Space-based angle-measurement-only short arc initial orbit determination method and system based on group optimization

Abstract

The invention provides a group optimization-based space-based angle-measurement-only short arc initial orbit determination method and system. The method comprises the following steps of: 1, setting fixed parameters; 2, initializing particles in the group; step 3, grouping the particles; 4, for all the particles, if the grouping identifier is 0, executing the step 5, otherwise, executing the step 6; 5, performing variation search and update on the particles in multiple directions; 6, updating the particles according to the tracking direction of the particles; 7, calculating a global optimal particle; and 8, repeating the steps 3-7 until a quit cycle condition is met, and outputting the orbit state quantity corresponding to the current global optimal particle. The method is easy to implement, has a certain anti-interference capability, and can stably and effectively solve the space-based angle-only-measurement short arc initial orbit determination problem.

Description

Technical Field

[0001] The present invention relates to the field of orbit determination technology, and in particular to a space-based short arc initial orbit determination method based on group optimization. Background Art

[0002] Space-based space target observation has the advantages of all-weather, all-day, and not being affected by the atmosphere. Therefore, since the 1990s, foreign countries have always regarded space-based observation as an indispensable monitoring means. At present, space-based observation still uses optical cameras as the main detection means. Based on the use of star calibration, optical cameras can achieve high angular measurement accuracy observation, and through the correlation between the previous and next imaging frames, the angular measurement data of the target over a period of time can be obtained. However, space-based optical observation means also have certain limitations, mainly manifested in that since it is only angular measurement data, and is limited by the observation field of view, the observation arc segment is usually not very long, and the geometric constraints on the target are insufficient in a short time. On the other hand, since the initial orbit determination of the space-based short arc with only angular measurement has a trivial solution, that is, the dynamic characteristics of the observation platform and the target are similar, it is more difficult to determine the initial orbit of the space-based short arc with only angular measurement. Since the initial orbit determination of the space-based short arc with only angular measurement requires finding a reasonable initial solution of the target to be used as the initial value of the precise orbit determination, only under reasonable initial values ​​can the precise orbit determination problem be solved as a "small residual" problem using gradients. The lack of geometric constraints on the target by only measuring the angle and observing the arc segment in a short period of time is also a common problem in this type of initial orbit determination problem.

