Space target collision early warning method based on GPU parallel computing and J2 perturbation term

Abstract

The invention discloses a space target collision early warning method based on GPU parallel computing and a J2 perturbation item, aims to solve the problems of high computing complexity and poor real-time performance of existing CPU processing space target collision risk assessment, and provides a multi-stage screening method based on GPU parallel computing and the J2 perturbation item. The method comprises the following steps: reading a TLE and calculating near / distant points and a reference check point at a GPU (Graphics Processing Unit); combining according to C (N, 2) and screening according to epoch, height and geocentric distance; taking a check point state as an initial value in a check interval, and adopting single-precision J2-RK iterative screening to obtain events NJ2pre and tJ2pre; the events are screened by using double-precision J2-RK in front and back check sections, and minimum distances distJ2 and tJ2 are output; and finally, SGP4 / SDP4 is used for parallel actuarial calculation to obtain a minimum distance distDC, a relative speed, a collision probability and the like. The method gives consideration to real-time performance and precision, significantly reduces the O (n) calculation cost, and is suitable for large-scale in-orbit target early warning.

Description

Technical Field

[0001] This invention relates to the field of space target collision warning technology, specifically to a space target collision warning method based on GPU parallel computing and J2 perturbation terms. Background Technology

[0002] Spacecraft in orbit and space debris are collectively referred to as space targets. Since the relative speeds between space targets can reach 10 km / s or higher, a collision would be catastrophic for the spacecraft. To ensure the safe operation of spacecraft during missions, an effective space target collision warning system must be established. Collision warning requires a collision risk assessment of all targets, resulting in a computational complexity of O(n²). To reduce computational load, existing collision warning technologies are generally based on the screening method proposed by Felix R. Hoots et al. in their paper "An analytic method to determine future close objects between objects." This method uses epochal screening, altitude screening, and geocentric distance screening to eliminate space targets, retaining only a small number of targets that may pose a collision hazard. Then, based on the TLE data of these space targets, the SGP4 / SDP4 model is used to calculate their spatial positions at various times within the warning period. If the distance between two space targets at a certain time is below a specified threshold (generally set at around 5 km), a collision risk is considered present.

[0003] With the development of human spaceflight, the number of space targets is increasing daily. Currently (first half of 2025), there are over 20,000 objects larger than 10cm in orbit. Even with the screening methods described above, the subsequent computational workload remains enormous. Relying on existing methods to process these objects using CPUs is insufficient due to the limited number of processor cores on a single machine (desktops or workstations typically have a dozen or so cores, and even high-end multi-processor servers only have a few dozen cores). Using large-scale server clusters for parallel processing would significantly increase computational costs.

[0004] Graphics cards (GPUs) can have thousands or even tens of thousands of parallel processing units. For the polynomial and trigonometric function operations that account for the majority of computation in collision warning algorithms, the data types and calculation methods are fixed, making them very suitable for parallel computing by GPUs. However, the SGP4 / SDP4 model requires double-precision floating-point calculations to ensure the accuracy of the results. Due to the cost and hardware limitations of GPUs, the double-precision floating-point processing performance of most GPUs is only 1 / 64 to 1 / 32 of their single-precision floating-point performance. Only a very few expensive, top-tier computing cards can achieve 1 / 4 to 1 / 2 of their single-precision floating-point performance in double-precision processing. Summary of the Invention

[0005] Based on the above analysis, this invention presents a spatial target collision warning method based on GPU parallel computing and J2 perturbation terms, the specific implementation of which is as follows:

[0006] S1: Acquire and read the TLE data of the spatial target, and transfer the TLE data to the GPU;

[0007] S2: Calculate the perigee, apogee, and reference checkpoint data of the spatial target in the GPU;

[0008] S3: Combine the spatial targets into target pairs and filter them in the GPU according to the data described in S2 to obtain target pair N. filter ;

