Early warning constellation k-means clustering method for multiple targets

Abstract

The invention relates to an early warning constellation k-means clustering method oriented to multiple targets. The invention relates to the technical field of spaceflight early warning constellation systems and multi-target clustering, and the method comprises the steps: obtaining target information, converting three-dimensional space coordinate information into two-dimensional space coordinate information through a visual plane projection method, and building a projection coordinate system; designing an initial value selection method of k-means clustering, and enabling the distribution of initial clustering centers to be relatively uniform; an outlier detection mechanism of a clustering target is designed, and class cluster division occupied by outliers is reduced; through plane projection, optimization k-means clustering, outlier detection and center detection methods, independent class cluster division of each satellite to a target group in a constellation is obtained. According to the method provided by the invention, the target group cluster division can be quickly obtained when the low-orbit early warning constellation faces more ballistic targets, so that the target coverage capability of the early warning constellation is improved.

Description

Technical Field

[0001] This invention relates to the field of aerospace early warning constellation systems and multi-objective clustering technology, and is a k-means clustering method for early warning constellations oriented towards multiple objectives. Background Technology

[0002] With the rapid growth in demand for space monitoring, early warning constellation systems play a core role in real-time tracking and threat assessment of multiple targets in fields such as military defense and aerospace monitoring. These systems utilize onboard infrared detectors and inter-satellite and space-to-ground communication links to detect, track, and guide strategic targets such as ballistic missile groups. However, when facing high-density target groups, the tracking capabilities of existing early warning constellation systems are limited by constellation size and sensor resources. The systems typically use preset thresholds to filter targets or employ fixed allocation strategies for tracking. When the number of targets exceeds the upper limit of the "two-to-one" tracking capability, the excess targets cannot be tracked. This bottleneck restricts system effectiveness in complex scenarios. Multi-objective clustering technology, as an important tool in data analysis, has formed a relatively mature algorithmic system in the field of data mining, such as density distribution-based or hierarchical clustering methods. However, existing methods have certain limitations in the application of early warning constellation systems: traditional clustering methods usually do not limit the cluster size, making it difficult to combine with the limited field of view of sensors; algorithm parameters rely on manual experience for adjustment, making it difficult to adapt to real-time changes in the number and distribution characteristics of targets in early warning scenarios; the clustering optimization objectives in the field of data mining differ from the optimization objectives of early warning constellation systems, making technology transfer difficult. Therefore, existing multi-objective clustering technologies have not yet been effectively applied to early warning constellation systems. Summary of the Invention

[0003] This invention explores a solution to enhance the tracking capability of early warning constellation systems by processing target information acquired by the early warning constellation system and effectively combining it with an improved multi-target clustering method.

[0004] This invention provides the following technical solutions: A k-means clustering method for early warning constellations oriented towards multiple objectives, the method comprising the following steps: Step 1: Obtain target information, transform the three-dimensional spatial coordinate information to two dimensions through view plane projection, and establish a projected coordinate system; Step 2: Design an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers; Step 3: Design an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions; Step 4: Obtain the independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection and center detection.

[0005] Preferably, step 1 specifically comprises: J2000 inertial coordinate system: with the Earth's center of mass as the origin, and the mean vernal equinox at epoch J2000 as... x axis, z The axis points towards the celestial pole of Beiping. y shaft and x , z The axes form a right-handed rectangular coordinate system; Projected coordinate system: The line of intersection between the plane passing through the origin and perpendicular to the centroid-satellite vector and the equatorial plane points outwards from the Earth. y The axis, the direction of the centroid-satellite vector is... z axis, x shaft and y , z The axes form a right-handed rectangular coordinate system; When a low-Earth orbit early warning satellite obtains the target's coordinate information from a ground station or a high-Earth orbit satellite, it will confirm and improve the accuracy of the information using its onboard scanning detectors before projecting it into the projected coordinate system. xy Projecting the target group onto the plane yields a two-dimensional projection. The coordinate transformation matrix is ​​calculated as follows: Since satellite coordinates can be given by ephemeris, and the target group centroid can be calculated, the centroid-satellite vector is: (1) The direction vector pointing outwards from the Earth's surface along the intersection of the plane passing through the origin and perpendicular to the centroid-satellite vector with the equatorial plane can be obtained by the cross product of the centroid-satellite vector and the unit vector along the z-axis of the J2000 coordinate system: (2) The coordinate transformation matrix is (3) in: (4) The coordinate transformation matrix is (5) After coordinate transformation, the coordinates of the target group in the J2000 system are converted to coordinates in the projected system. x , y The coordinates are the two-dimensional coordinates of the target on the projection plane.

[0006] Preferably, step 2 specifically comprises: Step 2.1: From the target group coordinates x A target is randomly selected uniformly from the sample, and the coordinates of the selected target are taken as the first center, denoted as: ; Step 2.2: Calculate the remaining target positions to The distance; using express and target coordinates The distance between them; Step 2.3: In x The second center is randomly selected according to the following probability formula. , (6) Step 2.4: To further select the center j Perform two steps; Step 2.5: Repeat step 2.4, selecting the number of cluster centers as... k Stop when the time comes.

