A method for solving the time sequence of fragment cloud disintegration based on spatiotemporal intersection characteristic statistics

Abstract

The application provides a debris cloud disintegration timing inversion method based on space-time intersection feature statistics, belongs to the field of disintegration timing inversion, and solves the problem of how to improve the accuracy of disintegration timing determination; the method comprises the following steps: traversing the standardized debris cloud orbit data after orbit propagation, calculating the closest distance time of each two pieces of debris; using an Epanechnikov kernel function to perform non-parametric probability density estimation on the closest distance time; combining the inverse function of the cumulative distribution function with the significance level to construct a confidence interval, and removing the debris outside the confidence interval; traversing the debris in the confidence interval, calculating the closest distance time of each two pieces of debris; using an Epanechnikov kernel function to perform non-parametric probability density estimation on the closest distance time; and taking the closest distance time corresponding to the maximum probability density estimation value as the disintegration time of the space target; the application has strong universality and strong robustness.

Description

Technical Field

[0001] This invention belongs to the field of spatial debris cloud disintegration time-series inversion technology, and particularly relates to a debris cloud disintegration time-series inversion method based on spatiotemporal intersection feature statistics. Background Technology

[0002] With the increasing frequency of space activities, the number of space targets is growing rapidly, leading to a sharp increase in the probability of collisions between them. Statistics show that tens of thousands of centimeter-sized or larger pieces of debris have been cataloged in low Earth orbit, a significant portion of which originated from space target disintegration events. Research on the origins of space target disintegration debris is of great value for debris cleanup, collision early warning systems, and monitoring the space environment, playing a crucial role in maintaining space security. The core of debris origin tracing lies in deducing the time, location, and cause of space target disintegration from the evolutionary characteristics of debris clouds. Currently, research on space debris mainly focuses on long-term debris evolution models, while research on debris origin tracing is relatively limited.

[0003] For example, in Qi Yue, Li Yiyong, Lai Jiazhe, et al. [Research on Short-Term Debris Cloud Source Tracing Method Based on Hoots Method [J]. Journal of Ordnance Equipment Engineering, 2017, 38(12):180-185.], the source tracing of disintegration events is achieved through spatial target proximity analysis and a simplified Hoots method. However, this method is based on the two-body assumption and has significant errors under complex perturbations. Furthermore, this method only studies the source tracing of short-term debris clouds and is not suitable for the source tracing of long-term debris clouds.

[0004] For example, application number 202010705381.9, publication number CN111831958A, invention title: "A Precise Calculation Method for Disintegration Time Based on the Minimum Enclosing Circle," involves iterating through the minimum enclosing circle radii of all debris at all times and selecting the point with the smallest radius as the disintegration time. However, this method relies on accurate high-precision initial orbits and has weak robustness. Furthermore, this method calculates the minimum enclosing circle in 1-second increments, which presents a significant computational burden for high-orbit space targets.

[0005] Therefore, research on the disintegration origins of fragment clouds considering complex perturbations and short- to long-term fragment cloud evolution is of great significance for sensing the space situation and maintaining space security. Summary of the Invention

[0006] To address the technical challenge of improving the accuracy of determining the time of disintegration, this invention proposes a fragment cloud disintegration time-series inversion method based on spatiotemporal intersection feature statistics. This method is applicable to inverting the disintegration time after a space target disintegration event. By statistically analyzing the closest moments between any two fragments (i.e., spatiotemporal intersection moments), the Epanechnikov kernel function is used to perform non-parametric probability density estimation on all closest moments to determine the disintegration time. Given the massive data volume in this invention, the Epanechnikov kernel function provides efficient data processing support for eliminating significant outliers and large errors, increasing the robustness of density estimation. This invention fully leverages the characteristics of fragment cloud data based on the distance features between pairs of fragments and effectively eliminates fragments with large errors, exhibiting high robustness and efficiency. It selects the closest moment corresponding to the maximum probability density estimate within the confidence interval as the space target disintegration time, resulting in low computational complexity and suitability for long-term fragment cloud source tracing studies.