[0009] S4: In the GPU, for the target pair N filter Perform J2 perturbation single-precision floating-point number filtering and output the target pairs N that meet the filtering criteria. filter With iteration time point t J2pre The iteration time point t J2pre The target refers to N filter The time point at which the minimum distance between two spatial targets equals the distance threshold selected by the single-precision floating-point number filter is used to pair the targets with N. filter and the iteration time point t J2pre Collectively referred to as event N J2pre ;

[0010] S5: The event N is processed in the GPU. J2pre Perform J2 perturbation double-precision floating-point number filtering and output events that meet the filtering criteria, denoted as event N. J2 ;

[0011] S6: The event N is processed in the GPU. J2 Perform the final calculation and output the target pair N that meets the conditions. DC and iteration time point t DC .

[0012] Preferably, the benchmark checkpoint mentioned in S2 refers to a time point set at a fixed interval within the warning period.

[0013] Preferably, the perigee, apogee, and reference checkpoint data mentioned in S2 are calculated using the SGP4 / SDP4 orbital model.

[0014] Preferably, the combination of the target pairs in S3 is C(N,2), where N is the number of the space targets.

[0015] Preferably, the screening in S3 includes height screening, epoch screening, and geocentric distance screening.

[0016] Preferably, the J2 perturbation single-precision floating-point number screening in S4 refers to: denoting the number of reference check points as N. check For each of the aforementioned target pairs N filter During the inspection interval from the i-th reference check point to the (i+1)-th reference check point, using the position and velocity data of the spatial target at the i-th reference check point as initial values, iterative parallel computation based on the Runge-Kutta method using single-precision floating-point numbers is performed in the GPU to calculate the minimum distance dist between the two spatial targets within the target pair during the inspection interval. J2pre Remove the dist J2pre dist J2pre >D J2pre The N mentioned filter , where 0≤i <N check D J2pre Distance threshold for filtering single-precision floating-point numbers for J2 perturbation.

[0017] Preferably, in the J2 perturbation single-precision floating-point number screening, the iteration step size h of the Runge-Kutta method is set to 5-10 s, wherein when the iteration step size h = 6 s, the D J2pre Set to 150-200m.

[0018] Preferably, the J2 perturbation double-precision floating-point number filtering in S5 refers to: for each event N J2pre At the iteration time point t J2pre Within a time period of 1-2 reference checkpoints before and after the reference checkpoints, using the position and velocity information of the spatial targets at the corresponding reference checkpoints as initial values, iterative parallel computation based on the Runge-Kutta method using double-precision floating-point numbers is performed in the GPU to calculate the minimum distance dist between the two targets during this time period. J2 Remove dist J2 dist J2 >D J2 The target pair, where D J2 The distance threshold for J2 perturbation double-precision floating-point filtering is used to finally sum all target pairs that pass the double-precision floating-point filtering to the minimum distance of dist. J2 Iteration time point t J2 The output is performed and collectively referred to as event N. J2 .

[0019] Preferably, the iteration step size h of the Runge-Kutta method in the J2 perturbation double-precision floating-point number screening is set to 0.2-0.5 s, wherein when the iteration step size h = 0.25 s, D J2 Set to 25-40m.

[0020] Preferably, the final calculation and output of the spatial target in S6 refers to: for each event N J2 ,set up =1s or 2s, in [t J2 - ,t J2 + The time period is subdivided into 500-2000 time points. The SGP4 / SDP4 orbital model is used in parallel on the GPU to calculate the position and velocity data of two spatial targets at each time point, and the minimum distance (dist) between the two spatial targets during this time period is calculated. DC Remove dist DC >D DC The target pair, where D DC To determine the final distance threshold for early warning, all targets that have passed this step are finally paired with N. DC The minimum distance is dist DC The iteration time point t DC Output the data and use relevant formulas to calculate other information such as relative speed, collision probability, and duration.