[0007] Preferably, step 2.4 includes the following two steps: Step 2.4.1: Calculate the distance from each target location to each center, and assign the target to the nearest center; Step 2.4.2: For and ,exist x The centroid is randomly selected according to the following probability distribution. j , (7) in, The closest to the center The set of all target coordinates, .

[0008] Preferably, step 3 specifically comprises: Calculation parameter definition, the first i Locally achievable density at a point LRD: (8) in, kN(i) It is a point of The nearest neighbor, It is a point i Time j distance, It is a point i To its first distance; Outlier LOF: (9)

[0009] Preferably, the LOF algorithm calculates the first step according to the following process: i Outlier factors at a single point; S1: Calculate the... i Euclidean distance from one point to other points; S2: Sort the distances from the previous step in ascending order and select the closest one. k A close neighbor; S3: Calculate the local reachability density of all points according to the LDR calculation formula; S4: Calculate the first according to the LOF calculation formula. i Outlier factors at each point.

[0010] Preferably, step 4 specifically comprises: Step 4.1: Coding design, number of observations num_observations To determine the number of visible satellites in the target group, the number of observation schemes options for k Value, individual initialization Row vectors refer to the scheme selected from 10 observations; clustering schemes are stored in the form of cell arrays. Step 4.2: Genetic operation design, including the generation of initial solutions and crossover operations; Step 4.3: Mutation operation: Mutate individual gene loci in individuals of the population through insertion and replacement.

[0011] A multi-target early warning constellation k-means clustering system, the system comprising: The information acquisition module acquires target information and transforms the three-dimensional spatial coordinate information into two dimensions through a view plane projection method to establish a projection coordinate system. The design module designs an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers. The detection module is designed with an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions. The partitioning module obtains an independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection, and center detection.

[0012] Preferably, for beamforming to compensate for skin curvature distortion, the driving layer structure is an array structure.

[0013] A computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a multi-target early warning constellation k-means clustering method.

[0014] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement a multi-target early warning constellation k-means clustering method.

[0015] The present invention has the following beneficial effects: This invention proposes a fast two-dimensional clustering method within the field of view plane of an early warning constellation sensor, based on the K-means clustering algorithm. First, based on the target observation geometry constructed using the Walker constellation, a method for projecting spatial targets onto the field of view plane is proposed, enabling the two-dimensionalization of spatial target information. Then, based on the two-dimensional target features, optimization algorithms are designed for K-means clustering, including initial value selection, outlier detection, and single-point detection. Finally, an improved genetic algorithm is designed to combine multiple feasible solutions to derive an optimal field of view pointing scheme.

[0016] The method of this invention can quickly obtain target group cluster classification when a low-Earth orbit early warning constellation faces a large number of ballistic targets, thereby improving the target coverage capability of the early warning constellation. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 The diagram shows the clustering method of the low-orbit early warning constellation of the present invention when facing multiple targets. Figure 2 The results are displayed as satellite 111 clustering results; Figure 3 The results are displayed as satellite clustering 116; Figure 4 The results are displayed as satellite 121 clustering results; Figure 5 The results are displayed as satellite clustering 126; Figure 6 The results are displayed as satellite 131 clustering results; Figure 7 The results are displayed as satellite 132 clustering results; Figure 8 The results are displayed as clustering results for satellite 141. Figure 9 The results are displayed as satellite clustering 142; Figure 10 The results are shown as satellite 151 clustering results. Figure 11 The results are displayed as satellite clustering 156; Figure 12 The graph shows the relationship between optimal fitness and algebra. Detailed Implementation

[0019] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0020] The present invention will be described in detail below with reference to specific embodiments. Specific Implementation Example 1: according to Figures 1 to 12 As shown, the specific optimization technical solution adopted by the present invention to solve the above-mentioned technical problems is: The present invention relates to a k-means clustering method for early warning constellations oriented towards multiple targets.

[0022] This invention provides a k-means clustering method for early warning constellations oriented towards multiple targets, the method comprising the following steps: Step 1: Obtain target information, transform the three-dimensional spatial coordinate information to two dimensions through view plane projection, and establish a projected coordinate system; Step 2: Design an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers; Step 3: Design an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions; Step 4: Obtain the independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection and center detection.

[0023] This invention proposes a fast two-dimensional clustering method within the field of view plane of an early warning constellation sensor, based on the K-means clustering algorithm. First, based on the target observation geometry constructed using the Walker constellation, a method for projecting spatial targets onto the field of view plane is proposed, enabling the two-dimensionalization of spatial target information. Then, based on the two-dimensional target features, optimization algorithms are designed for K-means clustering, including initial value selection, outlier detection, and single-point detection. Finally, an improved genetic algorithm is designed to combine multiple feasible solutions to derive an optimal field of view pointing scheme.

