Large-scale space target collision early warning combination screening method

Abstract

This invention discloses a large-scale space target collision early warning combination screening method, belonging to the field of space situational awareness. The implementation method is as follows: Preliminary screening of similar targets is performed based on the distance between intersection points on the orbital plane intersection line to quickly reduce the number of satellite combinations to be analyzed; by decomposing the analytical solution considering the minimum relative distance between satellites under J2 perturbation, it is divided into long-term terms and exact solutions; based on the evolution characteristics of the long-term terms, a second screening is performed using the trend characteristics of the long-term terms; a third screening is performed using the analytical exact solution considering the relative distance between satellites under J2 perturbation; based on the results of the third screening, satellite combinations with collision risk are determined, realizing large-scale space target collision early warning combination screening, thereby protecting the safety of space assets. This invention fully considers the long-term evolution characteristics of orbits under perturbation, significantly reducing the calculation time for early warning, and is suitable for rapid screening of long-term collision early warnings for large-scale space targets.

Description

Technical Field

[0001] This invention relates to a collision risk combination screening method for large-scale non-cooperative targets in space, belonging to the field of space situational awareness. Background Technology

[0002] With the rapid deployment of large low-Earth orbit satellite constellations, global communication coverage, high-precision navigation, and high-frequency remote sensing observation capabilities have been significantly enhanced. However, the continuous increase in the number of satellites has led to increasing congestion in orbital space, exacerbating conflicts in orbital resource allocation and causing frequent spacecraft approach incidents, seriously threatening the long-term safe operation of spacecraft in orbit. To ensure the safety of on-orbit assets, reduce unnecessary orbital maneuvers, and extend satellite mission lifespan, it is urgent to establish an efficient and accurate space target collision risk identification and early warning mechanism. However, existing collision early warning technologies suffer from a significant trade-off between computational efficiency and accuracy, making it difficult to meet the real-time early warning requirements of large-scale constellations.

[0003] Collision risk screening based on the geometric relationships between satellites is the most intuitive collision warning method and has naturally become a research hotspot. In particular, when conducting collision warnings for large-scale space targets, it is necessary to design reasonable screening strategies to reduce computation time while ensuring warning accuracy.

[0004] To improve computational efficiency, various screening strategies based on geometric configurations have been proposed in existing technologies. The prior art [1] (Casanova D, Tardioli C, Lemaître A. Space debris collision avoidance using athree-filter sequence[J].Monthly Notices of the Royal Astronomical Society,2014(4):3235-3242.) quickly eliminates target pairs that have no possibility of rendezvous by calculating the distance between perigee and apogee, thereby significantly reducing computational complexity. However, this method relies on an ideal Keplerian orbital model and does not consider the perturbation effects such as the non-spherical gravity of the Earth, resulting in large errors in long-term analysis.

[0005] In the quantitative assessment of collision risk, collision probability is the most representative indicator. Existing collision probability models are broadly divided into short-term encounter models and long-term encounter models. Short-term models typically assume constant relative velocity and straight-line relative trajectories, and are suitable for short-term near-ground encounters. The typical Foster–Estes model (JL Foster, HS Estes. AParametric Analysis of Orbital Debris Collision Probability and Maneuver Rate for Space Vehicles. NASA / JSC 25898, August 1992) calculates the collision probability by establishing a polar coordinate system on the encounter plane, but the accuracy of the calculation depends on the step size setting. Subsequent studies have improved this model by methods such as dimensional reduction or error function expansion to reduce the computational burden. Long-term models consider the nonlinearity of relative motion and the effects of orbital perturbations. For example, the method of Coppola et al. (Coppola VT, Woodburn J, Hujsak R. Effects of cross correlated covariance on spacecraft collision probability[C] / / AAS / AIAA Spaceflight MechanicsMeeting. 2004, 181.) solves by integrating the time variation of the probability density function over a given time span. However, such methods usually require a large amount of numerical integration, resulting in high computational complexity and making it difficult to meet real-time requirements.