[0021] The beneficial effects of this invention are as follows:

[0022] (1) By using the parallel computing capabilities of the GPU, the spatial target pairs are efficiently screened and J2 perturbation iterative calculations are performed, reducing the original amount of computation and meeting the time requirements for real-time collision warning, thus avoiding the bottleneck of single-machine or cluster processing of CPU.

[0023] (2) The multi-core parallel processing unit of the GPU is used to replace the expensive large-scale server cluster. At the same time, the J2 perturbation terms are filtered by single-precision floating-point numbers, which optimizes the resource consumption of double-precision calculation and achieves high-performance collision risk assessment.

[0024] (3) Combining the Runge-Kutta iteration method of the J2 perturbation term and the double-precision verification of the SGP4 / SDP4 model ensures the accuracy of the minimum distance calculation, effectively eliminates low-risk target pairs, and outputs key information such as relative velocity and collision probability, thereby improving the early warning level for the safe operation of spacecraft. With the technology described in this invention, there is no need to use a large-scale server cluster or expensive top-level computing card. Ordinary computers and GPUs with general performance can meet the time requirements for collision warning when the number of space targets increases significantly. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart of the present invention;

[0027] Figure 2 This is a graph showing the computational execution time in this invention;

[0028] Figure 3 This is a diagram showing the collision warning processing results in this invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] This invention implements an algorithm for filtering Time-Least-Least-Least-Least-Least-Least-Least-Least-N ...

[0031] TLE (Two-Line Elementset) is an orbital encoding method used to determine the relevant parameters of the orbit of a space target orbiting the Earth at a given epoch. Using a suitable prediction model, the real-time position and velocity of the space target on its orbit over a certain period can be calculated with a certain accuracy. The North American Aerospace Defense Command (NORAD) tracks all detectable space targets in Earth's orbit, generates corresponding TLE orbital data, and releases it to the public daily. It is the de facto standard for orbital elements of Earth's orbital targets and the basic data used by various countries for collision warning.

[0032] SGP4 / SDP4 Orbit Models: SGP4 (Simplified Conventional Perturbation Model 4) and SDP4 (Simplified Deep Space Perturbation Model 4) are the most commonly used mathematical models for orbit prediction. The SGP4 model is generally applied to near-Earth space targets with orbital periods of less than 225 minutes; SDP4 is an extension of the SGP4 model and is mainly used for high-orbit and deep-space targets with orbital periods of greater than 225 minutes.

[0033] J2 perturbation: Perturbation refers to the deviation in orbit caused by the attraction of other celestial bodies or other factors when a celestial body moves around another celestial body according to the laws of the two-body problem. Among them, the influence caused by the fact that the Earth is not a perfect sphere but an ellipsoid is called J2 perturbation. It is the main perturbation term for near-Earth space targets, and its influence on the orbit is 2-3 orders of magnitude or more than that of other perturbation terms.

[0034] The Runge-Kutta method is an important approach for solving nonlinear equations. Given the derivatives and initial values ​​of the equation, it uses an iterative method to avoid the complex process of solving nonlinear equations. Let the initial value problem be formulated as follows:

[0035]

[0036] The Runge-Kutta method for this problem is given by the following equation:

[0037]

[0038] in:

[0039]

[0040]

[0041]

[0042]

[0043] Where k1, k2, k3, and k4 represent four intermediate slopes.

[0044] Ephemeris filtering: One of the commonly used filtering methods for collision warning. The accuracy of orbit prediction is limited by the prediction duration; epoch filtering aims to eliminate space targets that have not been updated for a long time. Let the TLE (Time-Lapse Error) data of a certain space target be... At any given time, the warning time is [t]. B ,t E The warning time starts at t. B The warning period ends at time t. E At time t B - If the threshold value is greater than ΔT, then the target is removed, where ΔT is the screening threshold for this step.