[0007] To achieve the above objectives, the present invention is specifically implemented through the following technical solutions:

[0008] This invention provides a time-series inversion method for fragment cloud disintegration based on spatiotemporal intersection feature statistics, including:

[0009] Step 1: After standardizing the orbital data of the debris cloud following the disintegration event of the space target acquired by the ground-based telescope equipment, the data is then propagated along the orbit.

[0010] Step 2: Traverse the debris cloud orbit data after orbit propagation and calculate the first closest distance moment for all pairs of debris.

[0011] Step 3: Use the first Epanechnikov kernel function to perform non-parametric probability density estimation on all first closest moments to construct the cumulative distribution function; construct the confidence interval from the inverse function of the cumulative distribution function, and remove debris cloud orbit data that are outside the confidence interval.

[0012] Step 4: Traverse the debris cloud orbit data within the confidence interval and calculate the second closest distance time for all pairs of debris.

[0013] Step 5: Use the second Epanechnikov kernel function to perform non-parametric probability density estimation on all second closest distance moments, and take the second closest distance moment corresponding to the largest second probability density estimate as the disintegration moment of the space target.

[0014] In step one, the standardized operation method is as follows:

[0015] S11, through a mapping function, unifies the debris cloud orbit data to the J2000 geocentric inertial coordinate system;

[0016] S12 converts the timestamps of the debris cloud orbital data to Corrected Julian Day (MJD); the mapping function in S11 is:

[0017] ;

[0018] In the formula, The position coordinates of the debris cloud orbit data in the J2000 geocentric inertial coordinate system. The distance from the debris to the Earth's core. Right ascension of the ascending node, For true near point angle, This represents the track inclination angle.

[0019] In step one, the method of orbital propagation is as follows:

[0020] If the debris in the debris cloud orbit data is low-Earth orbit debris, then the HPOP model is used for orbit propagation;

[0021] If the debris in the debris cloud orbit data is medium-high orbit debris, then the SGP4 model is used for orbit propagation.

[0022] In step two, the method for calculating the first closest distance time is as follows:

[0023] ;

[0024] ;

[0025] In the formula, The moment when the two fragments are closest to each other. Let b be the index of the first fragment at the first closest time, b be the index of the second fragment at the first closest time, t be the time variable, and D(t) be the first distance function. For the first The geocentric distance vector of each fragment. Let b be the geocentric distance vector of the b-th fragment. For the first The position coordinates of the fragment in the J2000 geocentric inertial coordinate system. Let be the position coordinates of the b-th fragment in the J2000 geocentric inertial coordinate system.

[0026] Step 3: The first Epanechnikov kernel function is used to perform non-parametric probability density estimation on all first closest moments to construct the cumulative distribution function. The confidence interval is constructed from the inverse function of the cumulative distribution function. The method for eliminating debris cloud orbital data outside the confidence interval is as follows:

[0027] S21, use the first Epanechnikov kernel function to perform non-parametric probability density estimation on all first closest moments to obtain the first probability density estimate;

[0028] S22, construct the cumulative distribution function by performing a cumulative distribution estimate on the first probability density estimate;

[0029] S23, the confidence interval is constructed by combining the inverse function of the cumulative distribution function with the significance level;

[0030] S24: Retain debris cloud orbit data within the confidence interval and remove debris cloud orbit data outside the confidence interval.

[0031] In S21, the method for calculating the first probability density estimate is as follows:

[0032] ;

[0033] In the formula, This is the first probability density estimate. This represents the total number of all pairs of fragments in the fragment cloud orbital data. Let be the bandwidth of the first Epanechnikov kernel function, and n be the index of each pair of fragments in the fragment cloud orbital data. This is the first Epanechnikov kernel function. ; This is the set of the first closest moments.

[0034] In S22, the cumulative distribution function is constructed as follows:

[0035] ;

[0036] In the formula, The cumulative distribution function is... This is an estimate of the cumulative distribution function. is the input variable for the cumulative distribution function.

