A space disintegration event time reconstruction method based on statistics of fragment and main body debris intersection time

Abstract

The application provides a space disintegration event time reconstruction method based on fragment and main body wreckage intersection time statistics, belongs to the field of space disintegration event time reconstruction, and solves the problem of how to improve the accuracy of space disintegration event time reconstruction; comprising: constructing a coarse distance model based on the standardized fragment cloud after orbit propagation and the main body wreckage, calculating a first time set of the closest distance time of any fragment in the fragment cloud and the main body wreckage; constructing a first Gaussian kernel function to estimate a first probability density estimate value, constructing a confidence interval by estimating the inverse function of the cumulative distribution function, and removing the fragments outside the confidence interval; constructing a fine distance model based on the position coordinates of the fragment cloud and the main body wreckage in the confidence interval, calculating a second time set; constructing a second Gaussian kernel function to obtain the closest distance time corresponding to the maximum second probability density estimate value as the space disintegration event time; the application improves the accuracy, robustness and efficiency of the reconstructed disintegration time.

Description

Technical Field

[0001] The present invention belongs to the technical field of space disintegration event time reconstruction, and in particular relates to a space disintegration event time reconstruction method based on statistics of the intersection time between fragments and main wreckage. Background Art

[0002] With humanity's exploration and utilization of outer space, space activities have grown exponentially, leading to a significant increase in the amount of space debris, much of which is generated by spacecraft breakup events. Tracing the breakup of space debris is crucial for understanding its origin and evolution, as well as assessing its potential threat to orbiting spacecraft. The core of breakup tracing lies in reconstructing the time and location of space breakup events, as well as the physical characteristics of the breakup process, using observational data from debris clouds. Currently, research on space debris primarily focuses on debris cloud evolution modeling and orbital analysis.

[0003] For example, by combining multi-source observational data (such as radar and optical telescopes) with orbital mechanics models, high-precision orbit determination and evolution simulation of debris clouds can be achieved. Furthermore, methods based on probability density representations have been proposed to more efficiently describe the evolution of debris clouds. Simultaneously, ground-based simulation experiments are also being conducted to study the distribution characteristics of debris from satellite explosions and disintegration. These technical studies provide important theoretical foundations and methodological support for debris tracing.

[0004] Although existing technologies have made significant progress in orbit determination and evolution simulation of space debris, there are still some key shortcomings in tracing the disintegration source:

[0005] First, most existing disintegration models are based on simplified physical assumptions and cannot fully include all factors, such as satellite materials, interactions between debris, and momentum distribution at the moment of disintegration.

[0006] Secondly, although multi-source data fusion technology can improve the accuracy of orbit determination, the depth and breadth of data fusion still need to be further improved in disintegration tracing, especially in complex perturbation environments, and the adaptability and reliability of existing methods still face challenges.

[0007] Finally, existing technologies still lack research on tracing the time dimension of disintegration events, making it difficult to accurately determine the moment of disintegration, which affects subsequent research.

[0008] For example: Application number: 201711212888.5, Publication number: CN107992669A, Invention name: A method and system for determining the type of spacecraft disintegration events, a method for determining the type of spacecraft disintegration events based on a particle swarm optimization algorithm is proposed, which can efficiently distinguish and determine spacecraft explosion events and impact disintegration events, but does not reconstruct the time of the disintegration event.

[0009] The above-mentioned defects limit the accuracy and effectiveness of space debris disintegration tracing technology in practical applications, and new methods and technologies are urgently needed to break through the existing bottlenecks. Summary of the Invention

[0010] To address the technical challenges of reconstructing the moment of space disintegration in the presence of major debris and improving its accuracy, this paper proposes a method for reconstructing the moment of space disintegration based on statistics of the intersection of debris and major debris. This method is applicable to space disintegration events where major debris can be identified. By calculating the moment of closest approach between the debris and the major debris, a Gaussian kernel function is constructed for density estimation and analysis, allowing the peak value to be used to determine the moment of disintegration. The Gaussian kernel function constructed in this paper is smooth, robust, and versatile, effectively preserving marginal data and avoiding the problem of false rejection caused by data mutations.

