A screening method and system for space target collision warning combined with the cosine theorem

Abstract

This invention relates to the field of space target collision warning technology, specifically to a screening method and system for space target collision warning based on the law of cosines. The screening method includes: acquiring space targets; performing at least one screening to obtain screened space targets; wherein any one of the at least one screenings is a target relative position screening based on the law of cosines; and outputting the screened space targets. By adding target relative position screening based on the law of cosines, this invention reduces the number of target pairs used for subsequent calculations, thereby improving the processing efficiency of collision warning, reducing hardware size, and lowering computational costs.

Description

Technical Field

[0001] This invention relates to the field of space target collision early warning technology, and more specifically, to a screening method and system for space target collision early warning that incorporates the law of cosines. Background Technology

[0002] Spacecraft in orbit and space debris are collectively referred to as space targets. Since the relative speed between space targets can reach 10 km / s or higher, a collision would be fatal to the spacecraft.

[0003] To ensure the safe operation of spacecraft during missions, an effective space target collision early warning system must be established. Since collision early warning requires a collision risk assessment of all targets, the computational complexity is O(n²). To reduce computational load, existing collision early 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 appoaches between satellites." 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.

[0004] With the development of human spaceflight, the number of space targets is increasing day by day. Currently (first half of 2025), there are more than 20,000 objects larger than 10cm in orbit. Even if we filter them according to the above, the amount of subsequent calculations is still huge. Therefore, in practical applications, large-scale server clusters or high-end GPU computing cards are usually used for parallel processing, which results in high computing costs. Summary of the Invention

[0005] The purpose of this invention is to provide a screening method and system for space target collision warning that combines the cosine theorem, so as to solve the problem that the subsequent calculation is still huge after screening, resulting in high computational cost.

[0006] Firstly, a spatial target selection method combining the law of cosines is provided, including:

[0007] Acquire space targets;

[0008] Perform at least one screening to obtain the selected spatial targets; wherein any one of the at least one screenings is a target relative position screening based on the cosine theorem; wherein, the target relative position screening based on the cosine theorem only performs multiplication and addition / subtraction calculations, and the cosine and division calculations are completed in advance;

[0009] Output the filtered spatial targets.

[0010] Preferably, the step of acquiring the space target includes:

[0011] Read two lines of track element data;

[0012] Obtain the number of two orbital elements for each space target.

[0013] Preferably, the screening is used to eliminate space targets;

[0014] Among them, the space targets that were eliminated were those that were unlikely to pose a collision risk;

[0015] The remaining spatial targets after elimination are the filtered spatial targets.

[0016] Preferably, the screening for eliminating space targets includes:

[0017] Based on at least one preset target parameter, spatial targets that do not meet the requirements of at least one preset target parameter are eliminated.

[0018] As a further improvement to this scheme, the steps of conducting at least one screening include:

[0019] Calculations are performed for near and far locations and reference checkpoint data, including:

[0020] The SGP4 / SDP4 orbit prediction model is used 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.

[0021] Filter by altitude and distance from the Earth's center, including:

[0022] Generate target pairs based on the number of space targets;

[0023] For each target pair, determine whether it meets the removal criteria. Target pairs that meet the removal criteria are removed. The removal criteria include:

[0024] In the formula, For the threshold of high-level filtering, The larger of the two perigee heights. The smaller of the two apogee heights;

[0025] or, In the formula, and Let be the distance from the Earth's center when the two targets of a target pair cross the line of intersection. The threshold for filtering by distance from the Earth's center;

[0026] Target relative position selection based on the law of cosines includes:

[0027] Calculate the angles between target A and target B and the Earth's center O. The cosine value, where:

[0028] ;

[0029] In the formula, Let A be the distance between target A and the Earth's center O. Let B be the distance between the target B and the Earth's center O. The distance between targets A and B;

[0030] The shortest period for a space target orbiting the Earth is set at 84 minutes.

[0031] For each target pair, determine whether it meets the removal criteria. Target pairs that meet the removal criteria are removed. The removal criteria are as follows:

[0032] In the formula, The baseline checkpoint interval time.

[0033] Secondly, a space target collision early warning method combining the cosine theorem is provided, including:

[0034] Obtain the filtered spatial targets; wherein, the filtered spatial targets are output by the spatial target filtering method combined with the cosine theorem described above;

[0035] Calculate the collision probability of the target pair to determine the potential encounter time and spatial location with the highest collision risk;

[0036] Output the results.