[0006] The minimum relative distance between satellites is another important indicator for measuring collision risk. Relative motion analysis methods have evolved from the Clohessy–Wiltshire equation for circular orbits to the Tschauner–Hempel equation for elliptical orbits, and have gradually expanded to consider complex dynamic conditions such as J2 perturbations. In recent years, some studies (Wang Kexin, Dang Zhaohui. Minimum Inter-Satellite Distance Calculation Method Based on Deep Neural Network [J]. Aerospace Technology, 2024, (04): 76-84.) have used numerical methods or machine learning models to estimate the minimum inter-satellite distance, improving prediction accuracy, but the computational load remains large. Summary of the Invention

[0007] To address the trade-off between computational speed and accuracy in existing collision warning screening methods when dealing with large-scale space targets, this invention aims to provide a large-scale space target collision warning combined screening method. This method rapidly reduces the number of satellite combinations to be detected through a progressively more precise combined screening strategy. By separating the long-term evolution characteristics and the minimum value of the relative distance analytical solution between satellites, it quickly screens satellite combinations with collision risk. This achieves rapid early warning while maintaining computational accuracy, thereby protecting space assets.

[0008] The present invention is achieved through the following technical solution.

[0009] The large-scale space target collision early warning combination screening method disclosed in this invention quickly screens satellite combinations with collision risk by using the geometric relationship between satellites and the minimum relative distance. It performs preliminary screening of all satellite combinations based on the distance between the intersection points on the orbital plane intersection line, thereby quickly reducing the number of satellite combinations that need to be detected. Subsequently, it separates the long-term term and periodic term of the analytical solution of the relative distance between satellites and uses the functional characteristics of the long-term term for secondary screening. Finally, it uses the minimum value of the analytical solution of the relative distance between satellites for precise screening to determine the satellite combinations with collision risk.

[0010] The large-scale space target collision early warning combination screening method disclosed in this invention includes the following steps:

[0011] Step 1: Select a pair of satellites from the satellite constellation, calculate the orbital plane normal vectors of the two satellites based on the initial orbital six-element number of the satellite pair, and determine the intersection line of the orbital planes of the two satellites; then obtain the distance between the orbital plane intersection line and the intersection point of the two satellite orbits.

[0012] Input the initial six-element number of the two satellites' orbits. , Then, the direction of the intersection line between the two satellites and the orbital plane is calculated. It is the semi-major axis of the primary star's orbit. It is the eccentricity of the primary star's orbit. It is the orbital inclination of the primary star. It is the right ascension of the ascending node of the primary star. It is the argument of the perigee of the primary star. It is the angle of the main star's near point. It is from the semi-major axis of the star's orbit. It comes from the eccentricity of the star's orbit. It is from the inclination of the star's orbit. It is the right ascension of the star's ascending node. It is the angle of perigee of the star. It is from the near point of the star level;

[0013]

[0014] in, and It is the normal vector between the orbital plane of the primary star and the orbital plane of the secondary star.

[0015]

[0016] in, These represent the primary star and the secondary star, respectively.

[0017] Determine the direction of the satellite's apogee vector.

[0018]

[0019] in,

[0020]

[0021]

[0022]

[0023] Determine the angle between the line of intersection of the orbital plane and the direction of the Earth vector at the apogee of the primary and secondary stars' orbits:

[0024]

[0025] in, =0,1, representing the primary star and the secondary star respectively;

[0026] Then the distance between the orbital plane intersection line and the intersection points of the two satellite orbits was calculated. ,

[0027] .

[0029] Step 2: Traverse all candidate satellite pairs in the satellite constellation, repeating Step 1 for each pair; filter all the obtained distance values ​​to construct a preliminary filtered index matrix.

[0030] judge Check if the collision exceeds the set collision threshold, and retrieve the elements of the index matrix.

[0031]

[0032] From satellite database The combination of satellites to be detected is selected sequentially through the process. and ( Repeat step 1 to calculate the distance between the intersection line of the two satellite orbital planes and the orbital intersection point;

[0033] After traversing all satellite combinations, an index matrix is ​​obtained.

[0034]

[0035] Step 3: Based on the preliminary screening index matrix in Step 2, select satellite pairs in pairs, calculate their J2 perturbation long-term term distance, and apply this distance condition for secondary screening to obtain the secondary screening index matrix.

[0036] For the preliminary screening of the index matrix in step 2 Each element in ,if Then it is necessary to calculate the satellite corresponding to the subscript element. and Considering the long-term term of the relative distance at time t under J2 perturbation :

[0037]

[0038] in, The initial relative distance,

[0039]

[0040] in, As an intermediate variable; It is the difference between the six elements of the initial orbits of the two satellites, that is:

[0041]

[0042]

[0043]

[0044]

[0045] Among them, the superscript " "Indicates the average number of orbital elements, For the Earth's radius, The second harmonic constant of the Earth's gravitational field is denoted as . For intermediate variables;

[0046]

[0047] As can be seen from the above, based on the long-term term s of the relative distance... t The expression for the long-term term of the evolution of the relative distance between the two satellites is a time-varying, upward-opening quadratic function, with its extreme point appearing at... At that moment, when At that time, the relative distance between satellites increases monotonically with time.