[0011] To achieve the above object, the present invention is specifically implemented through the following technical solutions:

[0012] The present invention provides a method for reconstructing the time of a spatial disintegration event based on statistics of the time of intersection between debris and main wreckage, comprising:

[0013] Step 1: sequentially perform standardization processing and orbit propagation operations on the debris cloud orbit data and the main debris orbit data obtained by the space situational awareness and surveillance system after the space disintegration event;

[0014] Step 2: Based on the coordinates of the debris cloud and the main debris after orbital propagation, a coarse distance model is constructed. The time when any fragment in the debris cloud is closest to the main debris is calculated using the coarse distance model to obtain the first time set.

[0015] Step 3: Construct a first Gaussian kernel function for the first moment set, estimate a first probability density estimate for the first moment set using the first Gaussian kernel function, perform cumulative distribution on the first probability density estimate to construct an estimated cumulative distribution function, combine the inverse function of the estimated cumulative distribution function with the significance level to construct a confidence interval, and remove large error fragments outside the confidence interval;

[0016] Step 4: Based on the position coordinates of the debris cloud and the main wreckage within the confidence interval, a fine distance model is constructed. The fine distance model is used to calculate the time of the closest distance between any fragment in the debris cloud and the main wreckage within the confidence interval to obtain a second time set.

[0017] Step 5: Construct the second Gaussian kernel function of the second moment set, obtain the second probability density estimate of the second moment set by the second Gaussian kernel function, and take the closest distance moment corresponding to the maximum second probability density estimate as the moment of the spatial disintegration event.

[0018] In step 1, the standardization method is:

[0019] A conversion model from the TLE (Two-Line Element) to the J2000 Earth-centered inertial coordinate system is constructed. The orbital data of the debris cloud and the main debris are converted from the TLE to the J2000 Earth-centered inertial coordinate system by the conversion model. At the same time, the timestamps of the orbital data of the debris cloud and the main debris are converted to the Modified Julian Day (MJD). The conversion model is:

[0020] ;

[0021] Where, is the position coordinate of the debris cloud or main wreckage in the J2000 geocentric inertial coordinate system, is the distance from the debris or main wreckage to the center of the Earth, is the right ascension of the ascending node, is the true anomaly angle, is the orbital inclination.

[0022] In step 1, the orbital propagation method is:

[0023] If the orbits of the debris cloud and the main debris are in low orbit, the HPOP model is used for orbital propagation;

[0024] If the orbits of the debris cloud and the main debris are in medium and high orbits, the SGP4 model is used for orbital propagation.

[0025] In step 2, the coarse distance model constructed is:

[0026] ;

[0027] The moment when any fragment in the debris cloud is closest to the main wreckage The calculation method is:

[0028] ; Among them, all Constitute the first moment set ;

[0029] Where, is the distance between any fragment in the debris cloud and the main debris at that moment, and t is the time variable; is the position coordinate of the i-th fragment in the J2000 geocentric inertial coordinate system, r i (t)=[x i (t), y i (t), z i (t)] T ; is the position coordinate of the main debris in the J2000 geocentric inertial coordinate system, r0(t)=[x0(t), y0(t), z0(t)] T ; i is the fragment number, o is the main wreckage, and T is transposition.

[0030] In step 3, the first Gaussian kernel function constructed is:

[0031] ;

[0032] The method for estimating the first probability density estimate of the first moment set by the first Gaussian kernel function is:

[0033] ;

[0034] Where, is the value of the first Gaussian kernel function, and e is a natural constant; is the first probability density estimate, is the total number of fragments in the fragment cloud, is the bandwidth of the first Gaussian kernel function.

[0035] In step 3, the method for constructing an estimated cumulative distribution function by performing cumulative distribution on the first probability density estimate is:

[0036] ;

[0037] Where, To estimate the cumulative distribution function, To estimate the cumulative distribution function value, is the input variable for estimating the cumulative distribution function;

[0038] In step 3, the confidence interval constructed by combining the inverse function of the estimated cumulative distribution function with the significance level is:

[0039] CI=[F -1 (α / 2), F -1 (1-α / 2)];

[0040] Where CI is the confidence interval, F -1 () is the inverse function of the estimated cumulative distribution function, and α is the significance level.