[0037] Thirdly, a spatial target selection system combining the law of cosines is provided, including:

[0038] Space target acquisition module, configured to acquire space targets;

[0039] The filtering module is configured to perform at least one filtering operation to obtain the filtered spatial targets. Among them, any one of the at least one filtering operations is a target relative position filtering based on the law of cosines. When filtering the target relative position based on the law of cosines, only multiplication and addition / subtraction calculations are performed, while cosine and division calculations are completed in advance.

[0040] as well as,

[0041] The space target output module is configured to output the filtered space targets.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] This method and system for screening space target collision warning, which combines the law of cosines, reduces the number of target pairs used for subsequent calculations by adding target relative position screening based on the law of cosines. This improves the processing efficiency of collision warning, reduces hardware size, and lowers computing costs. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the spatial target screening method steps of the present invention;

[0045] Figure 2 This is a schematic diagram of the screening method steps of the present invention;

[0046] Figure 3 This is a schematic diagram of the steps of the space target collision early warning method of the present invention;

[0047] Figure 4 This is a schematic diagram of the spatial target screening system of the present invention;

[0048] Figure 5 This is a schematic diagram illustrating the running time of the target relative position screening process without the inclusion of the cosine theorem in this invention;

[0049] Figure 6 This is a schematic diagram illustrating the running time of the target relative position screening based on the cosine theorem in this invention;

[0050] Figure 7 This is a schematic diagram of the collision warning processing event of the present invention. Detailed Implementation

[0051] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0052] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0053] In addition, the technical terms appearing in the background art and embodiments are explained as follows:

[0054] TLE data (Two-Line Element set): Two-Line Element set (TLE) is a track encoding method.

[0055] SGP4 / SDP4 models: Simplified Genertal Perturbations 4 (SGP4) and Simplified Deep-space Perturbations 4 (SDP4) are the most commonly used mathematical models for orbit prediction based on TLE data.

[0056] Screening: Collision warning first requires eliminating spatial targets, retaining only those that may pose a collision hazard to reduce subsequent computational load. This step is called screening. Among them, epoch screening, altitude screening, and geocentric distance screening are all commonly used screening methods for collision warning, and will not be listed here.

[0057] The first embodiment provides a spatial target screening method that combines the law of cosines. The core objective is to add target relative position screening based on the law of cosines to the traditional epoch screening, height screening, and geocentric distance screening, so as to reduce the workload of subsequent calculations.

[0058] See Figure 1 The specific steps are as follows:

[0059] Step S1.1: Obtain TLE data;

[0060] Read the TLE data file to obtain the TLE data for each spatial target.

[0061] TLE data is used to track all detectable space targets in Earth's orbit, generating corresponding TLE orbital data which is released daily. It serves as the de facto standard for orbital elements of Earth-orbiting targets and is fundamental data for collision warning. By using TLE data to determine the relevant parameters of the orbit of a space target orbiting the Earth at a given epoch, and using a suitable orbital prediction model, the real-time position and velocity of the space target within a certain time period can be calculated with a certain accuracy.

[0062] Preferably, the orbit prediction model includes at least one of the following: analytical prediction model (SGP4 / SDP4 model), numerical integration prediction model (Runge-Kutta numerical integration model, Posen integration model), or a hybrid enhancement model. It should be emphasized that the orbit prediction models used in this embodiment are all existing well-known technologies, which can be obtained by those skilled in the art through publicly available literature; furthermore, any new orbit prediction models that subsequently emerge are applicable to the screening method disclosed in this embodiment and fall within the protection scope of this application.

[0063] Step S1.2: Perform at least one filtering to obtain the filtered spatial targets;

[0064] Specifically, at least one screening means that spatial targets that do not meet the requirements of at least one preset target parameter are eliminated. The remaining spatial targets after elimination are the screened spatial targets.

[0065] This can be further subdivided into the following situations:

[0066] In the first case, only one screening is performed. This screening eliminates spatial targets that do not meet the requirements based on a target parameter, resulting in the filtered spatial targets.

[0067] Another possibility is that this screening process may involve multiple target parameters, and the spatial target must be met simultaneously to be retained; otherwise, it will be rejected.

[0068] In the second scenario, multiple screenings are performed. Taking two screenings as an example: In the first screening, spatial targets that do not meet the requirements are eliminated based on one or more target parameters, resulting in the spatial targets after the first coarse selection; in the second screening, spatial targets that do not meet the requirements are eliminated from the spatial targets after the first coarse selection based on one or more other target parameters, resulting in the spatial targets after screening.