[0003] When the observation data of the target is rich and the geometric constraints on the target are strong, the initial orbit determination can achieve higher accuracy. For example, Reference 1 (Chen Long, Non-cooperative common-view observation and initial orbit determination of LEO space targets, Acta Optica Sinica, Vol. 41, No. 19) provides a method for initial orbit determination for the same target of ground-based optical and laser observations. The observation data are from different stations and include laser observation data. The initial orbit determination of the ground-based angular arc segment can use the traditional Gauss method, Laplace method, and Gooding method. For example, Reference 2 (Liu Lin, Initial orbit calculation method considering the influence of the earth's flattening perturbation, Acta Astronomica Sinica, 2003, Vol. 44, No. 2) provides a Laplace initial orbit determination method considering flattening perturbation. Reference 3 (Liu Xiangchun, Research on orbit determination method of space debris by space-based photography tracking, 2009, National University of Defense Technology, master's degree thesis) provides the application of Laplace initial orbit calculation in space. The traditional Gauss method, Laplace method, and Gooding method are mainly applicable to the initial orbit determination of ground-based long arc segment targets. When processing only angle measurement data of space-based observations in a short period of time, the iteration will not converge or converge to a trivial solution, and the success rate of the solution is low. In order to make the traditional algorithms adapt to the application scenarios of space-based observations, a large number of literatures have improved the traditional algorithms in different directions. Literature 4 (Huang Pu, Initial orbit calculation method for low-orbit satellites to high-orbit satellites with only angle measurement, Flight Mechanics, 2020, Vol. 38, No. 1) established an extended Laplace dynamic model for initial orbit solution. Literature 5 (Wang Xueying, A space-based optical GEO target positioning method and initial orbit algorithm observation geometry evaluation, Aerospace Control, 2012, Vol. 30, No. 2) uses the generalized Laplace algorithm to calculate the initial orbit of space-based optical multi-platform multi-observation arc segments. Reference 6 (Zhao Kexin, Problems and methods for initial orbit determination of space-based optical space target monitoring, Acta Aeronautica Sinica, 2022, Vol. 44, No. 1) gives a mathematical representation of the trivial solution and improves the original Laplace octave equation to a septave equation for solution. Reference 7 (Zhao Kexin, A new method for space-based initial orbit determination using 3-dimensional azimuth observation, Acta Astronomica Sinica, 2022, Vol. 63, No. 5) derives the analytical form of the slant range condition equation based on the improved Gauss equation, and uses orbital energy constraints to eliminate the singularities of the equation group in the solution. Patent document 1 (A method for determining the initial orbit of a low-orbit target satellite based on space-based satellite angle measurement data, patent number CN103927289A) discloses a method for determining the initial orbit of a low-orbit target satellite based on space-based satellite angle measurement data. 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 for the observation line of sight vector, and adds certain constraints on the basis of the traditional Laplace method to form a conditional equation containing constraints for iteration.With the development of computer technology, more and more numerical calculation methods have been proposed. Most of the existing space-based initial orbit determination methods that only measure short arc angles have reduced the dimension of the solution space, using part of the observation data to reduce the original 6-dimensional solution space to 2 dimensions. For example, Reference 8 (Zhang Pin, Initial orbit determination method for low-orbit space debris using distance search, Spacecraft Engineering, 2017, Vol. 26, No. 2) searches for distance information at two moments and converts the pure angle initial orbit determination problem into an initial orbit determination problem based on two position vectors. In addition, Reference 9 (Zhang Pin, A method for initial orbit determination of space targets using only angle observations, 2017, Wuhan University, Master's thesis) studies the application efficiency of Gauss method, Gooding method and dual-distance search numerical method in space-based optical observation systems. Reference 10 (Liu Lei, Research on initial orbit determination of space targets based on space-based surveillance, 2010, National University of Defense Technology, Doctoral thesis) focuses on the application of dual-distance search numerical method, Gauss method and Laplace method in space-based direction finding initial orbit determination and corresponding improvements. Patent document 2 (Method and system flow for determining the initial orbit of space debris for a space-based optical monitoring platform, patent publication number CN115828037A) constructs a dual-distance search numerical method optimization model, and performs multiple initializations and iterations on the distances between the starting point and the end point to calculate the optimal solution. In addition to the above numerical solution methods that are reduced to 2D space, document 11 (Li Xinran, Extremely short arc orbit determination method based on evolutionary computing, 2018, University of Science and Technology of China, doctoral dissertation) and document 12 (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 problem of extremely short arc orbit determination from an evolutionary perspective, constructed a 3D (a, e, M in Kepler roots) optimization model, and implemented it based on three different evolutionary mechanisms: genetic algorithm, particle swarm algorithm, and differential evolution algorithm. Reference 13 (Song Kezhen, Extremely Short Arc Space-Based Orbit Determination Method Based on Genetic Algorithm, Spacecraft Engineering, 2019, Vol. 28, No. 5) divides a, e, M and i, Ω, ω in the 6-dimensional optimization problem into two 3-dimensional optimization problems based on genetic algorithm for solution. The genetic, particle swarm, differential progressive and other algorithms in the above references all belong to swarm optimization algorithms. Typical swarm optimization algorithms include genetic algorithm, ant colony optimization algorithm, particle swarm optimization algorithm, differential evolution algorithm, artificial peak swarm algorithm, firefly swarm optimization, cuckoo search algorithm, cat swarm optimization, etc. These swarm optimization algorithms have shown the potential to solve optimization problems in different fields. Swarm optimization algorithms are also used in ground measurement and control to determine the orbit of spacecraft.Reference 14 (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 ground measurement and control equipment, multiple sets of orbital elements, system objective equations and particle swarm algorithm, and is not applicable to space-based short arc segment data with only angle measurement.

[0004] The existing space-based short arc initial orbit determination method only measures angles, and performs a certain dimensionality reduction. Although the low dimension makes it easier to solve, the dimensionality reduction is not equivalent. The dimensionality reduction process has too high a degree of confidence in some observation data, which makes it difficult to find outliers in the data. Based on the orbit rationality constraint, the present invention constructs a 6-dimensional solution space search model, and designs a new swarm optimization strategy inspired by the cat swarm optimization algorithm. Some particles are used to search for better directions, and some particles are used to track on a certain memory basis, searching for solutions in the 6-dimensional solution space. The variation mode of particles in the search mode and the update mode of particles in the tracking mode are different from the original cat swarm optimization. Summary of the invention

[0005] In view of the defects in the prior art, the purpose of the present invention is to provide a method and system for determining the initial orbit of a space-based short arc with only angle measurement based on swarm optimization.

[0006] According to the present invention, a space-based short arc initial orbit determination method based on group optimization and angle measurement is provided, comprising:

[0007] Step S1: construct a 6-dimensional solution space optimization problem model;

[0008] Step S2: The 6-dimensional solution space optimization problem model uses a swarm optimization method to search in the 6-dimensional solution space to obtain the orbital state quantity corresponding to the global optimal particle;

[0009] Among them, the 6-dimensional solution space optimization problem model models the problem of initial orbit determination of the short arc by space-based angle measurement only as a constrained optimization problem model.