[0041] In step 4, the fine distance model constructed is:

[0042] ;

[0043] The moment when any fragment in the debris cloud is closest to the main debris within the confidence interval The calculation method is:

[0044] ; Among them, all Constructing the second moment set ;

[0045] Where, is the distance between any fragment in the debris cloud and the main wreckage within the confidence interval; is the position coordinate of the kth fragment within the confidence interval in the J2000 geocentric inertial coordinate system, r k (t)=[x k (t),y k (t),z k (t)] T ; k is the fragment index within the confidence interval.

[0046] In step 5, the second Gaussian kernel function constructed is:

[0047] ;

[0048] The method for obtaining the second probability density estimate of the second moment set by the second Gaussian kernel function is:

[0049] ;

[0050] Where, is the second Gaussian kernel function value; is the second probability density estimate, is the total number of fragments within the confidence interval, is the bandwidth of the second Gaussian kernel function.

[0051] In step 5, the closest distance moment corresponding to the maximum second probability density estimate is taken as the time of the spatial disintegration event The method is:

[0052] .

[0053] The beneficial effects of the present invention are:

[0054] 1. The present invention sequentially performs standardization processing on the debris cloud orbital data and the main debris orbital data obtained by the space situational awareness and surveillance system after a space disintegration event, aligning the coordinate system and calibrating the timestamp to ensure the accuracy and consistency of the timestamp. It also performs orbit propagation based on the orbit type, taking into account perturbations such as the Earth's non-spherical gravity and atmospheric drag on low-orbit debris, as well as the superimposed three-body gravitational effect and solar and lunar gravitational perturbations on medium- and high-orbit debris, making it easy to understand and implement.

[0055] 2. Theoretically, the moment when the debris and the main debris are closest is the most correlated moment between them, i.e., the breakup moment. Therefore, for breakup events that could produce main debris, the present invention establishes coarse and fine distance models for the debris cloud and the main debris after orbital propagation. This coarse-fine dual-stage optimization model strategy accurately determines the moment of closest approach. The moment of spacecraft breakup is determined based on this moment of closest approach between the main debris and the debris cloud, improving temporal resolution.

[0056] 3. Constructing a Gaussian kernel function for non-parametric probability density estimation can improve computational efficiency, be applicable to large-scale fragmented clouds, and increase anti-interference capabilities. Based on the constructed coarse-fine dual-stage optimization model strategy, the constructed Gaussian kernel function is called twice, which is smooth, robust, and versatile. It can effectively retain edge data and avoid the problem of false rejection caused by data mutation.

[0057] 4. Construct a confidence interval by using the inverse function of the constructed cumulative distribution function, delete the fragmented data outside the confidence interval, and eliminate large errors or erroneous fragmented data, thereby improving robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0059] Figure 1 This is a first moment set schematic diagram provided by the present invention.

[0060] Figure 2 It is a schematic diagram of estimating the first probability density estimate of the first moment set by the first Gaussian kernel function provided by the present invention.

[0061] Figure 3 It is a schematic diagram of the estimated cumulative distribution function value obtained by estimating the cumulative distribution function provided by the present invention.

[0062] Figure 4 This is a schematic diagram of the second moment set provided by the present invention.

[0063] Figure 5 It is a schematic diagram of a second probability density estimation value of a second moment set obtained by a second Gaussian kernel function provided by the present invention. DETAILED DESCRIPTION

[0064] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0065] The embodiment of the present invention provides a method for reconstructing the time of a space disintegration event based on statistics of the intersection time of debris and main wreckage, which is applicable to space disintegration events that can determine the main wreckage, including:

[0066] Step 1: sequentially perform standardization processing and orbit propagation operations on the debris cloud orbit data and the main debris orbit data obtained by the space situational awareness and surveillance system after the space disintegration event;

[0067] Among them, the main debris refers to the structural components that are easy to be optically detected and imaged, such as engine components, spacecraft shells, etc., which are left after the disintegration of space targets after a space disintegration event.