[0069] It should be noted that three, four, or even more rounds of screening can be performed here. Each screening can involve one or more target parameters. If there are multiple parameters, the space target must meet all the requirements to be retained; otherwise, it will be rejected. The target parameters need to be predetermined based on the different screening methods. Specifically, target parameters refer to quantitative indicators used to characterize the orbital features or motion state of a space target. They are obtained based on orbital dynamics principles or measured orbital data (such as TLE data) and are the core judgment basis for constructing space target collision warning screening rules. They are used to set screening thresholds and formulate screening conditions to achieve accurate rejection of target pairs with no collision risk.

[0070] The selection of target parameters must match the screening method. For example, the target parameters for height screening are perigee altitude and apogee altitude, the target parameter for geocentric distance screening is geocentric distance at the intersection of the orbital plane, and the target parameter for angle screening is geocentric angle. These parameters can be used individually as the basis for a single screening, or multiple parameters can be combined to form screening conditions. Different parameters can also be selected successively in multiple progressive screenings to achieve hierarchical and precise screening of space targets.

[0071] As the core of this embodiment, at least one of the screening processes must involve screening the target's relative position based on the law of cosines. Specifically, this includes:

[0072] Only one screening is performed, based on the target's relative position according to the law of cosines;

[0073] After multiple screenings, the results include:

[0074] The target relative position screening based on the cosine theorem is used before other screenings, that is, the target relative position screening based on the cosine theorem is used as the first screening.

[0075] The target relative position selection based on the cosine theorem is the final selection after other selections.

[0076] Alternatively, the target relative position selection based on the cosine theorem can be performed in the middle of other selections. Assuming four selections are performed, the target relative position selection based on the cosine theorem can be the second or third selection. If five selections are performed, the target relative position selection based on the cosine theorem can be the second, third, or fourth selection.

[0077] Step S1.3: Output the filtered spatial targets for subsequent calculations and result output;

[0078] Subsequent calculations can employ optimization and computational methods commonly used in related engineering projects. The main purpose is to conduct accurate collision risk assessments on the high-risk spatial target pairs retained after screening and to output results that can be directly used for early warning decisions.

[0079] It is important to clarify here that high-risk spatial target pairs are the spatial targets obtained after step S1.2. Typically, the filtered spatial targets appear as pairs (target pairs). This is because most filtering methods perform the filtering operation on a pair basis. Essentially, a collision is a relative event between two targets; therefore, it is a necessary condition for two targets to arrive at the same spatial location at the same time. A single spatial target has no collision object and cannot constitute a collision risk. Therefore, a high-risk spatial target pair is a combination of two spatial targets that meet the collision risk threshold condition.

[0080] It is possible that the selected spatial targets are a combination of multiple spatial targets (more than 2), which is a very extreme case.

[0081] This also shows that the space target to be eliminated can be a single space target (or multiple space targets). This is because if a certain space target does not meet the basic conditions for collision warning, then there is no risk of collision when it is paired with any target, and it can be eliminated in advance to reduce the amount of calculation required for subsequent pairing.

[0082] In summary, the selected or eliminated spatial targets mentioned above are merely definitions of the actions to be performed, not a limitation on the number of spatial targets.

[0083] The second embodiment, based on the first embodiment, provides a spatial target screening method combining the law of cosines. Specifically, step S1.2 is improved to obtain a specific method for performing at least one screening. See [link to relevant documentation]. Figure 2 ,include:

[0084] Step S2.1: Calculate the near and far points and reference checkpoint data;

[0085] Calculate the perigee and apogee altitudes of a space target using the SGP4 / SDP4 orbit prediction model (where the altitudes are for...). The goal is to set two height values ​​as specific values ​​that meet the rejection criteria during subsequent height filtering, as well as the x, y, and z axis position and velocity information at each benchmark checkpoint, and save them for calculation in subsequent steps.

[0086] Among them, the SGP4 model is generally applied to near-Earth space targets with an orbital period 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 an orbital period of more than 225 minutes.

[0087] Step S2.2: Perform height (including epoch) and geocentric distance filtering;

[0088] Based on the number of space targets Generate the corresponding For each pair of objectives, determine whether the objective pairs are satisfied. or The exclusion criteria. Refer to the explanation in step 2.1, for... The target's perigee and apogee have been set to specific values ​​that satisfy the height screening, so epoch screening is also performed in this step. Finally, all target pairs that pass this step are output to obtain the spatial targets after the first coarse selection.