[0045] Altitude filtering: One of the commonly used filtering methods for collision warning. Calculate the perigee and apogee altitudes of two space targets. Perigee refers to the point on the elliptical orbit of the space target around the Earth that is closest to the Earth's center; apogee refers to the point on the elliptical orbit of the space target around the Earth that is farthest from the Earth's center. Target pairs that satisfy qQ>D1 are eliminated, where D1 is the altitude filtering threshold, q is the larger of the two perigee altitudes, and Q is the smaller of the two apogee altitudes.

[0046] Earth-center distance filtering: One of the commonly used filtering methods for collision warning. Calculate the intersection line of the orbital planes of two space targets, and obtain the distances r0 and r1 from the Earth's center when the two targets pass through the intersection line. Remove target pairs that satisfy |r0-r1|>Δd, where Δd is the threshold for earth-center distance filtering.

[0047] This invention mainly consists of the following steps:

[0048] S1: TLE data reading

[0049] The TLE data file is retrieved and read, and the TLE data of each spatial target is transferred to the graphics card's video memory. The TLE data is first read from the file into the computer's memory, and then copied to the GPU video memory through the computer's PCI-Express bus.

[0050] S2: Calculation of perigee and reference checkpoint data

[0051] The number of space targets is set to N. Based on this number N, perigee, apogee, and baseline checkpoint data are computed in parallel on the GPU. The baseline checkpoint refers to the data set during the warning time [t] to ensure the accuracy of the Runge-Kutta method. B ,t EWithin a fixed time interval, the position and velocity information of each reference checkpoint are calculated in parallel by the GPU using the SGP4 / SDP4 orbital model and stored in video memory. When using the Runge-Kutta method, the pre-stored values ​​of the corresponding reference checkpoint position and velocity information are used as initial and intermediate values ​​for correction. The interval between reference checkpoints is 5-10 minutes. The GPU has ⌈N / 256⌉ thread control blocks, each containing 256 threads. Each thread uses the SGP4 / SDP4 orbital model to calculate the perigee and apogee altitudes of a space target, as well as the x, y, and z-axis position and velocity information at each reference checkpoint, and stores this information in video memory for subsequent calculations. To ensure calculation accuracy, expired Time-Like Expiration (TLE) data needs to be removed. B - For spatial targets with a height greater than ΔT, set the apogee altitude of that target to 0.

[0052] S3: Height Filtering, Ephemeris Filtering, and Geocentric Distance Filtering

[0053] Based on the number N of space targets, generate corresponding target pairs N. pair , where N pair =C(N,2)=(N*(N-1) / 2), for these N... pair Height filtering, epoch filtering, and geocentric distance filtering are performed in parallel on the GPU: The GPU has a total of ⌈N... pair There are 256 thread control blocks, each containing 256 threads. Each thread determines whether a target satisfies the elimination condition qQ>D1 or |r0-r1|>Δd. Referring to S2, for t... B The target with -t0 > ΔT has already set its apogee altitude to 0, so epoch filtering is performed simultaneously in this step. Finally, all targets are paired with N. pair The goal of this step is to output the target.

[0054] S4: J2 Perturbation Single-Precision Floating-Point Number Filtering

[0055] Let N be the number of target pairs passing through S3. filter Warning time [t] B ,t E The number of baseline checkpoints within [ ] is N check For each N filter In each inspection interval, i.e. from the i-th reference inspection point to the (i+1)-th reference inspection point, where 0≤i <N checkUsing the position and velocity data of the spatial target at the i-th baseline checkpoint as initial values, the minimum distance dist between the two targets during the check interval is calculated by iterative parallel computation using the Runge-Kutta method based on the J2 perturbation term in the GPU through single-precision floating-point operations. J2pre Remove dist J2pre dist J2pre >D J2pre N filter D J2pre To determine the distance threshold for J2 perturbation single-precision floating-point number filtering, considering factors such as the time interval between benchmark checkpoints, the orbital velocity of the space target, and the precision of the single-precision floating-point number, the iteration step size h is set to 5-10s. Specifically, when the iteration step size h=6s, D... J2pre Set the distance to 150-200m. Finally, set the minimum distance between all target pairs that have passed this step to dist. J2pre Iteration time point t J2pre The output is a combination of target pairs and time points, which is called an "event".