[0068] Debris refers to space objects that are difficult to be detected and imaged optically after the disintegration of space targets in a space disintegration event. The sizes and shapes of the fragments vary, ranging from a few centimeters to tens of centimeters. One disintegration will produce hundreds or thousands of fragments.

[0069] Step 2: Based on the coordinates of the debris cloud and the main debris after orbital propagation, a coarse distance model is constructed. The time when any fragment in the debris cloud is closest to the main debris is calculated using the coarse distance model to obtain the first time set.

[0070] Step 3: Construct a first Gaussian kernel function for the first moment set, estimate a first probability density estimate for the first moment set using the first Gaussian kernel function, perform cumulative distribution on the first probability density estimate to construct an estimated cumulative distribution function, combine the inverse function of the estimated cumulative distribution function with the significance level to construct a confidence interval, and remove large error fragments outside the confidence interval;

[0071] Step 4: Based on the position coordinates of the debris cloud and the main wreckage within the confidence interval, a fine distance model is constructed. The fine distance model is used to calculate the time of the closest distance between any fragment in the debris cloud and the main wreckage within the confidence interval to obtain a second time set.

[0072] Step 5: Construct the second Gaussian kernel function of the second moment set, obtain the second probability density estimate of the second moment set by the second Gaussian kernel function, and take the closest distance moment corresponding to the maximum second probability density estimate as the moment of the spatial disintegration event.

[0073] In step 1, the standardization method is:

[0074] A conversion model from the TLE (Two-Line Element) to the J2000 Earth-centered inertial coordinate system is constructed. The orbital data of the debris cloud and the main debris are converted from the TLE to the J2000 Earth-centered inertial coordinate system by the conversion model. At the same time, the timestamps of the orbital data of the debris cloud and the main debris are converted to the Modified Julian Day (MJD). The conversion model is:

[0075] ;

[0076] Where, is the position coordinate of the debris cloud or main wreckage in the J2000 geocentric inertial coordinate system, is the distance from the debris or main wreckage to the center of the Earth, is the right ascension of the ascending node, is the true anomaly angle, is the orbital inclination.

[0077] In step 1, the orbital propagation method is:

[0078] If the orbits of the debris cloud and the main debris are in low orbit (orbit altitude ≤ 8370km), the HPOP (High Precision Orbit Propagator) model is used for orbital propagation, taking into account perturbations such as the Earth's non-spherical gravity and atmospheric drag;

[0079] If the orbits of the debris cloud and the main debris are in medium-high orbits (orbit altitude > 8370km), the SGP4 (Simplified General Perturbations4) model is used for orbital propagation considering the three-body gravitational effect and the gravitational perturbations of the sun and the moon.

[0080] In step 2, the coarse distance model constructed is:

[0081] ;

[0082] The moment when any fragment in the debris cloud is closest to the main wreckage The calculation method is:

[0083] ; Among them, all Constitute the first moment set ;

[0084] Where, is the distance between any fragment in the debris cloud and the main debris, t is the time variable, and is uniformly discretized on the time axis. The discrete window Δt is preferably set at Δt=10s for low orbit and Δt=60s for medium and high orbits; is the position coordinate of the i-th fragment in the J2000 geocentric inertial coordinate system, ri (t)=[x i (t), y i (t), z i (t)] T ; is the position coordinate of the main debris in the J2000 geocentric inertial coordinate system, r0(t)=[x0(t), y0(t), z0(t)] T ; i is the fragment number, o is the main wreckage, and T is transposition.

[0085] In step 3, the first Gaussian kernel function constructed is:

[0086] ;

[0087] The method for estimating the first probability density estimate of the first moment set by the first Gaussian kernel function is:

[0088] ;

[0089] Where, is the value of the first Gaussian kernel function, and e is a natural constant; is the first probability density estimate, is the total number of fragments in the fragment cloud, is the bandwidth of the first Gaussian kernel function.