[0048] if and That is, long-term terms It monotonically increases over time, and in The relative distance between satellites, of which The threshold representing the secondary screening will be used to filter the index matrix from the initial screening. After setting the elements with no collision risk to 0, we obtain the index matrix for secondary filtering. .

[0049] Step 4: Based on the secondary screening index matrix of Step 3, select satellite pairs in pairs, calculate the minimum relative distance between satellites within a certain time range, and apply this distance criterion to perform a third screening. Finally, obtain the index matrix of the three screenings. The number of rows and columns of the items with an element of 1 in the index matrix is ​​the ordinal number of the satellite combination with collision risk.

[0050] For the preliminary screening of the index matrix in step 3 Each element in ,if Then calculate the satellite and By considering the minimum relative distance under J2 perturbation, the risk of satellite collision is determined by judging whether the minimum value is greater than the safety threshold.

[0051] The minimum relative distance can be considered as the average mean aperitoneal angle of the primary star. To find the minimum value of a function, we need to solve the following quartic equation in one variable.

[0052]

[0053] in,

[0054]

[0055]

[0056]

[0057] All are constants and can be calculated using the following formula:

[0058]

[0059] in, The parameters in the formula are:

[0060]

[0061] in, ,

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] After solving the quartic equation in one variable to obtain the value of x, the different Minimum value of x Distance threshold In comparison, if Then the satellite and There is a risk of collision.

[0077] Beneficial effects:

[0078] This invention discloses a large-scale space target collision early warning combination screening method, which rapidly screens satellite combinations with collision risk based on the geometric relationships between satellites and the minimum relative distance. The invention initially screens all satellite combinations based on the distance between the intersection points on the orbital plane intersection line, quickly reducing the number of satellite combinations to be detected. Subsequently, the analytical solution of the relative distance between satellites is separated into long-term and periodic terms, and a secondary screening is performed using the functional characteristics of the long-term term. Finally, the minimum value of the analytical solution of the relative distance between satellites is used for precise screening to determine the satellite combinations with collision risk. This invention fully considers the long-term evolution characteristics of orbits under perturbation, significantly reducing the calculation time for early warning, and is suitable for rapid screening of long-term collision early warning for large-scale space targets. Attached Figure Description

[0079] Figure 1 This is a schematic diagram of the large-scale space target collision early warning combined screening method of the present invention;

[0080] Figure 2 This is a comparison diagram of the relative distance evolution between the analytical method and the numerical method in this invention. Detailed Implementation

[0081] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0082] To verify the effectiveness of this invention in large-scale constellation collision risk assessment, and to ensure that there is a collision risk among these satellites, a small random range of six roots was set based on the six roots of the main satellite orbit, and 1000 satellites were randomly generated for mathematical simulation verification.

[0083] The six root numbers of the main satellite orbit are:

[0084]

[0085] The range of random six-root numbers is:

[0086]

[0087] The collision threshold is set as follows:

[0088]

[0089] like Figure 1 As shown in the figure, the specific implementation steps of the large-scale space target collision early warning combination screening method disclosed in this embodiment are as follows:

[0090] Step 1: Select a pair of satellites from the satellite constellation and input their initial orbital root numbers. Calculate the orbital plane normal vectors of the two satellites and determine the line of intersection of their orbital planes. Then calculate the distance between the line of intersection and the point of intersection of the two satellite orbits.

[0091] Input the initial six-element number of the two satellites' orbits. , Then, the direction of the intersection line between the two satellites and the orbital plane is calculated. It is the semi-major axis of the primary star's orbit. It is the eccentricity of the primary star's orbit. It is the orbital inclination of the primary star. It is the right ascension of the ascending node of the primary star. It is the argument of the perigee of the primary star. It is the angle of the main star's near point. It is from the semi-major axis of the star's orbit. It comes from the eccentricity of the star's orbit. It is from the inclination of the star's orbit. It is the right ascension of the star's ascending node. It is the angle of perigee of the star. It is from the near point of the star level;

[0092] Determine the intersection vector of the orbital planes of the two satellites. ,

[0093]

[0094] in, and It is the normal vector between the target orbital plane and the orbital plane to be detected.

[0095]

[0096] in, These represent the primary star and the secondary star, respectively.

[0097] Determine the direction of the satellite's apogee vector.