[0089] Step S2.3: Perform target relative position filtering based on the law of cosines on the spatial targets after the first coarse selection;

[0090] Set the target number of pairs to be determined through step S2.2. Warning period The number of baseline checkpoints within is For each target pair (target A and target B), the time interval at each baseline checkpoint is... That is, from the first The first baseline checkpoint to the... One benchmark checkpoint, Calculate the first The angles between target A and target B and the Earth's center O at each benchmark checkpoint time. The cosine value of the cosine can be obtained according to the Law of Cosines:

[0091] ;

[0092] in, Let A be the distance between target A and the Earth's center O. Let B be the distance between the target B and the Earth's center O. Let be the distance between targets A and B. According to Newton's second law and the law of universal gravitation, the shortest period for a space target orbiting the Earth is 84 minutes. Therefore, it can be known that when... Under the condition that (the time unit in the formula is minutes), even if target A and target B are on the same orbital plane and moving towards each other, a collision will not occur within the interval of the baseline checkpoint, thus satisfying the rejection condition for screening.

[0093] Since the interval between baseline checkpoints is a fixed value set in advance, it can be calculated beforehand. The result During the screening process, there is no need to perform relatively time-consuming cosine and division calculations; only time-consuming multiplication and addition / subtraction calculations are required for judgment. , It is the cosine value of the critical angle, that is, it satisfies It exceeds the requirements for screening.

[0094] As a preferred embodiment, the benchmark checkpoint interval time The timeframe is 5-10 minutes, which can be determined by considering both the duration of the warning period and the number of spatial targets. The baseline checkpoint refers to the point within the warning period. The position and velocity information of each space target at these reference checkpoints are pre-calculated and stored using SGP4 / SDP4 in the processing steps of this algorithm, according to fixed time intervals.

[0095] It should be noted that in the technical solution of this embodiment:

[0096] The accuracy of orbit prediction is limited by the prediction duration; epoch filtering involves eliminating space targets that have not been updated for a long time. Let the TLE (Time-Lapse Error) data of a certain space target be... The warning period begins at [time]. At any time, if Then remove the target, where The threshold for epoch filtering.

[0097] Altitude filtering requires calculating the perigee and apogee altitudes of two spatial targets and eliminating those that meet the criteria. The target is correct, among which It is a threshold for high-level filtering. The larger of the two perigee heights. It is the smaller of the two apogee heights.

[0098] The Earth-center distance screening method calculates the intersection of the orbital planes of two space targets, determining the distance from the Earth's center when the two targets pass through the intersection. and Eliminate those that meet the requirements The target is correct, among which This is the threshold for filtering based on the distance from the Earth's center.

[0099] Figure 5 The time taken to run the target relative position filtering without the cosine theorem is shown. Figure 6 The time taken to run the target relative position filtering process based on the law of cosines is shown. See also Figure 5 and Figure 6 The images show the collision warning analysis performed on TLE data from June 20, 2025, which contained 27,430 spatial targets. The screenshots show the time taken for subsequent steps with and without the addition of target relative position filtering based on the cosine theorem. The time taken for subsequent steps with this filtering method is only 1 / 4 of the original.

[0100] The third embodiment provides a space target collision early warning method combining the cosine theorem. See [link to relevant documentation]. Figure 3 Specifically, it includes:

[0101] Step S3.1: Obtain the filtered spatial targets. The filtered spatial targets are output by step S1.3.

[0102] Step S3.2: Calculate the collision probability of the target pair and determine the potential encounter time and spatial location with the highest collision risk.

[0103] First, calculate the relative distance between the target pair at each benchmark checkpoint and extract the shortest relative distance within the warning period; then, combine the target's external dimensions and the covariance of the trajectory prediction error, and use a probabilistic collision model (such as the PC model) to calculate the collision probability.

[0104] Step S3.3, Result Output, including:

[0105] Risk level output: Based on preset thresholds (such as collision probability threshold, shortest relative distance threshold), target pairs are divided into four levels: "no risk", "low risk", "medium risk" and "high risk".

[0106] Early warning information output: For high / medium risk target pairs, generate an early warning report including target number, potential encounter time, encounter location, collision probability, and risk level;

[0107] Data visualization output: Output target pair orbit simulation trajectory diagram, relative distance time series curve diagram, collision probability heat map, intuitively presenting risk characteristics for decision-makers' reference.

[0108] As a preferred embodiment Figure 7 The data shows the collision warning processing results, specifically the collision warning analysis of TLE data from June 20, 2025, which contained 27,430 spatial targets. The alarm threshold was set to 5.5 km. Each line in the output represents one warning event, totaling approximately 300,000 events.

[0109] This embodiment provides a space target collision warning method that incorporates the law of cosines. By adding target relative position filtering based on the law of cosines, the number of target pairs used for subsequent calculations is reduced to approximately 1 / 3 to 1 / 4 of the original number. This can improve the processing efficiency of collision warning, or reduce hardware size and computational costs.