[0090] In step 3, the method for constructing an estimated cumulative distribution function by performing cumulative distribution on the first probability density estimate is:

[0091] ;

[0092] Where, To estimate the cumulative distribution function, To estimate the cumulative distribution function value, is the input variable for estimating the cumulative distribution function;

[0093] In step 3, the confidence interval constructed by combining the inverse function of the estimated cumulative distribution function with the significance level is:

[0094] CI=[F -1 (α / 2), F -1 (1-α / 2)];

[0095] Where CI is the confidence interval, F -1 () is the inverse function of the estimated cumulative distribution function, and α is the significance level.

[0096] In step 4, the fine distance model constructed is:

[0097] ;

[0098] Preferably, the low orbit is set to Δt=1s, and the high orbit is set to Δt=10s.

[0099] The moment when any fragment in the debris cloud is closest to the main debris within the confidence interval The calculation method is:

[0100] ; Among them, all Constructing the second moment set ;

[0101] Where, is the distance between any fragment in the debris cloud and the main wreckage within the confidence interval; is the position coordinate of the kth fragment within the confidence interval in the J2000 geocentric inertial coordinate system, r k (t)=[x k (t),y k (t),z k (t)] T ; k is the fragment index within the confidence interval.

[0102] In step 5, the second Gaussian kernel function constructed is:

[0103] ;

[0104] The method for obtaining the second probability density estimate of the second moment set by the second Gaussian kernel function is:

[0105] ;

[0106] Where, is the second Gaussian kernel function value; is the second probability density estimate, is the total number of fragments within the confidence interval, is the bandwidth of the second Gaussian kernel function.

[0107] In step 5, the closest distance moment corresponding to the maximum second probability density estimate is taken as the time of the spatial disintegration event The method is:

[0108] .

[0109] In order to illustrate the technical solution of the present invention, a specific example is now provided:

[0110] Step 1: Sequentially perform standardization processing and orbit propagation operations on the debris cloud orbit data and the main debris orbit data after the space disintegration event obtained by the space situational awareness and surveillance system.

[0111] The Centaur upper stage (Centaur Upper Stage) is a series of liquid hydrogen and liquid oxygen upper stages for rockets. Since the Atlas-Centaur rocket of the 1960s, it has evolved into several models, including the Centaur I, Centaur II, Centaur IIA, and Centaur G. These models are widely used on Delta, Atlas, and Vulcan launch vehicles, as well as on the Space Shuttle. In September 2024, a US Centaur upper stage disintegrated in orbit. The disintegration was first detected by Slingshot Aerospace, a US commercial space situational awareness company, on September 16, 2024. The Russian space company JSC Vimpel subsequently conducted a systematic cataloging of the space debris generated by the incident. This cataloged debris data totaled 143 pieces, including the main debris, with orbital epochs between September 16 and 17.

[0112] The conversion model converts the orbital data of the debris cloud and the main debris from TLE to the J2000 geocentric inertial coordinate system; at the same time, the timestamps of the orbital data of the debris cloud and the main debris are converted to the modified Julian day (MJD).

[0113] The debris cloud and the main debris are medium- and high-orbit debris (orbit altitude > 8370km). Considering the three-body gravitational effect and the gravitational perturbations of the sun and the moon, the SGP4 model is used for orbital propagation.

[0114] Step 2: Based on the position coordinates of the debris cloud and the main debris after orbital propagation, a coarse distance model is constructed. The time of the closest distance between any fragment in the debris cloud and the main debris is calculated by the coarse distance model, and the first time set is obtained as follows: Figure 1 shown.

[0115] Step 3: Construct the first Gaussian kernel function of the first moment set, and estimate the first probability density estimate of the first moment set by the first Gaussian kernel function, such as Figure 2 shown.

[0116] The cumulative distribution of the first probability density estimate is constructed to estimate the cumulative distribution function, such as Figure 3 As shown. The confidence interval is constructed by combining the inverse function of the estimated cumulative distribution function with the significance level:

[0117] CI 95% =[F -1 (α / 2),F -1 (1-α / 2)], and the confidence interval is [2024-09-04 22:00:43, 2024-09-07 14:18:16];

[0118] Remove the large error fragment data outside the confidence interval; in this example, a total of 19 large error fragment data are removed, and 124 fragment track data are retained after screening.