[0010] Preferably, the step S1 comprises:

[0011] The solution space of the 6-dimensional solution space optimization problem model is constructed as follows: is the six-dimensional orbital state quantity in is the three-dimensional space position of the target in the inertial coordinate system, is the three-dimensional space velocity in the inertial coordinate system;

[0012] Construct the objective function of the 6-dimensional solution space optimization problem model, including:

[0013]

[0014] Where M represents the number of samples in the short arc segment of space-based optical observation, represents the measured value of the pointing vector of the i-th sampling point, Represented by the orbital state quantity 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.

[0015] The fixed parameter setting in the 6-dimensional solution space optimization problem model includes: setting the minimum observation distance ρ min , the maximum observation distance ρ max , the minimum value of the orbital semi-major axis a min , the maximum value of the orbital semi-major axis a max , the total number of search groups N seek , the total number of tracking groups N track , the number of search directions N dir , position mutation probability α, 0<α<1, mutation range factor β, β>0, maximum number of iterations T max , the maximum number of iterations allowed without progress is T improve , loss function threshold f thresh .

[0016] Preferably, the step S2 adopts:

[0017] Step S2.1: Initialize particles in the group;

[0018] Step S2.2: Re-group the particles randomly, where any N seek The grouping flag of the group particle is set to 0, and the remaining N track The grouping flag of each group of particles is set to 1;

[0019] Step S2.3: For all particles, update them according to the grouping identifiers in turn;

[0020] Step S2.4: Calculate the global optimal particle; repeatedly trigger steps S2.2 to S2.4 until the preset loop exit condition is met; output the orbital state quantity corresponding to the current global optimal particle.

[0021] Preferably, the step S2.1 comprises:

[0022] Step S2.1.1: Calculate the maximum extreme value ρ of the observed distance limit If limit < max , then let ρ max =ρ limit ; Otherwise, no change;

[0023] Step S2.1.2: randomly generate an observation distance ρ according to a uniform distribution within the observation distance range;

[0024] Step S2.1.3: Calculate the lower limit of the distance change rate and the upper limit of the rate of change of distance

[0025]

[0026] Step S2.1.4: Within the range of distance change rate Randomly generate distance change rate according to uniform distribution

[0027] Step S2.1.5, calculate the orbital state quantity

[0028]

[0029] in, represents the position vector and velocity vector of the space-based optical observation platform itself, is the pointing vector of the target relative to the space-based optical observation platform, ρ is the distance of the target relative to the observation platform, is the distance change rate, is the direction change vector;

[0030] Step S2.1.6: Based on orbital state quantity Calculate the loss function value

[0031] Step S2.1.7: Tracking direction Initialize to

[0032] Step S2.1.8: Initialize the group ID to 0; Repeat steps S2.1.2 to S2.1.8 until N seek +N track Initialization of particles.

[0033] Preferably, the step S2.3 comprises:

[0034] When the grouping mark is 0, move the particle to N dir Search and update in each direction; when the grouping flag is 1, the particles are updated according to the tracking direction of the particles.

[0035] Preferably, when the grouping identifier is 0, the particle is moved to N dir Search and update in various directions, including:

[0036] Step S2.3.1: Move the particle to N dir Search in directions, among which the first αN dirThe position of the track is mutated in one direction, and the speed of the track is mutated in the other directions; where α represents the probability of position mutation;

[0037] Step S2.3.2: Calculate N dir The loss function values ​​corresponding to the particles after mutation in each direction;

[0038] Step S2.3.3: Search and obtain N dir The particle state with the smallest particle loss function after the direction mutation like The corresponding loss function Smaller than the original state of this group of particles Corresponding loss function, the orbital state of this group of particles is updated to Particle tracking direction Updated to

[0039]

[0040] The particle loss function value is updated as Otherwise, all properties of the particle remain unchanged.

[0041] Preferably, the variation of the position of the track comprises:

[0042]

[0043] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation, β is the range control factor of variation, and each direction corresponds to a different random number To achieve different directions corresponding to different like If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraint conditions;

[0044] The constraints are: the minimum and maximum value constraints of the geocentric two-body energy integral and the orbital semi-major axis;

[0045]

[0046] The scalar r represents the orbital position. The scalar v represents the orbital velocity. The size of ; μ is the gravitational constant;

[0047] The variation of the orbital velocity comprises:

[0048]

[0049] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation. If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraints.

