculate the objective function

[0090] Specifically, the objective function is calculated as follows:[[]]

[0091]

[0092] Among them,[[]] represents the pointing vector of the guessed orbit uniquely determined by the six parameters of the observation distance ρ m , the distance rate , the right ascension α m , the declination δ m , the right ascension rate , and the declination rate relative to the observation station at time t i , represents the pointing vector of the space debris relative to the observation station at time t i calculated from the right ascension α i and declination δ i in Step S1.1; represents the inner product calculation of two vectors; c1, c2, and c3 represent the eccentricity constraint coefficient, the distance constraint coefficient, and the distance rate constraint coefficient respectively; e m represents the eccentricity corresponding to the guessed orbit, g(ρ m ) is the distance constraint function, is the distance rate constraint function; the observation distance ρ mThe unit of [quantity] is: the Earth's radius (6378.137 km); the unit of time is: hour, that is, the unit of the rate of change of distance is: Earth's radius per hour.

[0093] The defined objective function comprehensively considers the observed values, orbital rationality, and the constraints of the observation equipment capabilities. Meanwhile, the objective function is defined at any position in the distance - rate of change of distance space. Even if the corresponding orbit at some positions is not reasonable, perhaps a parabolic orbit or a hyperbolic orbit, it is still defined and the derivative can be calculated. It's just that the objective function values corresponding to these orbits will be relatively large. The purpose of the optimization solution is to converge to the position of the smaller extreme value of the objective function and will not converge to an unreasonable orbit.

[0094] In step S7, it is judged whether the objective function reaches the convergence condition. If the convergence condition is not reached, then calculate the gradient of the objective function corresponding to the current distance and rate of change of distance, and use the gradient - based optimization algorithm to update the current distance and rate of change of distance, and repeat steps S6 to S7; if the convergence condition is reached, then end the calculation, and calculate the corresponding position and velocity according to the current distance and rate of change of distance.

[0095] Specifically, the convergence conditions include: (1) the objective function is less than a predefined threshold; (2) the standard deviation of the objective function in the historical record is less than a predefined threshold; (3) the maximum number of iterations is reached. Meeting any one of the conditions ends the iteration.

[0096] If the convergence condition is not reached, then calculate the gradient of the objective function corresponding to the current and use the gradient - based optimization algorithm to update the current distance and rate of change of distance

[0097]

[0098] and repeat steps S6 to S7 for iterative update until the corresponding objective function reaches the convergence condition.

[0099] Specifically, after the calculation methods of the objective function and its gradient are determined, use the gradient - based optimization algorithm for iterative solution. The current distance and rate of change of distance are updated in a certain direction and step size, and then use formula 7 to calculate the objective function corresponding to the current

[0100] ​​Gradient-based optimization algorithms can include Gradient Descent with Momentum, Root Mean Square Prop (RMSRrop), Adaptive Gradient (AdaGrad), or Adaptive Momentum (Adam), etc.

[0101] If the convergence condition is reached, the calculation ends and the current is calculated according to Formula 3 for the position and velocity of the orbit.

[0102] Example 2:

[0103] Figure 2 This is the time-consuming test result of an initial orbit determination method for space debris with only angle measurement short arc observation data in the embodiments of the present invention.

[0104] Next, the effectiveness of the method of the present invention is verified in combination with the measured data. For a certain high-orbit debris, the angle-only observation arc segments during the period from December 27, 2019 to January 13, 2020 are used to perform rapid initial orbit determination by the method of Embodiment 1 above. Among them, the Adam algorithm is selected as the gradient-based optimization algorithm. After execution, all arc segments achieve convergence. In an environment equipped with an 11th Gen Intel(R) Core(TM) i5-11500@2.70GHz processor and running Python 3.8.5, the execution efficiency of each arc segment is as Figure 2 shown.

[0105] Furthermore, the precise orbit determination results of multiple arc segments are used as the reference values for comparison, and the initial orbit determination results of independent arc segments without other prior information are compared with the above reference values. The deviations of the semi-major axis of the orbit, the inclination of the orbit, and the eccentricity of the orbit are respectively as shown in Appendix Figure 3 to Appendix Figure 5 shown.