[0098]

[0099] in,

[0100]

[0101]

[0102]

[0103] Determine the angle between the line of intersection of the orbital plane and the direction of the Earth vector at the apogee of the primary and secondary stars' orbits:

[0104]

[0105] in, These represent the primary star and the secondary star, respectively.

[0106] Then the distance between the intersection line of the orbital plane and the intersection point of the two satellite orbits was calculated.

[0107]

[0108] Step 2: Traverse all possible satellite pairs in the satellite constellation, repeating the calculation process of Step 1 for each pair. Filter all calculated distance values ​​to construct a preliminary filtered index matrix;

[0109] From satellite database The combination of satellites to be detected is selected sequentially through the process. and ( Input the six roots of the selected satellite combination into step 1 to calculate the distance between the intersection line of the orbital planes of the two satellites and the orbital intersection point. In this simulation analysis, N=1000.

[0110] Seek Then, determine whether the collision exceeds the set collision threshold and obtain the elements of the index matrix.

[0111]

[0112] After traversing all satellite combinations, an index matrix can be obtained.

[0113]

[0114] Step 3: Based on the preliminary screening index matrix in Step 2, select satellite pairs in pairs, calculate their J2 perturbation long-term term distance, and apply this distance condition for secondary screening to obtain the secondary screening index matrix.

[0115] For the preliminary screening of the index matrix in step 2 Each element in ,if Then it is necessary to calculate the satellite and Considering the long-term term of the relative distance at time t under J2 perturbation . Based on the six-digit data from the two satellites, it can be represented as follows:

[0116]

[0117] in,

[0118]

[0119]

[0120] Among them, the superscript " "" indicates the average number of orbital elements.

[0121] From the above equation, it can be seen that, based on the long-term term s of the relative distance... t The expression for the long-term term of the evolution of the relative distance between the two satellites is a time-varying, upward-opening quadratic function, with its extreme point appearing at... At that moment, when At that time, the relative distance between satellites increases monotonically with time.

[0122] if and That is, long-term terms It monotonically increases over time, and in The relative distance between satellites, of which This represents the threshold for secondary screening. It can be calculated using the following formula:

[0123]

[0124] in, It is the difference between the six elements of the initial orbits of the two satellites.

[0125] The index matrix of the initial screening After setting the elements with no collision risk to 0, we obtain the index matrix for secondary filtering. .

[0126] Step 4: Based on the secondary screening index matrix of Step 3, select satellite pairs in pairs, calculate the minimum relative distance between satellites within a certain time range, and apply this distance criterion to perform a third screening. Finally, obtain the index matrix of the three screenings. The number of rows and columns of the items with an element of 1 in the index matrix is ​​the ordinal number of the satellite combination with collision risk.

[0127] For the preliminary screening of the index matrix in step 3 Each element in ,if Then calculate the satellite and By considering the minimum relative distance under J2 perturbation, the risk of satellite collision is determined by judging whether the minimum value is greater than the safety threshold.

[0128] Solve the following quartic equation in one variable.

[0129]

[0130] in,

[0131]

[0132]

[0133] All are constants and can be calculated using the following formula:

[0134]

[0135] in, The parameters in the formula are:

[0136]

[0137]

[0138] in, ,

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152] After solving the quartic equation in one variable to obtain the value of x, the different Minimum value of x Distance threshold In comparison, if Then the satellite and There is a risk of collision.

[0153] The screening results and time consumption of this invention are shown in Table 1 below.

[0154] Table 1. Time and Results of Each Screening Round

[0155]

[0156] The baseline numerical method directly processed all the initial data, taking 59,393.101 seconds and yielding 4,950 high-risk satellite pairs. Comparison showed that the satellite pairs selected by the method of this invention were completely consistent with those selected by the numerical method.

[0157] To better quantify the accuracy, the evolution of the relative distance between satellites was simulated and analyzed using both the method in step 4 and the numerical method. The results are as follows: Figure 2As shown in the figure, the distance curves obtained by the two methods are highly consistent throughout the simulation period. Quantitative analysis shows that the maximum absolute value of the error does not exceed 95.4 meters, which is within an acceptable range, thus verifying the correctness of the analytical model proposed in this invention and the effectiveness of the proposed screening method.

[0158] This completes the rapid assessment for early warning of large-scale space target collisions.