[0119] Step 4: Based on the position coordinates of the debris cloud and the main wreckage within the confidence interval, a fine distance model is constructed. The time of the closest distance between any fragment in the debris cloud and the main wreckage within the confidence interval is calculated by the fine distance model, and the second time set is obtained as follows: Figure 4 shown.

[0120] Step 5: Construct the second Gaussian kernel function of the second moment set, and obtain the second probability density estimate of the second moment set by the second Gaussian kernel function, such as Figure 5 As shown, the closest distance moment corresponding to the maximum second probability density estimate is taken as the time of the spatial disintegration event, and the disintegration time is 2024-09-06 12:35:40 (Beijing time).

[0121] The beneficial effects of the present invention are:

[0122] 1. The present invention sequentially performs standardization processing on the debris cloud orbital data and the main debris orbital data obtained by the space situational awareness and surveillance system after a space disintegration event, aligning the coordinate system and calibrating the timestamp to ensure the accuracy and consistency of the timestamp. It also performs orbit propagation based on the orbit type, taking into account perturbations such as the Earth's non-spherical gravity and atmospheric drag on low-orbit debris, as well as the superimposed three-body gravitational effect and solar and lunar gravitational perturbations on medium- and high-orbit debris, making it easy to understand and implement.

[0123] 2. Theoretically, the moment when the debris and the main debris are closest is the most correlated moment between them, i.e., the breakup moment. Therefore, for breakup events that could produce main debris, the present invention establishes coarse and fine distance models for the debris cloud and the main debris after orbital propagation. This coarse-fine dual-stage optimization model strategy accurately determines the moment of closest approach. The moment of spacecraft breakup is determined based on this moment of closest approach between the main debris and the debris cloud, improving temporal resolution.

[0124] 3. Constructing a Gaussian kernel function for non-parametric probability density estimation can improve computational efficiency, be applicable to large-scale fragmented clouds, and increase anti-interference capabilities. Based on the constructed coarse-fine dual-stage optimization model strategy, the constructed Gaussian kernel function is called twice, which is smooth, robust, and versatile. It can effectively retain edge data and avoid the problem of false rejection caused by data mutation.

[0125] 4. Construct a confidence interval by using the inverse function of the constructed cumulative distribution function, delete the fragmented data outside the confidence interval, and eliminate large errors or erroneous fragmented data, thereby improving robustness.

[0126] 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 modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for reconstructing the time of spatial disintegration events based on the statistics of the intersection time of debris and main wreckage, characterized in that: include: Step 1: sequentially perform standardization processing and orbit propagation operations on the debris cloud orbit data and the main debris orbit data obtained by the space situational awareness and surveillance system after the space disintegration event; Step 2: Based on the coordinates of the debris cloud and the main debris after orbital propagation, a coarse distance model is constructed. The time when any fragment in the debris cloud is closest to the main debris is calculated using the coarse distance model to obtain the first time set. Step 3: Construct a first Gaussian kernel function for the first moment set, estimate a first probability density estimate for the first moment set using the first Gaussian kernel function, perform cumulative distribution on the first probability density estimate to construct an estimated cumulative distribution function, combine the inverse function of the estimated cumulative distribution function with the significance level to construct a confidence interval, and remove large error fragments outside the confidence interval; Step 4: Based on the position coordinates of the debris cloud and the main wreckage within the confidence interval, a fine distance model is constructed. The fine distance model is used to calculate the time of the closest distance between any fragment in the debris cloud and the main wreckage within the confidence interval to obtain a second time set. Step 5: Construct the second Gaussian kernel function of the second moment set, obtain the second probability density estimate of the second moment set by the second Gaussian kernel function, and take the closest distance moment corresponding to the maximum second probability density estimate as the moment of the spatial disintegration event.

2. The method for reconstructing the time of a spatial disintegration event based on the statistics of the intersection time of debris and main wreckage according to claim 1, characterized in that: In step 1, the standardization method is: A conversion model from TLE to J2000 Earth-centered inertial coordinate system is constructed. The conversion model converts the orbital data of the debris cloud and the main debris from TLE to the J2000 Earth-centered inertial coordinate system. At the same time, the timestamps of the orbital data of the debris cloud and the main debris are converted to the Modified Julian Day (MJD). The conversion model is: ； Where, is the position coordinate of the debris cloud or main wreckage in the J2000 geocentric inertial coordinate system, is the distance from the debris or main wreckage to the center of the Earth, is the right ascension of the ascending node, is the true anomaly angle, is the orbital inclination.