[0050] Preferably, when the grouping identifier is 1, updating the particles according to the tracking direction of the particles includes:

[0051] Step S2.3.4: Calculate new tracking direction

[0052]

[0053] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 6-dimensional, is the optimal particle that all particles in the group have passed through in the current iteration;

[0054] Step S2.3.5: Calculate the new orbital state

[0055]

[0056] Step S2.3.6: Determine the new orbital state Whether the constraints are met, if so, calculate the loss function and update the particle attributes to as well as If the constraints are not met, all properties of the particle remain unchanged.

[0057] Preferably, the preset exit loop condition includes: reaching the set upper limit of the number of iterations T max ; The loss function value corresponding to the current global optimal particle is less than the set threshold f thresh ; and in T improve One of the following is the case where the global optimal particle is not updated within the iteration.

[0058] According to the present invention, a space-based short arc initial orbit determination system based on group optimization and angle measurement is provided, comprising:

[0059] Module M1: Constructing a 6-dimensional solution space optimization problem model;

[0060] Module M2: The 6-dimensional solution space optimization problem model uses the swarm optimization method to search in the 6-dimensional solution space to obtain the orbital state quantity corresponding to the global optimal particle;

[0061] Among them, the 6-dimensional solution space optimization problem model models the problem of initial orbit determination of the short arc by space-based angle measurement only as a constrained optimization problem model.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] 1. Aiming at the difficulty of solving the initial orbit of the short arc with only angle measurement in the space, the present invention constructs a 6-dimensional solution space search model based on the orbit rationality constraint condition. The observation data of all sampling points are treated without exception, which improves the anti-interference ability of the solution;

[0064] 2. Aiming at the constructed 6-dimensional variable optimization problem, the present invention designs a new group optimization strategy, which uses some particles to search for a better direction and some particles to track based on a certain memory, so as to search and solve in the constrained solution space;

[0065] 3. The method of the present invention is reasonable, simple to calculate, and easy to implement. It can be effectively applied to the initial orbit determination of a short arc based on space-based angle measurement only, and improves the robustness of the solution to the problem of initial orbit determination of a short arc based on space-based angle measurement only. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] 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:

[0067] Figure 1 It is a flow chart of the present invention.

[0068] Figure 2 The short arc initial orbit determination result obtained for working condition 1.

[0069] Figure 3 The short arc initial orbit determination result obtained for working condition 2. DETAILED DESCRIPTION

[0070] 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.

[0071] Example 1

[0072] According to a method for determining an initial orbit of a space-based short arc with only angle measurement based on group optimization provided by the present invention, Figure 1 As shown, including:

[0073] Step S1: construct a 6-dimensional solution space optimization problem model;

[0074] Step S2: The 6-dimensional solution space optimization problem model uses a swarm optimization method to search in the 6-dimensional solution space to obtain the orbital state quantity corresponding to the global optimal particle;

[0075] Among them, the 6-dimensional solution space optimization problem model models the problem of initial orbit determination of the short arc by space-based angle measurement only as a constrained optimization problem model.

[0076] Specifically, the step S1 includes:

[0077] The solution space of the 6-dimensional solution space optimization problem model is constructed as follows: is the six-dimensional orbital state quantity in is the three-dimensional space position of the target in the inertial coordinate system, is the three-dimensional space velocity in the inertial coordinate system;

[0078] Construct the objective function of the 6-dimensional solution space optimization problem model, including:

[0079]

[0080] Where M represents 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. represents the measured value of the pointing vector (unit vector) of the i-th sampling point, Represented by the orbital state quantity The estimated value of the pointing vector (unit vector) of the orbital position inferred from the determined orbit relative to the measured position of the space-based optical observation platform.

[0081] The fixed parameter setting in the 6-dimensional solution space optimization problem model includes: setting the minimum observation distance ρ min , the maximum observation distance ρ max , the minimum value of the orbital semi-major axis a min , the maximum value of the orbital semi-major axis a max , the total number of search groups N seek , the total number of tracking groups N track , the number of search directions N dir , position mutation probability α, 0<α<1, mutation range factor β, β>0, maximum number of iterations T max , the maximum number of iterations allowed without progress is T improve , loss function threshold f thresh Among them, the observation distance range ρ min , maxis the prior information of the space-based observation platform. For near-Earth targets, the minimum value of the orbital semi-major axis is a min Can be set to 6500km, the maximum value of the orbital semi-major axis a max Can be set to 80000km.

[0082] Specifically, the step S2 includes:

[0083] Step S2.1: Initialize particles in the group;

[0084] Step S2.2: Re-group the particles randomly, where any N seek The grouping flag of the group particle is set to 0, and the remaining N track The grouping flag of each group of particles is set to 1;

[0085] Step S2.3: For all particles, update them according to the grouping identifiers in turn;

[0086] Step S2.4: Calculate the global optimal particle; repeatedly trigger steps S2.2 to S2.4 until the preset loop exit condition is met; output the orbital state quantity corresponding to the current global optimal particle.