[0106] Figure 3 This is the deviation of the semi-major axis of the orbit in the initial orbit determination result of an initial orbit determination method for space debris with only angle measurement short arc observation data in the embodiments of the present invention; Figure 4 This is the deviation of the inclination of the orbit in the initial orbit determination result of an initial orbit determination method for space debris with only angle measurement short arc observation data in the embodiments of the present invention; Figure 5 This is the deviation of the eccentricity of the orbit in the initial orbit determination result of an initial orbit determination method for space debris with only angle measurement short arc observation data in the embodiments of the present invention.

[0107] As can be seen from the figure, for the problem of initial orbit confirmation of short arcs with only angle measurement, the method of the present invention can improve the algorithm efficiency while ensuring calculation convergence, and the accuracy of initial orbit determination is within an acceptable range.

[0108] Embodiment 3:

[0109] The present invention also provides a system for quickly determining the initial orbit of space debris with only angle measurement of short arcs. The system for quickly determining the initial orbit of space debris with only angle measurement of short arcs can be implemented by executing the process steps of the method for quickly determining the initial orbit of space debris with only angle measurement of short arcs. That is, those skilled in the art can understand the method for quickly determining the initial orbit of space debris with only angle measurement of short arcs as a preferred embodiment of the system for quickly determining the initial orbit of space debris with only angle measurement of short arcs.

[0110] The system for quickly determining the initial orbit of space debris with only angle measurement of short arcs includes:

[0111] Module M1, which acquires the observation data of the angle measurement arc segment of space debris;

[0112] Module M2, which performs polynomial fitting on the observation data;

[0113] Module M3, which calculates the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial sphere coordinate system at the midpoint moment of the arc segment based on the polynomial fitting;

[0114] Module M4, which calculates the rate of change of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial sphere coordinate system at the midpoint moment of the arc segment based on the polynomial fitting;

[0115] Module M5, which sets the initial values of the distance and the rate of change of distance at the midpoint moment of the arc segment and assigns them to the current distance and the rate of change of distance respectively;

[0116] Module M6, which calculates the objective function corresponding to the current distance and the rate of change of distance based on the pointing vector and the rate of change of the pointing vector;

[0117] Module M7, which determines whether the objective function reaches the convergence condition. If the convergence condition is not reached, it calculates the gradient of the objective function corresponding to the current distance and the rate of change of distance, and uses the gradient-based optimization algorithm to update the current distance and the rate of change of distance, and repeats the execution of Module M6 to Module M7; if the convergence condition is reached, it ends the calculation, and calculates the corresponding position and velocity according to the current distance and the rate of change of distance.

[0118] Those skilled in the art know that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc. to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or structures within the hardware component.

[0119] The specific embodiments of the present invention have been described above. 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. Without conflict, the embodiments of the present application and the features in the embodiments can be combined arbitrarily with each other.

Claims

1. A method for quickly determining the initial orbit of space debris with only angle measurement in short arcs, characterized in that, It includes the following steps: Step S1, obtaining the observation data of the space debris's single-angle measurement arc segment; Step S2, performing polynomial fitting on the observation data; Step S3, based on the polynomial fitting, calculating the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint time of the arc segment; Step S4, based on the polynomial fitting, calculating the rate of change of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint time of the arc segment; Step S5, setting the initial values of the distance and the rate of change of distance at the midpoint time of the arc segment, and respectively assigning them to the current distance and the rate of change of distance; Step S6, based on the pointing vector and the rate of change of the pointing vector, calculating the objective function corresponding to the current distance and the rate of change of distance; Step S7, determining whether the objective function reaches the convergence condition. If it does not reach the convergence condition, calculating the gradient of the objective function corresponding to the current distance and the rate of change of distance, and using a gradient-based optimization algorithm to update the current distance and the rate of change of distance, and repeating steps S6 to S7; If it reaches the convergence condition, ending the calculation, and calculating the corresponding position and velocity according to the current distance and the rate of change of distance.

2. The method for quickly determining the initial orbit of space debris with only angle measurement in short arcs according to claim 1, characterized in that, In the step S1, the observation data includes the time t at multiple sampling moments i , the position of the observation station in the J2000 geocentric celestial coordinate system the velocity of the observation station the right ascension α of the space debris relative to the observation station i , the declination δ i , where the subscript i ranges from 1, 2, ……, M, and M is the total number of sampling points of the observation data.