[0159] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for screening large-scale space target collision early warning combinations, characterized in that: Includes the following steps, Step 1: Select a pair of satellites from the satellite constellation. Based on the initial orbital six-element number of the satellite pair, calculate the orbital plane normal vectors of the two satellites and determine the intersection line of the orbital planes of the two satellites; then obtain the distance between the intersection line of the orbital planes and the intersection point of the orbits of the two satellites. Step 2: Traverse all candidate satellite pairs in the satellite constellation, repeating Step 1 for each pair; filter all the obtained distance values ​​and construct a preliminary filtering index matrix after preliminary filtering; Step 3: Based on the preliminary screening index matrix in Step 2, arbitrarily select satellite pairs, calculate the long-term distance variation trend of satellite pairs considering J2 perturbation, traverse to obtain the long-term distance variation trend of all satellite pairs, and apply this variation trend to perform secondary screening, thereby obtaining the secondary screening index matrix. Step 4: Based on the secondary screening index matrix in Step 3, select satellite pairs again by traversing them in pairs, calculate the analytical solution of the minimum relative distance under J2 perturbation, and obtain the satellite combination with collision risk.

2. The method as described in claim 1, characterized in that: The initial orbital root number of the satellite pair described in step 1 is: , , It is the semi-major axis of the primary star's orbit. It is the eccentricity of the primary star's orbit. It is the orbital inclination of the primary star. It is the right ascension of the ascending node of the primary star. It is the argument of the perigee of the primary star. It is the angle of the main star's near point. It is from the semi-major axis of the star's orbit. It comes from the eccentricity of the star's orbit. It is from the inclination of the star's orbit. It is the right ascension of the star's ascending node. It is the angle of perigee of the star. It is from the near point of the star.

3. The method as described in claim 1, characterized in that: The method for determining the intersection line of the orbital planes of the two satellites is as follows: Based on the initial orbital root numbers of the two satellites and the orbital plane normal vectors of the two satellites, determine the intersection vector of the orbital planes of the two satellites. : in, and It is the normal vector between the orbital plane of the primary star and the orbital plane of the secondary star. in, , representing the primary star and the secondary star respectively.

4. The method as described in claim 1, characterized in that: The method for obtaining the distance between the intersection line of the orbital plane and the intersection point of the two satellite orbits is as follows: Determine the direction of the satellite's apogee vector. in, Determine the angle between the line of intersection of the orbital plane and the direction of the Earth vector at the apogee of the primary and secondary stars' orbits: in, These represent the primary star and the secondary star, respectively. This allows us to obtain the distance between the intersection line of the orbital plane and the intersection point of the two satellite orbits. , 。 5. The method as described in claim 1, characterized in that: The implementation method for step 2 is as follows: judge Check if the collision exceeds the set collision threshold, and retrieve the elements of the index matrix. From satellite database The combination of satellites to be detected is selected sequentially through the process. and ( Repeat step 1 to calculate the distance between the intersection line of the two satellite orbital planes and the orbital intersection point; After traversing all satellite combinations, an index matrix is ​​obtained. 。 6. The method as described in claim 1, characterized in that: The specific implementation method for step 3 is as follows: For the preliminary screening of the index matrix in step 2 Each element in ,if Then it is necessary to calculate the satellite corresponding to the subscript element. and Considering the long-term term of the relative distance at time t under J2 perturbation : in, The initial relative distance, As an intermediate variable; It is the difference between the six elements of the initial orbits of the two satellites, that is: in, Among them, the superscript " "Indicates the average number of orbital elements, For the Earth's radius, The second harmonic constant of the Earth's gravitational field is denoted as . As an intermediate variable; The long-term term of the evolution of the relative distance between the two satellites is a time-varying, upward-opening quadratic function, with its extreme point appearing at... At that moment, when At that time, the relative distance between satellites increases monotonically with time; if Then the long term is The term is monotonically increasing, and if the long term is in... Relative distance between satellites If the two satellites are in good condition, then it is determined that there is no risk of collision. The threshold representing the secondary screening; for For each element that is 1, calculate the corresponding... and The index matrix for secondary filtering is obtained. ; 。 7. The method as described in claim 1, characterized in that: The specific implementation method for step 4 is as follows: For the preliminary screening of the index matrix in step 3 Each of them The elements, calculating satellites and By considering the minimum relative distance under J2 perturbation, and then determining whether the minimum value is greater than the safety threshold, it is possible to determine whether the satellite is at risk of collision. The minimum relative distance is equivalent to the mean mean aperimeter angle of the principal star. To find the minimum value of a function, we need to solve the following quartic equation in one variable. in, All are constants, calculated by the following formula: in, After solving the quartic equation in one variable to obtain the value of x, the different Minimum value of x Distance threshold In comparison, if Then the satellite and There is a risk of collision.

8. The method as described in claim 7, characterized in that: The , Represented as, in, , .

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