[0087] Wherein, the step S2.1 comprises:

[0088] Step S2.1.1: Calculate the maximum extreme value ρ of the observed distance limit If limit < max , then let ρ max =ρ limit ; otherwise, no change.

[0089] Step S2.1.2: randomly generate an observation distance ρ according to a uniform distribution within the observation distance range;

[0090] Step S2.1.3: Calculate the lower limit of the distance change rate and the upper limit of the rate of change of distance

[0091]

[0092] Step S2.1.4: Within the range of distance change rate Randomly generate distance change rate according to uniform distribution

[0093] Step S2.1.5: Calculate orbital state quantities

[0094]

[0095] in, represents the position vector and velocity vector of the space-based optical observation platform itself, is the pointing vector (unit vector) of the target relative to the space-based optical observation platform, ρ is the distance of the target relative to the observation platform, is the distance change rate, is the direction change vector;

[0096] Step S2.1.6: Based on orbital state quantity Calculate the loss function value

[0097] Step S2.1.7: Tracking direction Initialized to 0, that is

[0098] Step S2.1.8: Initialize the group ID to 0; Repeat steps S2.1.2 to S2.1.8 until N seek +N track Initialization of particles.

[0099] Wherein, the step S2.3 comprises:

[0100] When the grouping mark is 0, move the particle to N dir Search and update in each direction; when the grouping flag is 1, the particles are updated according to the tracking direction of the particles.

[0101] When the grouping mark is 0, the particle is moved to N dir Search and update in various directions, including:

[0102] Step S2.3.1: Move the particle to N dir Search in directions, among which the first αN dir The position of the track is mutated in one direction, and the speed of the track is mutated in the other directions; where α represents the probability of position mutation;

[0103] Step S2.3.2: Calculate N dir The loss function values ​​corresponding to the particles after mutation in each direction;

[0104] Step S2.3.3: Search and obtain N dir The particle state with the smallest particle loss function after the direction mutation like The corresponding loss function Smaller than the original state of this group of particles Corresponding loss function, the orbital state of this group of particles is updated to Particle tracking direction Updated to

[0105]

[0106] The particle loss function value is updated as Otherwise, all properties of the particle remain unchanged.

[0107] The variation of the position of the track includes

[0108]

[0109] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation, β is the range control factor of variation, and each direction corresponds to a different random number Different directions can correspond to different like If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraint conditions;

[0110] The constraints are: the minimum and maximum value constraints of the geocentric two-body energy integral and the orbital semi-major axis;

[0111]

[0112] The scalar r represents the orbital position. The scalar v represents the orbital velocity. The size of; μ is the gravitational constant, μ = 3.986004418 × 10 14 m 3 / s 2 ;

[0113] The variation of the orbital velocity comprises:

[0114]

[0115] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation. If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraints.

[0116] When the grouping identifier is 1, the particles are updated according to the tracking direction of the particles, including:

[0117] Step S2.3.4: Calculate new tracking direction

[0118]

[0119] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 6-dimensional, is the optimal particle that all particles in the group have passed through in the current iteration;

[0120] Step S2.3.5: Calculate the new orbital state

[0121]

[0122] Step S2.3.6: Determine the new orbital state Whether the constraints are met, if so, calculate the loss function and update the particle attributes to as well as If the constraints are not met, all properties of the particle remain unchanged.

[0123] The preset exit loop condition includes: reaching the set upper limit of the number of iterations T max ; The loss function value corresponding to the current global optimal particle is less than the set threshold f thresh ; and in T improve One of the following is the case where the global optimal particle is not updated within the iteration.

[0124] The present invention also provides a space-based short arc initial orbit determination system based on swarm optimization, which only uses angle measurement to determine the space-based short arc. The space-based short arc initial orbit determination system based on swarm optimization can be realized by executing the process steps of the space-based short arc initial orbit determination method based on swarm optimization, that is, those skilled in the art can understand the space-based short arc initial orbit determination method based on swarm optimization as a preferred implementation of the space-based short arc initial orbit determination system based on swarm optimization.

[0125] Example 2

[0126] Embodiment 2 is a preferred embodiment of Embodiment 1

[0127] According to the present invention, a space-based short arc initial orbit determination method based on group optimization and angle measurement is provided, comprising:

[0128] For space-based angle measurement data, if an arc segment contains M observations of the target, the easily available data include: exposure time series t i , Satellite position corresponding to the exposure time and speed The direction of the target relative to the satellite at the time of exposure The subscript i takes values ​​of 1, 2, ..., M.