[0110] The above method is only one example of this embodiment. Other methods that use the technical solutions disclosed in the first and second embodiments to obtain filtered space targets and then use them for space target collision warning all fall within the protection scope of this application.

[0111] The fourth embodiment provides a spatial target screening system combining the law of cosines, see [link to previous embodiment]. Figure 4 ,include:

[0112] The TLE data acquisition module is configured to read TLE data files and acquire TLE data for each spatial target.

[0113] The filtering module is configured to perform at least one filtering operation to obtain the filtered spatial targets.

[0114] as well as,

[0115] The space target output module is configured to output the filtered space targets.

[0116] Preferably, in at least one of the screening processes performed by the screening module, the target relative position screening must be based on the law of cosines.

[0117] This embodiment provides a spatial target screening system incorporating the law of cosines. By adding target relative position screening based on the law of cosines, the number of target pairs used for subsequent calculations is reduced to approximately 1 / 3 to 1 / 4 of the original. This can improve the processing efficiency of collision warnings, or reduce hardware size and computational costs.

[0118] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent scope of this application.

Claims

1. A spatial target selection method combining the law of cosines, characterized in that, include: Acquire space targets; Perform at least one screening to obtain the selected spatial targets; wherein any one of the at least one screenings is a target relative position screening based on the cosine theorem; wherein, the target relative position screening based on the cosine theorem only performs multiplication and addition / subtraction calculations, and the cosine and division calculations are completed in advance; Output the filtered spatial targets.

2. The spatial target screening method combining the law of cosines according to claim 1, characterized in that, The steps for acquiring the space target include: Read two lines of track element data; Obtain the number of two orbital elements for each space target.

3. The spatial target screening method combining the law of cosines according to claim 1, characterized in that, The filtering is used to eliminate space targets; Among them, the space targets that were eliminated were those that were unlikely to pose a collision risk; The remaining spatial targets after elimination are the filtered spatial targets.

4. The spatial target screening method combining the law of cosines according to claim 3, characterized in that, The filtering process for eliminating space targets includes: Based on at least one preset target parameter, spatial targets that do not meet the requirements of at least one preset target parameter are eliminated.

5. The spatial target screening method combining the law of cosines according to claim 1, characterized in that, The steps for performing at least one screening include: Perform calculations for near and far locations and baseline checkpoint data; Filter by altitude and distance from the Earth's center; Perform target relative position screening based on the law of cosines.

6. The spatial target screening method combining the law of cosines according to claim 5, characterized in that, The steps for calculating near-far location and reference checkpoint data include: The SGP4 / SDP4 orbit prediction model is used 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.

7. The spatial target screening method combining the law of cosines according to claim 5, characterized in that, The steps for screening based on altitude and distance from the Earth's center include: Generate target pairs based on the number of space targets; For each target pair, determine whether it meets the removal criteria. Target pairs that meet the removal criteria are removed. The removal criteria include: In the formula, For the threshold of high-level filtering, The larger of the two perigee heights. The smaller of the two apogee heights; or, In the formula, and Let be the distance from the Earth's center when the two targets of a target pair cross the line of intersection. This is the threshold for filtering based on the distance from the Earth's center.

8. The spatial target screening method combining the law of cosines according to claim 1 or 5, characterized in that, The steps for selecting the relative position of a target based on the law of cosines include: Determine if the exclusion criteria are met: ； In the formula, Let A be the distance between target A and the Earth's center O. Let B be the distance between the target B and the Earth's center O. The distance between targets A and B. The cosine value of the critical angle is calculated in advance; among which, In the formula, The baseline checkpoint interval time; Remove target pairs that meet the removal criteria.

9. A space target collision early warning method combining the law of cosines, characterized in that, include: Obtain the filtered spatial targets; wherein the filtered spatial targets are output by the spatial target filtering method combined with the law of cosines as described in claim 1; Calculate the collision probability of the target pair to determine the potential encounter time and spatial location with the highest collision risk; Output the results.

10. A spatial target screening system combining the law of cosines, characterized in that, include: Space target acquisition module, configured to acquire space targets; The filtering module is configured to perform at least one filtering operation to obtain the filtered spatial targets. Among them, any one of the at least one filtering operations is a target relative position filtering based on the law of cosines. When filtering the target relative position based on the law of cosines, only multiplication and addition / subtraction calculations are performed, while cosine and division calculations are completed in advance. as well as, The space target output module is configured to output the filtered space targets.

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