[0056] Since a total of N needs to be processed filter *N check The number of "target pairs * inspection intervals" is calculated iteratively, exceeding the video memory capacity. Therefore, batch processing is required, with each batch being N in size. batch (Each thread control block contains a multiple of 256 threads), meaning a total of ⌈N threads are executed. filter *N check / N batch There are ⌉ batches, and the GPU here has a total of N. batch There are 256 thread control blocks, and each thread control block contains 256 threads.

[0057] S5: J2 Perturbation Double Precision Floating-Point Filtering

[0058] Let N be the number of events passing through S4. J2pre For each event, in t J2pre Within a time period of 1-2 reference checkpoints before and after the target, using the position and velocity information of the spatial targets at the corresponding reference checkpoints as initial values, iterative parallel computation based on the Runge-Kutta method using J2 perturbation terms is performed in the GPU using double-precision floating-point numbers to calculate the minimum distance dist between the two targets during this time period. J2 Remove dist J2 dist J2 >D J2 The target pair, where D J2To filter the distance threshold using double-precision floating-point numbers for J2 perturbation, considering factors such as the time interval between reference checkpoints, the target's orbital velocity, and the precision of the double-precision floating-point numbers, the iteration step size h is set to 0.2-0.5 s. Specifically, when the iteration step size h = 0.25 s, D... J2 Set the distance to 25-40m. Finally, set the minimum distance between all target pairs that have passed this step to dist. J2 Iteration time point t J2 Output the results.

[0059] S6: Final Calculation and Output

[0060] Set the number of events passing through S5 to N. J2 For each event, set =1s or 2s, in [t J2 - ,t J2 + The time period is subdivided into 500-2000 time points. The SGP4 / SDP4 orbital model is used in parallel on the GPU to calculate the position and velocity data of two spatial targets at each time point, and the minimum distance (dist) between the two targets within this time period is calculated. DC Remove dist DC >D DC The target pair, where D DC The distance threshold for final early warning was set to 5km in the project. Finally, all targets that passed through this step were compared with N. DC The minimum distance is dist DC Time point t DC Output the data and use relevant formulas to calculate other information such as relative speed, collision probability, and duration.

[0061] like Figure 2 As shown, without the need for large-scale server clusters or expensive top-of-the-line computing cards, ordinary computers and GPUs with average performance can meet the time requirements for collision warning when the number of space targets increases significantly.

[0062] like Figure 3 As shown, Figure 3 The data presented in this invention is based on the collision warning analysis of TLE data from June 20, 2025, which contains 27,430 space targets. The alarm threshold is set to 5.5 km, and each line in the output represents one warning event, totaling approximately 300,000.

[0063] Further analysis revealed that the J2 perturbation single-precision floating-point screening step (cuda_j2pre_check) accounts for the majority of the processing time. With the advancements in GPU performance over the past decade, current mainstream mid-to-low-end graphics cards, such as the Nvidia GeForce RTX 3050, offer more than twice the single-precision floating-point performance of the test environment described in this paper. This translates to a roughly halving of the time required for this step. Therefore, using the technology of this invention can significantly reduce the hardware cost of collision warning systems.