[0129] In the geocentric inertial coordinate system, if the satellite position at the time of optical camera exposure is The distance between the target and the satellite is ρ, then the target position and speed satisfy

[0130]

[0131] in, are the position vector and velocity vector of the space-based optical observation platform itself, is the pointing vector (unit vector) of the target relative to the space-based optical observation platform, ρ is the distance of the target relative to the observation platform, is the distance change rate, is the direction change vector.

[0132] Track state quantity to be solved is a 6-dimensional vector.

[0133] If the measured observation vector of an arc segment is Then the least squares model is to obtain the orbital state of a set of space debris at time t The estimated position relative to the satellite observation vector is satisfied by Compared with the measured value As close as possible, the degree of closeness is the objective function, also known as the loss function. The orbital state quantity that minimizes the objective function is the solution to the least squares problem.

[0134]

[0135] Constraining the solution space of the initial short arc orbit determined by the space-based angle measurement is an effective means to avoid the solution from converging to an unreasonable orbit. The conditions that can be constrained include the energy constraint of the geocentric two-body, the semi-major axis of the target orbit, and the observation distance constraint. The observation distance range ρ min , max is the prior information of the space-based observation platform. For near-Earth targets, the minimum value of the orbital semi-major axis is a min Can be set to 6500km, the maximum value of the orbital semi-major axis a max Can be set to 80000km.

[0136] The minimum and maximum constraints of the energy integral of the two-body geocentric system and the semi-major axis of the orbit are:

[0137]

[0138] The scalar r represents the orbital position. The scalar v represents the orbital velocity. The size of μ is the gravitational constant, μ = 3.986004418 × 10 14 m 3 / s 2 .

[0139] In order to solve the above constrained least squares problem, if a gradient-based method is used, the gradient may disappear or become extremely large outside the constraint range or at the edge. In order to avoid gradient calculation, the present invention uses a group optimization-based method to search and solve.

[0140] There are many methods for swarm optimization. Inspired by cat swarm optimization, this paper designs two particle update methods to adapt to this solution scenario. One is search particle, and the other is tracking particle. Search particle randomly tries within a certain range near itself, and tracking particle is updated according to the direction information in memory. Particles enter search mode or tracking mode according to group identification. The group identification of particles is randomly assigned after each iteration.

[0141] According to the above design, at the beginning of the solution, the parameter settings need to be fixed, including the minimum observation distance ρ min , the maximum observation distance ρ max , the minimum value of the orbital semi-major axis a min , the maximum value of the orbital semi-major axis a max , the total number of search groups N seek , the total number of tracking groups N track , the number of search directions N dir , position mutation probability α (0<α<1), mutation range factor β (β>0).

[0142] Then the particles in the group are initialized. The particle properties include the track state (6-dimensional vector), tracking direction (6-dimensional vector), group identification and loss function value.

[0143] The particle initialization process utilizes the idea of ​​2D solution, but this value is only used as state initialization. After the initialization is completed, the degrees of freedom of the solution space will be restored to 6 dimensions, and finally the optimal particle search will be performed in the 6-dimensional solution space.

[0144] According to the constraints of formula 3, calculate the maximum extreme value ρ of the observation distance limit If ρ limit < max , then let ρ max =ρ limit ; Otherwise, no change is made. Randomly generate observation distance ρ and distance change rate according to uniform distribution in 2D space Calculate the initial value of the track state according to Formula 1. Calculate the loss function value f according to Formula 2. Tracking direction Initialized to 0, that is The group identifier is initialized to 0.

[0145] Then the particles are grouped, where any N seek The grouping flag of the group particle is set to 0, and the remaining N track The grouping flag of each particle is set to 1. Particles with grouping flag 0 are updated in search mode. Particles with grouping flag 1 are updated in tracking mode.

[0146] In search mode, the particle is near itself N dir The first αN dir The position of the track is mutated in one direction, and the speed of the track is mutated in the remaining directions.

[0147] The method to mutate the position of the track is

[0148]

[0149] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation, β is the range control factor of variation, and each direction corresponds to a different random number Different directions can correspond to different like If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraints.

[0150] The method to vary the orbital velocity is

[0151]

[0152] in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation. If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraints.

[0153] Calculate N dir The loss function values ​​of the particles after the particles mutate in different directions. Find the particle state with the minimum particle loss function like The corresponding loss function Smaller than the original state of this group of particles Corresponding loss function, the orbital state of this group of particles is updated to Particle tracking direction Updated to

[0154]

[0155] The particle loss function value is updated as Otherwise, all properties of the particle remain unchanged.