[0037] In S23, the constructed confidence interval is:

[0038] CI=[F -1 (α / 2), F -1 [(1-α / 2)];

[0039] In the formula, CI represents the range of the confidence interval, and F... -1 () is the inverse function of the cumulative distribution function, and α is the significance level.

[0040] In step four, the method for calculating the second closest distance time is as follows:

[0041] ;

[0042] ;

[0043] In the formula, Let c be the index of the first fragment used to calculate the second closest distance between the two fragments, and d be the index of the second fragment used to calculate the second closest distance. For the second distance function, Let c be the geocentric distance vector of the c-th fragment. Let d be the geocentric distance vector of the d-th fragment. Let be the position coordinates of the c-th fragment in the J2000 geocentric inertial coordinate system. Let c,d be the position coordinates of the d-th fragment in the J2000 geocentric inertial coordinate system, where c,d∈CI.

[0044] In step five, the second Epanechnikov kernel function is used to perform non-parametric probability density estimation on all second closest distance moments. The method of taking the second closest distance moment corresponding to the largest second probability density estimate as the disintegration moment of the space target is as follows:

[0045] ;

[0046] In the formula, This is the second probability density estimate. This represents the total number of all pairs of fragments in the fragment cloud orbital data that are within the confidence interval. denoted as the bandwidth of the second Epanechnikov kernel function, and m as the index of each pair of fragments in the fragment cloud orbital data within the confidence interval. This is the second Epanechnikov kernel function. ; This is the set of the second closest moments;

[0047] Among them, the second probability density estimate The second closest moment corresponding to the peak is the moment when the space target disintegrates. : .

[0048] The beneficial effects of this invention are:

[0049] 1. Perform standardization operations on the debris cloud orbit data, convert the debris cloud orbit data to the J2000 geocentric inertial coordinate system, and align the coordinate system; unify the timestamps to International Atomic Time for timestamp calibration to ensure the accuracy and consistency of the timestamps.

[0050] 2. Corresponding orbital propagation models were used for low-Earth orbit debris and medium-to-high-Earth orbit debris, respectively; perturbations such as the non-spherical gravity of the Earth and atmospheric drag of low-Earth orbit debris were considered; and the superposition of the three-body gravitational effect and the gravitational perturbations of the Sun and Moon were considered for medium-to-high-Earth orbit debris.

[0051] 3. Based on the minimum distance between any two fragments, the corresponding time is determined as the most relevant time, that is, the time when the fragments are most likely to disintegrate. Therefore, this invention iterates through and calculates the times when the closest distance between any two fragments in the fragment cloud orbit data is.

[0052] 4. For the closest moments of all pairwise fragments, the Epanechnikov kernel function is used to perform non-parametric probability density estimation, which improves computational efficiency and increases the robustness of density estimation. It can run efficiently for massive datasets and can support the subsequent removal of large error data with significant outliers.

[0053] 5. Construct a confidence interval by combining the inverse function of the constructed cumulative distribution function with the significance level, and remove fragment cloud orbit data that are outside the confidence interval range, thereby eliminating large-error fragment data and improving the accuracy of determining the time of disintegration.

[0054] 6. For the filtered debris cloud orbital data, the closest distance time between each pair of debris is calculated again. The Epanechnikov kernel function is used to perform non-parametric probability density estimation. The closest distance time at the peak of the probability density estimate is determined as the disintegration time. This reduces the amount of computation and improves the accuracy of determining the disintegration time, making it suitable for the source tracing research of long-term debris clouds.

[0055] 7. Based on the distance characteristics between pairs of fragments, this invention fully explores the characteristics of fragment cloud data and effectively removes fragment data with large errors, thus possessing high robustness and efficiency. Attached Figure Description

[0056] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0057] Figure 1 This is a schematic diagram of the first closest distance moment provided by the present invention.

[0058] Figure 2 This is a schematic diagram of the first probability density estimate provided by the present invention.