3. The method for reconstructing the time of a spatial disintegration event based on statistics of the time of intersection between debris and main wreckage according to claim 2, characterized in that: In step 1, the orbital propagation method is: If the orbits of the debris cloud and the main debris are in low orbit, the HPOP model is used for orbital propagation; If the orbits of the debris cloud and the main debris are in medium and high orbits, the SGP4 model is used for orbital propagation.

4. The method for reconstructing the time of a spatial disintegration event based on statistics of the intersection time of debris and main wreckage according to claim 3, characterized in that: In step 2, the coarse distance model constructed is: ; The moment when any fragment in the debris cloud is closest to the main wreckage The calculation method is: ; Among them, all Constitute the first moment set ; Where, is the distance between any fragment in the debris cloud and the main debris at that moment, and t is the time variable; is the position coordinate of the i-th fragment in the J2000 geocentric inertial coordinate system, r i (t)=[x i (t), y i (t), z i (t)] T ; is the position coordinate of the main debris in the J2000 geocentric inertial coordinate system, r0(t)=[x0(t), y0(t), z0(t)] T ; i is the fragment number, o is the main wreckage, and T is transposition.

5. The method for reconstructing the time of a spatial disintegration event based on the statistics of the intersection time of debris and main wreckage according to claim 4, characterized in that: In step 3, the first Gaussian kernel function constructed is: ； The method for estimating the first probability density estimate of the first moment set by the first Gaussian kernel function is: ； Where, is the value of the first Gaussian kernel function, and e is a natural constant; is the first probability density estimate, is the total number of fragments in the fragment cloud, is the bandwidth of the first Gaussian kernel function.

6. The method for reconstructing the time of a spatial disintegration event based on statistics of the time of intersection between debris and main wreckage according to claim 5, characterized in that: In step 3, the method for constructing an estimated cumulative distribution function by performing cumulative distribution on the first probability density estimate is: ； Where, To estimate the cumulative distribution function, To estimate the cumulative distribution function value, are the input variables for estimating the cumulative distribution function.

7. The method for reconstructing the time of a spatial disintegration event based on statistics of the intersection time of debris and main wreckage according to claim 6, characterized in that: In step 3, the confidence interval constructed by combining the inverse function of the estimated cumulative distribution function with the significance level is: CI=[F -1 (α / 2),F -1 (1−α / 2)]: Where CI is the confidence interval, F -1 () is the inverse function of the estimated cumulative distribution function, and α is the significance level.

8. The method for reconstructing the time of a spatial disintegration event based on statistics of the time of intersection between debris and main wreckage according to claim 7, characterized in that: In step 4, the fine distance model constructed is: ； The moment when any fragment in the debris cloud is closest to the main debris within the confidence interval The calculation method is: ; Among them, all Constructing the second moment set ; Where, is the distance between any fragment in the debris cloud and the main wreckage within the confidence interval; is the position coordinate of the kth fragment within the confidence interval in the J2000 geocentric inertial coordinate system, r k (t)=[x k (t),y k (t),z k (t)] T ; k is the fragment index within the confidence interval.

9. The method for reconstructing the time of a spatial disintegration event based on statistics of the time of intersection between debris and main wreckage according to claim 8, characterized in that: In step 5, the second Gaussian kernel function constructed is: ； The method for obtaining the second probability density estimate of the second moment set by the second Gaussian kernel function is: ； Where, is the second Gaussian kernel function value; is the second probability density estimate, is the total number of fragments within the confidence interval, is the bandwidth of the second Gaussian kernel function.

10. The method for reconstructing the time of a spatial disintegration event based on statistics of the time of intersection between debris and main wreckage according to claim 9, characterized in that: In step 5, the closest distance moment corresponding to the maximum second probability density estimate is taken as the time of the spatial disintegration event The method is: 。

Images