[0156] In tracking mode, particles are updated according to the tracking direction.

[0157] First calculate the new tracking direction

[0158]

[0159] in It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 6-dimensional, It is the best particle that all particles in the group have passed by in the current iteration.

[0160] Then calculate the new orbital state

[0161]

[0162] Determine the new orbital state Whether the constraints are met, if so, calculate the loss function and update the particle attributes to as well as If the constraints are not met, all properties of the particle remain unchanged.

[0163] When all particles are updated, the global optimal particle is calculated and a group iteration is completed. In the next round of group optimization, particles are randomly reassigned to enter the search or tracking mode. When the number of iterations reaches the set upper limit of the number of iterations, or the loss function value corresponding to the current global optimal particle is less than the set threshold, or the global optimal particle is not updated within the specified iteration period, the loop is exited.

[0164] The effectiveness of the method of the present invention is verified by combining simulation data. The scene of the space-based observation platform detecting high-orbit targets is constructed, and the angle measurement error is 2" (1σ). The actual orbit state of the target is [-36652.861027km, 19113.53058km, -8133.468249km, -0.967179km / s, -2.497631km / s, -1.515569km / s]. In the simulation, the working conditions without outliers and the working conditions with outliers are set respectively. The target states under the two working conditions are the same, and the working condition one has no outliers. The working condition two simulates the existence of outliers and simulates a more severe working condition, that is, the initial value of the particle is constructed by the outliers.

[0165] Set the minimum observation distance ρ min =5000km, maximum observation distance ρ max = 45000km, total number of search groups N seek =50, total number of tracking groups N track =50, number of search directions N dir =40, position variation probability α=0.5, variation range factor β=0.05.

[0166] By using the method of the present invention, the estimated value of the orbit state quantity obtained in working condition 1 is [-36554.3525329km, 19052.33202909km, -8128.27203409km, -0.97219409km / s, -2.50028225km / s, -1.51354155km / s]. The true value and the estimated value of the target position during the observation period are as follows: Figure 2 As shown. The observation error of the first sampling point of the arc in working condition 2 is larger than that of other sampling points, exceeding the set 2" (1σ) angle measurement error, which is a wild value. This point is still retained in the processing, and the particle state is initialized through this point. The final orbit state quantity converges to the estimated value [-36198.83253988km, 18832.6721754km, -8112.16266961km, -0.99589308km / s, -2.54223181km / s, -1.46495019km / s]. The true value and estimated value of the target position during the observation period are as follows Figure 3 Although the result is slightly worse than that of working condition 1, it is still within the acceptable range for determining the initial orbit of the short arc by measuring the angle of the space-based system.

[0167] 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.

[0168] 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 space-based short arc initial orbit determination method based on group optimization, characterized in that: include: Step S1: construct a 6-dimensional solution space optimization problem model; Step S2: The 6-dimensional solution space optimization problem model uses a swarm optimization method to search in the 6-dimensional solution space to obtain the orbital state quantity corresponding to the global optimal particle; Among them, the 6-dimensional solution space optimization problem model models the problem of initial orbit determination of the short arc by space-based angle measurement only as a constrained optimization problem model.

2. The method for determining the initial orbit of a space-based short arc by angle measurement based on group optimization according to claim 1, characterized in that: The step S1 comprises: The solution space of the 6-dimensional solution space optimization problem model is constructed as follows: is the six-dimensional orbital state quantity in is the three-dimensional space position of the target in the inertial coordinate system, is the three-dimensional space velocity in the inertial coordinate system; Construct the objective function of the 6-dimensional solution space optimization problem model, including: Where M represents the number of samples in the short arc segment of space-based optical observation, represents the measured value of the pointing vector of the i-th sampling point, Represented by the orbital state quantity 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. The fixed parameter setting in the 6-dimensional solution space optimization problem model includes: setting the minimum observation distance ρ min , the maximum observation distance ρ max , the minimum value of the orbital semi-major axis a min , the maximum value of the orbital semi-major axis a max , the total number of search groups N seek , the total number of tracking groups N track , the number of search directions N dir , position mutation probability α, 0<α<1, mutation range factor β, β>0, maximum number of iterations T max , the maximum number of iterations allowed without progress is T improve , loss function threshold f thresh .

3. The method for determining the initial orbit of a space-based short arc by angle measurement based on group optimization according to claim 2, characterized in that: The step S2 adopts: Step S2.1: Initialize particles in the group; Step S2.2: Re-group the particles randomly, where any N seek The grouping flag of the group particle is set to 0, and the remaining N track The grouping flag of each group of particles is set to 1; Step S2.3: For all particles, update them according to the grouping identifiers in turn; Step S2.4: Calculate the global optimal particle; repeatedly trigger steps S2.2 to S2.4 until the preset loop exit condition is met; output the orbital state quantity corresponding to the current global optimal particle.