[0059] Figure 3 This is a schematic diagram of the cumulative distribution function estimate provided by the present invention.

[0060] Figure 4 This is a schematic diagram of the second closest distance moment provided by the present invention.

[0061] Figure 5This is a schematic diagram of the second probability density estimate provided by the present invention. Detailed Implementation

[0062] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0063] This invention provides a method for time-series inversion of fragment cloud disintegration based on spatiotemporal intersection feature statistics, including:

[0064] Step 1: After standardizing the orbital data of the debris cloud following the disintegration event of the space target acquired by the ground-based telescope equipment, the data is then propagated along the orbit.

[0065] Step 2: Traverse the debris cloud orbit data after orbit propagation and calculate the first closest distance moment for all pairs of debris.

[0066] Step 3: Use the first Epanechnikov kernel function to perform non-parametric probability density estimation on all first closest moments to construct the cumulative distribution function; construct the confidence interval from the inverse function of the cumulative distribution function, and remove debris cloud orbit data that are outside the confidence interval.

[0067] Step 4: Traverse the debris cloud orbit data within the confidence interval and calculate the second closest distance time for all pairs of debris.

[0068] Step 5: Use the second Epanechnikov kernel function to perform non-parametric probability density estimation on all second closest distance moments, and take the second closest distance moment corresponding to the largest second probability density estimate as the disintegration moment of the space target.

[0069] In step one, the standardized operation method is as follows:

[0070] S11, through the mapping function, unifies the debris cloud orbit data to the J2000 geocentric inertial coordinate system and aligns the coordinate system;

[0071] S12 converts the timestamps of the debris cloud orbital data to Corrected Julian Day (MJD) for timestamp calibration to ensure accuracy and consistency; the mapping function in S11 is:

[0072] ;

[0073] In the formula, The position coordinates of the debris cloud orbit data in the J2000 geocentric inertial coordinate system. The distance from the debris to the Earth's core. Right ascension of the ascending node, For true near point angle, This represents the track inclination angle.

[0074] In step one, the method of orbital propagation is as follows:

[0075] If the debris in the debris cloud orbit data is low-Earth orbit debris (orbit altitude ≤ 8370km), considering perturbations such as Earth's non-spherical gravity and atmospheric drag, the HPOP (High Precision Orbit Propagator) model is used for orbit propagation.

[0076] If the debris in the debris cloud orbit data is medium-high orbit debris (orbit altitude > 8370km), considering the three-body gravitational effect and the gravitational perturbation of the sun and moon, the SGP4 (Simplified General Perturbations4) model is used for orbit propagation.

[0077] In step two, the method for calculating the first closest distance time is as follows:

[0078] ;

[0079] ;

[0080] In the formula, The moment when the two fragments are closest to each other. Let b be the index of the first fragment at the first closest time, b be the index of the second fragment at the first closest time, t be the time variable, and D(t) be the first distance function. For the first The geocentric distance vector of each fragment. Let b be the geocentric distance vector of the b-th fragment. For the first The position coordinates of the fragment in the J2000 geocentric inertial coordinate system. Let be the position coordinates of the b-th fragment in the J2000 geocentric inertial coordinate system.

[0081] Step 3: The first Epanechnikov kernel function is used to perform non-parametric probability density estimation on all first closest moments to construct the cumulative distribution function. The confidence interval is constructed from the inverse function of the cumulative distribution function. The method for eliminating debris cloud orbital data outside the confidence interval is as follows:

[0082] S21, use the first Epanechnikov kernel function to perform non-parametric probability density estimation on all first closest moments to obtain the first probability density estimate;

[0083] S22, construct the cumulative distribution function by performing a cumulative distribution estimate on the first probability density estimate;

[0084] S23, the confidence interval is constructed by combining the inverse function of the cumulative distribution function with the significance level;

[0085] S24: Retain debris cloud orbit data within the confidence interval and remove debris cloud orbit data outside the confidence interval.