[0064] The prior description of this disclosure is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to this disclosure will be apparent to those skilled in the art, and the general principles defined herein may be applied to other variations without departing from the spirit or scope of this disclosure. Therefore, this disclosure is not intended to be limited to the examples and designs described herein, but should be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0065] The embodiments of the present invention have been described in detail above. The description of the embodiments above is only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A space target collision warning method based on GPU parallel computing and J2 perturbation term, characterized in that, Comprising: S1: obtaining and reading TLE data of the space target, and inputting the TLE data into a GPU; S2: calculating perigee, apogee and reference checkpoint data of the space target in the GPU; S3: Combining the spatial targets into target pairs and filtering in the GPU according to the data in S2 resulting in target pairs N filter ; S4: In the GPU, for the target pair N filter Perform J2 perturbation single-precision floating-point number filtering and output the target pairs N that meet the filtering criteria. filter With iteration time point t J2pre The iteration time point t J2pre The target refers to N filter The time point at which the minimum distance between two spatial targets equals the distance threshold selected by the single-precision floating-point number filter is used to pair the targets with N. filter and the iteration time point t J2pre Collectively referred to as event N J2pre ; S5: performing J2 perturbation double-precision floating-point number screening on the event N in the GPU J2pre and outputting events meeting the screening condition, denoted as event N J2 ; S6 : in the GPU the event N J2 perform a final calculation and output the target pair N DC and iteration time point t DC that meet the conditions.

2. The method of claim 1, wherein, The reference checkpoint in S2 refers to a time point set at a fixed interval within a pre-warning time period.

3. The method of claim 1, wherein, The perigee, apogee and reference checkpoint data in S2 are calculated by SGP4 / SDP4 orbit model.

4. The method of claim 1, wherein, The combination mode of the target pair in S3 is C(N, 2), wherein N is the number of space targets.

5. The method of claim 1, wherein, The screening in S3 includes height screening, epoch screening and geocentric distance screening.

6. The method of claim 1, wherein, The J2 perturbation single-precision floating-point number screening in S4 refers to recording the number of reference checkpoints as N check For each target pair N filter In the inspection interval from the i-th reference checkpoint to the i+1-th reference checkpoint, the position data and velocity data of the space target at the i-th reference checkpoint are used as initial values, and the J2 perturbation term-based Runge-Kutta method is iteratively calculated in parallel in the GPU to calculate the minimum distance dist between the two space targets in the target pair in the inspection interval J2pre The dist J2pre The dist J2pre > D J2pre The N filter , where 0≤i check D J2pre is the distance threshold of the J2 perturbation single-precision floating-point number screening.

7. The method of space object collision warning according to claim 6, wherein, The iteration step length h of the Runge-Kutta method in the J2 perturbation single precision floating point number screening is set to 5-10s, wherein in the case of the iteration step length h = 6s, the D J2pre is set to 150-200m.

8. The method of claim 1, wherein, The J2 perturbation double-precision floating-point filtering mentioned in S5 refers to: for each event N... J2pre At the iteration time point t J2pre Within a time period of 1-2 reference checkpoints before and after the reference checkpoints, using the position and velocity information of the spatial targets at the corresponding reference checkpoints as initial values, iterative parallel computation based on the Runge-Kutta method using double-precision floating-point numbers is performed in the GPU to calculate the minimum distance dist between the two targets during this time period. J2 Remove dist J2 dist J2 >D J2 The target pair, where D J2 The distance threshold for J2 perturbation double-precision floating-point filtering is used to finally sum all target pairs that pass the double-precision floating-point filtering to the minimum distance of dist. J2 Iteration time point t J2 The output is performed and collectively referred to as event N. J2 .

9. The method of space object collision warning according to claim 8, wherein, The iteration step length h of the Runge-Kutta method in the J2 perturbation double-precision floating-point number screening is set to 0.2-0.5s, wherein in the case of iteration step length h = 0.25s, D J2 is set to 25-40m.

10. The method of space object collision warning of claim 1, wherein, S6 in the final calculation and output the space target: for each of the event N J2 , set =1s or 2s, in the period of [t J2 - , t J2 + ] is divided into 500-2000 time points, in the GPU using SGP4 / SDP4 orbit model to calculate the position data and velocity data of each time point of two space targets, the minimum distance dist DC between the two space targets in this period is calculated, the target pair dist DC >D DC is removed, where D DC is the distance threshold for final warning, finally the target pair N DC and the minimum distance dist DC of the iteration time point t DC are output, and other information such as relative velocity, collision probability, duration is calculated using related formula.

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