4. The method for determining the initial orbit of a space-based short arc by angle measurement based on group optimization according to claim 3 is characterized in that: The step S2.1 comprises: Step S2.1.1: Calculate the maximum extreme value ρ of the observed distance limit If limit < max , then let ρ max =ρ limit ; Otherwise, no change; Step S2.1.2: randomly generate an observation distance ρ according to a uniform distribution within the observation distance range; Step S2.1.3: Calculate the lower limit of the distance change rate and the upper limit of the rate of change of distance Step S2.1.4: Within the range of distance change rate Randomly generate distance change rate according to uniform distribution Step S2.1.5, calculate the orbital state quantity in, represents the position vector and velocity vector of the space-based optical observation platform itself, is the pointing vector of the target relative to the space-based optical observation platform, ρ is the distance of the target relative to the observation platform, is the distance change rate, is the direction change vector; Step S2.1.6: Based on orbital state quantity Calculate the loss function value Step S2.1.7: Tracking direction Initialize to Step S2.1.8: Initialize the group ID to 0; Repeat steps S2.1.2 to S2.1.8 until N seek +N track Initialization of particles.

5. The method for determining the initial orbit of a space-based short arc by angle measurement based on group optimization according to claim 3 is characterized in that: The step S2.3 comprises: When the grouping mark is 0, move the particle to N dir Search and update in each direction; when the grouping flag is 1, the particles are updated according to the tracking direction of the particles.

6. The method for determining the initial orbit of a space-based short arc by angle measurement based on group optimization according to claim 5, characterized in that: When the grouping mark is 0, the particle is moved to N dir Search and update in various directions, including: Step S2.3.1: Move the particle to N dir Search in directions, among which the first αN dir The position of the track is mutated in one direction, and the speed of the track is mutated in the other directions; where α represents the probability of position mutation; Step S2.3.2: Calculate N dir The loss function values ​​corresponding to the particles after mutation in each direction; Step S2.3.3: Search and obtain N dir The particle state with the smallest particle loss function after the direction mutation like The corresponding loss function Smaller than the original state of this group of particles Corresponding loss function, the orbital state of this group of particles is updated to Particle tracking direction Updated to The particle loss function value is updated as Otherwise, all properties of the particle remain unchanged.

7. The method for determining the initial orbit of a space-based short arc by angle measurement based on group optimization according to claim 6, characterized in that: The variation of the position of the track includes in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation, β is the range control factor of variation, and each direction corresponds to a different random number To achieve different directions corresponding to different like If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraint conditions; The constraints are: the minimum and maximum value constraints of the geocentric two-body energy integral and the orbital semi-major axis; The scalar r represents the orbital position. The scalar v represents the orbital velocity. The size of ; μ is the gravitational constant; The variation of the orbital velocity comprises: in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 3-dimensional, corresponding to Three-dimensional variation. If the constraints are not met, keep direction, yes The corresponding modulus value is scaled to satisfy the constraints.

8. The method for determining the initial orbit of a space-based short arc by angle measurement based on group optimization according to claim 5, characterized in that: When the grouping identifier is 1, the particles are updated according to the tracking direction of the particles, including: Step S2.3.4: Calculate new tracking direction in, It is a random number generated in the range of -0.5 to 0.5 according to a uniform distribution. is 6-dimensional, is the optimal particle that all particles in the group have passed through in the current iteration; Step S2.3.5: Calculate the new orbital state Step S2.3.6: Determine the new orbital state Whether the constraints are met, if so, calculate the loss function and update the particle attributes to as well as If the constraints are not met, all properties of the particle remain unchanged.

9. The method for determining the initial orbit of a space-based short arc with only angle measurement based on group optimization according to claim 2, characterized in that: The preset exit loop condition includes: reaching the set upper limit of the number of iterations T max ; The loss function value corresponding to the current global optimal particle is less than the set threshold f thresh ; and in T improve One of the following is the case where the global optimal particle is not updated within the iteration.

10. A space-based short arc initial orbit determination system based on group optimization, characterized in that: include: Module M1: Constructing a 6-dimensional solution space optimization problem model; Module M2: The 6-dimensional solution space optimization problem model uses the swarm optimization method to search in the 6-dimensional solution space to obtain the orbital state quantity corresponding to the global optimal particle; Among them, the 6-dimensional solution space optimization problem model models the problem of initial orbit determination of the short arc by space-based angle measurement only as a constrained optimization problem model.

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