[0086] In S21, the method for calculating the first probability density estimate is as follows:

[0087] ;

[0088] In the formula, This is the first probability density estimate. This represents the total number of all pairs of fragments in the fragment cloud orbital data. Let be the bandwidth of the first Epanechnikov kernel function, and n be the index of each pair of fragments in the fragment cloud orbital data. This is the first Epanechnikov kernel function. ; This is the set of the first closest moments.

[0089] In S22, the cumulative distribution function is constructed as follows:

[0090] ;

[0091] In the formula, The cumulative distribution function is... This is an estimate of the cumulative distribution function. is the input variable for the cumulative distribution function.

[0092] In S23, the constructed confidence interval is:

[0093] CI=[F -1 (α / 2), F -1 [(1-α / 2)];

[0094] In the formula, CI represents the range of the confidence interval, and F... -1 () is the inverse function of the cumulative distribution function, and α is the significance level.

[0095] In step four, the method for calculating the second closest distance time is as follows:

[0096] ;

[0097] ;

[0098] In the formula, Let c be the index of the first fragment used to calculate the second closest distance between the two fragments, and d be the index of the second fragment used to calculate the second closest distance. For the second distance function, Let c be the geocentric distance vector of the c-th fragment. Let d be the geocentric distance vector of the d-th fragment. Let be the position coordinates of the c-th fragment in the J2000 geocentric inertial coordinate system. Let c,d be the position coordinates of the d-th fragment in the J2000 geocentric inertial coordinate system, where c,d∈CI. t is the time variable, which is the time axis for unified discretization. Preferably, a discrete window Δt is set: Δt=10s for low orbit and Δt=60s for medium and high orbit.

[0099] In step five, the second Epanechnikov kernel function is used to perform non-parametric probability density estimation on all second closest distance moments. The method of taking the second closest distance moment corresponding to the largest second probability density estimate as the disintegration moment of the space target is as follows:

[0100] ;

[0101] In the formula, This is the second probability density estimate. This represents the total number of all pairs of fragments in the fragment cloud orbital data that are within the confidence interval. denoted as the bandwidth of the second Epanechnikov kernel function, and m as the index of each pair of fragments in the fragment cloud orbital data within the confidence interval. This is the second Epanechnikov kernel function. ; This is the set of the second closest moments;

[0102] Among them, the second probability density estimate The second closest moment corresponding to the peak is the moment when the space target disintegrates. : .

[0103] To illustrate the technical solution of the present invention, a specific example is provided below:

[0104] Step one involves standardizing the orbital data of the debris cloud following a space target disintegration event, obtained through ground-based telescope equipment, and then propagating it onto the orbit.

[0105] On September 6, 2024, the American commercial space company Slingshot Aerospace detected the disintegration of the upper stage of the Centaur spacecraft. Russia's JSC Vimpel cataloged hundreds of pieces of debris generated by the event. Along with the orbital elements, they provide parameters such as the area-to-mass ratio and orbital uncertainties for each space object, facilitating accurate orbit calculations. This cataloging includes 143 pieces of debris with orbital epochs between September 16th and 17th.

[0106] Aligning the coordinate system: Using the mapping function from two rows of roots to J2000, the orbit is unified to the geocentric inertial coordinate system; calibrating the timestamp: The timestamp is converted to the modified Julian day (MJD) and the orbit is propagated.

[0107] Step 2: Traverse the debris cloud orbit data after orbit propagation, and calculate the first closest distance moment for all pairs of debris, such as... Figure 1 As shown.

[0108] Step 3: Use the first Epanechnikov kernel function to perform non-parametric probability density estimation on all first nearest distance moments, and obtain the first probability density estimate as follows: Figure 2 As shown; the cumulative distribution function estimate of the first probability density estimate is calculated using the cumulative distribution function, as shown below. Figure 3 As shown; the inverse function of the constructed cumulative distribution function is combined with the significance level to construct a confidence interval with a 5% confidence level:

[0109] CI 95% =[F -1 (0.025),F -1 [(0.975)] = [2024-09-06 10:09:40, 2024-09-07 06:09:47];

[0110] After removing debris cloud orbital data that are outside the confidence interval, the number of debris within the confidence interval is 107.