3. The method for quickly determining the initial orbit of space debris with only angle measurement in a short arc according to claim 2, characterized in that, In the step S2, for the right ascension α i and the declination δ i in the observation data, polynomial fitting is respectively performed on the time t i , and the right ascension αcorresponding to the midpoint t m m , declination δ m , right ascension rate and declination rate are calculated by using the polynomial fitting parameters. If the total number M of sampling points in the observation data is less than 30, a quadratic polynomial is used for fitting. When the number of sampling points reaches 30 or more, a cubic polynomial is used for fitting.

4. The method for rapidly determining the initial orbit of space debris with only angle measurement in short arcs according to claim 3, characterized in that, In the step S3, the pointing vector corresponding to the midpoint t of the arc segment m at a certain moment is calculated from the right ascension and declination obtained by fitting, and the calculation formula is as follows:

5. The method for quickly determining the initial orbit of space debris with only angle measurement in short arc according to claim 4, characterized in that, In the step S4, calculate the midpoint t of the arc segment m At the moment m , the change rate of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system 6. The method for quickly determining the initial orbit of space debris with only angle measurement in a short arc according to claim 6, characterized in that The said step S6 includes the following sub-steps: Step S6.1, calculate the midpoint t based on the pointing vector and the change rate of the pointing vector m At the moment, guess the position of the orbit and velocity Step S6.2, according to the position at the midpoint moment and speed Recursively calculate the position values of the guessed orbits at all observation moments, and calculate the pointing vector of the guessed orbit relative to the observation station at the moment Step S6.3, calculating the eccentricity, distance constraint function, and rate-of-change-of-distance constraint function corresponding to the guessed orbit; Step S6.5, calculate the objective function 7. The method for quickly determining the initial orbit of space debris with only angle measurement in a short arc according to claim 7, characterized in that In the step S6.3, according to the observed distance ρ m , the rate of change of distance calculate the eccentricity e m , and the formula is: where μ is the geocentric gravitational constant, μ = 3.986004418×10 14 m 3 / s 2 , the scalar r m represents the magnitude of the position , and the scalar v m represents the magnitude of the velocity ; If the upper and lower limits of the observation distance are ρ max and ρ min respectively, and the upper and lower limits of the distance rate of change are then the calculation methods of the distance constraint function g(ρ m ) and the distance rate of change constraint function are as follows 8. The method for quickly determining the initial orbit of space debris with only angle measurement in short arcs according to claim 1, characterized in that, In the step S6.5, the objective function is calculated by the formula: Among them, represents the pointing vector of the guessed orbit uniquely determined by six parameters: the observation distance ρ m , the distance rate of change right ascension α m , declination δ m , the rate of change of right ascension the rate of change of declination at time t i relative to the observing station, represents the pointing vector of the space debris relative to the observing station at time t i calculated from the right ascension α i and declination δ i in step S1, represents the inner product calculation of two vectors. c1, c2, and c3 respectively represent the eccentricity constraint coefficient, distance constraint coefficient, and distance rate of change constraint coefficient. e m represents the eccentricity corresponding to the guessed orbit. g(ρ m ) is the distance constraint function, is the distance rate of change constraint function. The unit of the observation distance ρ m is: Earth radius (6378.137 km), and the unit of time is: hour, that is, the unit of the distance rate of change is: Earth radius / hour.

9. The method for quickly determining the initial orbit of space debris with only angle measurement and short arc according to claim 1, characterized in that, In the step S7, the gradient of the objective function is calculated as follows:

10. A space debris single-angle measurement short-arc rapid initial orbit determination system, characterized in that, It includes: Module M1, obtaining the observation data of the space debris's single-angle measurement arc segment; Module M2, performing polynomial fitting on the observation data; Module M3, based on the polynomial fitting, calculating the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint time of the arc segment; Module M4, based on the polynomial fitting, calculating the rate of change of the pointing vector of the space debris relative to the observation station in the J2000 geocentric celestial coordinate system at the midpoint time of the arc segment; Module M5, setting the initial values of the distance and the rate of change of distance at the midpoint time of the arc segment, and respectively assigning them to the current distance and the rate of change of distance; Module M6, based on the pointing vector and the rate of change of the pointing vector, calculating the objective function corresponding to the current distance and the rate of change of distance; Module M7, determining whether the objective function reaches the convergence condition. If it does not reach the convergence condition, calculating the gradient of the objective function corresponding to the current distance and the rate of change of distance, and using a gradient-based optimization algorithm to update the current distance and the rate of change of distance, and repeating modules M6 to M7; If it reaches the convergence condition, ending the calculation, and calculating the corresponding position and velocity according to the current distance and the rate of change of distance.

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