[0111] Step four: Iterate through the debris cloud orbit data within the confidence interval, and calculate the second closest distance time for all pairs of debris, as shown below. Figure 4 As shown.

[0112] Step 5: Use the second Epanechnikov kernel function to perform non-parametric probability density estimation for all second closest time points, such as... Figure 5 As shown, the second closest distance time corresponding to the obtained maximum second probability density estimate is taken as the disintegration time of the space target. The final disintegration time of the space target is: 2024-09-06 13:04:38 (Beijing time).

[0113] The beneficial effects of the embodiments of the present invention are:

[0114] 1. Perform standardization operations on the debris cloud orbit data, convert the debris cloud orbit data to the J2000 geocentric inertial coordinate system, and align the coordinate system; unify the timestamps to International Atomic Time for timestamp calibration to ensure the accuracy and consistency of the timestamps.

[0115] 2. Corresponding orbital propagation models were used for low-Earth orbit debris and medium-to-high-Earth orbit debris, respectively; perturbations such as the non-spherical gravity of the Earth and atmospheric drag of low-Earth orbit debris were considered; and the superposition of the three-body gravitational effect and the gravitational perturbations of the Sun and Moon were considered for medium-to-high-Earth orbit debris.

[0116] 3. Based on the minimum distance between any two fragments, the corresponding time is determined as the most relevant time, that is, the time when the fragments are most likely to disintegrate. Therefore, this invention iterates through and calculates the times when the closest distance between any two fragments in the fragment cloud orbit data is.

[0117] 4. For the closest moments of all pairwise fragments, the Epanechnikov kernel function is used to perform non-parametric probability density estimation, which improves computational efficiency and increases the robustness of density estimation. It can run efficiently for massive datasets and can support the subsequent removal of large error data with significant outliers.

[0118] 5. Construct a confidence interval by combining the inverse function of the constructed cumulative distribution function with the significance level, and remove fragment cloud orbit data that are outside the confidence interval range, thereby eliminating large-error fragment data and improving the accuracy of determining the time of disintegration.

[0119] 6. For the filtered debris cloud orbital data, the closest distance time between each pair of debris is calculated again. The Epanechnikov kernel function is used to perform non-parametric probability density estimation. The closest distance time at the peak of the probability density estimate is determined as the disintegration time. This reduces the amount of computation and improves the accuracy of determining the disintegration time, making it suitable for the source tracing research of long-term debris clouds.

[0120] 7. Based on the distance characteristics between pairs of fragments, this invention fully explores the characteristics of fragment cloud data and effectively removes fragment data with large errors, thus possessing high robustness and efficiency.

[0121] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for deagglomeration timing inversion of a debris cloud based on spatiotemporal encounter feature statistics, characterized in that, The application relates to a method for determining a breakup time of a space target, comprising the following steps: Step one: performing a standardization operation on the fragment cloud orbit data of a space target breakup event obtained by a ground-based telescope device, and then performing orbit propagation; Step two: traversing the fragment cloud orbit data after orbit propagation, and calculating the first closest distance time of all pairs of fragments; Step three: adopting a first Epanechnikov kernel function to perform non-parametric probability density estimation on all the first closest distance times, and constructing a cumulative distribution function; constructing a confidence interval by the inverse function of the cumulative distribution function, and removing the fragment cloud orbit data out of the range of the confidence interval, which comprises the following steps: S21: adopting the first Epanechnikov kernel function to perform non-parametric probability density estimation on all the first closest distance times, and obtaining a first probability density estimation value; wherein the calculation method of the first probability density estimation value is as follows: ； wherein is a first probability density estimate, is a total number of all pairs of fragments in the debris cloud orbit data, is a bandwidth of a first Epanechnikov kernel, n is an index of a pair of fragments in the debris cloud orbit data, is a first Epanechnikov kernel, ; is a set of first closest distance times; S22: performing cumulative distribution estimation on the first probability density estimation value to construct a cumulative distribution function; S23: constructing a confidence interval by the inverse function of the cumulative distribution function combined with a significance level; S24: retaining the fragment cloud orbit data within the range of the confidence interval, and removing the fragment cloud orbit data out of the range of the confidence interval; Step four: traversing the fragment cloud orbit data within the range of the confidence interval, and calculating the second closest distance time of all pairs of fragments; Step five: adopting a second Epanechnikov kernel function to perform non-parametric probability density estimation on all the second closest distance times, and taking the second closest distance time corresponding to the maximum second probability density estimation value as the breakup time of the space target.

2. The method according to claim 1, wherein, In step one, the method for performing the standardization operation is as follows: S11: unifying the fragment cloud orbit data to the J2000 geocentric inertial coordinate system through a mapping function; S12: converting the time stamp of the fragment cloud orbit data into a modified Julian day MJD; wherein the mapping function in S11 is as follows: ； wherein is the position coordinate of the debris cloud orbit data in the J2000 Earth-Centered Inertial coordinate system, is the distance of the debris to the Earth's center, is the longitude of the ascending node, is the true anomaly, is the orbital inclination.

3. The method according to claim 2, wherein, In step one, the method for orbit propagation is as follows: If the fragments in the fragment cloud orbit data are low-orbit fragments, the HPOP model is adopted for orbit propagation; If the fragments in the fragment cloud orbit data are medium-orbit or high-orbit fragments, the SGP4 model is adopted for orbit propagation.

4. The method according to claim 3, wherein, In step two, the calculation method of the first closest distance time is as follows: ； ； wherein is the first closest approach time of the pair of fragments, is the index of the first fragment for which the first closest approach time is calculated, b is the index of the second fragment for which the first closest approach time is calculated, t represents the time variable, D(t) is the first distance function, is the geocentric distance vector of the first fragment, is the geocentric distance vector of the bth fragment, is the position coordinate of the first fragment in the J2000 geocentric inertial coordinate system, is the position coordinate of the bth fragment in the J2000 geocentric inertial coordinate system.

5. The debris cloud disintegration timing inversion method based on spatiotemporal intersection feature statistics according to claim 1 or 4, characterized in that, In S22, the construction method of the cumulative distribution function is as follows: ； wherein is the cumulative distribution function, is the cumulative distribution function estimate, is the input variable of the cumulative distribution function.

6. The method according to claim 5, wherein, In S23, the constructed confidence interval is as follows: CI=[F -1 (α / 2), F -1 (1 - α / 2)]; where CI is the range of the confidence interval, F -1 () is the inverse function of the cumulative distribution function, and a is the significance level.

7. The method according to claim 6, wherein, In step four, the calculation method of the second closest distance time is as follows: ； ； wherein, is the second closest distance time of the pair of fragments, c is the index of the first fragment for which the second closest distance time is calculated, d is the index of the second fragment for which the second closest distance time is calculated, is the second distance function, is the geocentric distance vector of the cth fragment, is the geocentric distance vector of the dth fragment, is the position coordinate of the cth fragment in the J2000 geocentric inertial coordinate system, is the position coordinate of the dth fragment in the J2000 geocentric inertial coordinate system, c, d e CI.

8. The method according to claim 7, wherein, In step five, the method for adopting the second Epanechnikov kernel function to perform non-parametric probability density estimation on all the second closest distance times, and taking the second closest distance time corresponding to the maximum second probability density estimation value as the breakup time of the space target is as follows: ； wherein is a second probability density estimate, is a total number of all pairs of fragments in the debris cloud orbit data within the range of the confidence interval, is a bandwidth of a second Epanechnikov kernel, m is an index of a pair of fragments in the debris cloud orbit data within the range of the confidence interval, is a second Epanechnikov kernel, ; is a set of second nearest distance times; The second probability density estimation value The second nearest distance corresponding to the peak is the spatial target disintegration moment : .

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