[0024] The method of this invention can quickly obtain target group cluster classification when a low-Earth orbit early warning constellation faces a large number of ballistic targets, thereby improving the target coverage capability of the early warning constellation. Specific Implementation Example 2: The only difference between Embodiment 2 and Embodiment 1 of this application is that: Step 1 specifically involves: J2000 inertial coordinate system: with the Earth's center of mass as the origin, and the mean vernal equinox at epoch J2000 as... x axis, z The axis points towards the celestial pole of Beiping.y shaft and x , z The axes form a right-handed rectangular coordinate system; Projected coordinate system: The line of intersection between the plane passing through the origin and perpendicular to the centroid-satellite vector and the equatorial plane points outwards from the Earth. y The axis, the direction of the centroid-satellite vector is... z axis, x shaft and y , z The axes form a right-handed rectangular coordinate system; When a low-Earth orbit early warning satellite obtains the target's coordinate information from a ground station or a high-Earth orbit satellite, it will confirm and improve the accuracy of the information using its onboard scanning detectors before projecting it into the projected coordinate system. xy Projecting the target group onto the plane yields a two-dimensional projection. The coordinate transformation matrix is ​​calculated as follows: Since satellite coordinates can be given by ephemeris, and the target group centroid can be calculated, the centroid-satellite vector is: (1) The direction vector pointing outwards from the Earth's surface along the intersection of the plane passing through the origin and perpendicular to the centroid-satellite vector with the equatorial plane can be obtained by the cross product of the centroid-satellite vector and the unit vector along the z-axis of the J2000 coordinate system: (2) The coordinate transformation matrix is (3) in: (4) The coordinate transformation matrix is (5) After coordinate transformation, the coordinates of the target group in the J2000 system are converted to coordinates in the projected system. x , y The coordinates are the two-dimensional coordinates of the target on the projection plane. Specific Implementation Example 3: The only difference between Embodiment 3 and Embodiment 2 of this application is that: Step 2 specifically involves: Step 2.1: From the target group coordinates x A target is randomly selected uniformly from the sample, and the coordinates of the selected target are taken as the first center, denoted as: ; Step 2.2: Calculate the remaining target positions to The distance; using express and target coordinates The distance between them; Step 2.3: In x The second center is randomly selected according to the following probability formula. , (6) Step 2.4: To further select the center j Perform two steps; Step 2.5: Repeat step 2.4, selecting the number of cluster centers as... k Stop when the time comes. Specific Implementation Example 4: The only difference between Embodiment 4 and Embodiment 3 of this application is that: The two steps in step 2.4 include: Step 2.4.1: Calculate the distance from each target location to each center, and assign the target to the nearest center; Step 2.4.2: For and ,exist x The centroid is randomly selected according to the following probability distribution. j , (7) in, The closest to the center The set of all target coordinates, . Specific Implementation Example 5: The difference between Embodiment 5 and Embodiment 4 of the present invention lies only in: Step 3 specifically involves: Calculation parameter definition, the first i Locally achievable density at a point LRD: (8) in, kN(i) It is a point of The nearest neighbor, It is a point i Time j distance, It is a point i To its first distance; Outlier LOF: (9) Specific Implementation Example Six: The difference between Embodiment Six and Embodiment Five of the present invention lies only in: The LOF algorithm calculates the first LOF value according to the following process. i Outlier factors at a single point; S1: Calculate the... i Euclidean distance from one point to other points; S2: Sort the distances from the previous step in ascending order and select the closest one. k A close neighbor; S3: Calculate the local reachability density of all points according to the LDR calculation formula; S4: Calculate the first according to the LOF calculation formula. i Outlier factors at each point. Specific Implementation Example 7: The difference between Embodiment Seven and Embodiment Six of the present invention lies only in: Step 4 specifically involves: Step 4.1: Coding design, number of observations num_observations To determine the number of visible satellites in the target group, the number of observation schemes options for k Value, individual initialization Row vectors refer to the scheme selected from 10 observations; clustering schemes are stored in the form of cell arrays. Step 4.2: Genetic operation design, including the generation of initial solutions and crossover operations; Step 4.3: Mutation operation: Mutate individual gene loci in individuals of the population through insertion and replacement. Specific Implementation Example 8: The difference between Embodiment 8 and Embodiment 7 of the present invention lies only in: This invention provides a multi-target early warning constellation k-means clustering system, the system comprising: The information acquisition module acquires target information and transforms the three-dimensional spatial coordinate information into two dimensions through a view plane projection method to establish a projection coordinate system. The design module designs an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers. The detection module is designed with an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions. The partitioning module obtains an independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection, and center detection. Specific Implementation Example Nine: The difference between Embodiment Nine and Embodiment Eight of the present invention lies only in: The present invention provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a multi-target early warning constellation k-means clustering method.

[0033] The method includes the following steps: Step 1: Obtain target information, transform the three-dimensional spatial coordinate information to two dimensions through view plane projection, and establish a projected coordinate system; Step 2: Design an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers; Step 3: Design an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions; Step 4: Obtain the independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection and center detection.

[0034] This invention proposes a fast two-dimensional clustering method within the field of view plane of an early warning constellation sensor, based on the K-means clustering algorithm. First, based on the target observation geometry constructed using the Walker constellation, a method for projecting spatial targets onto the field of view plane is proposed, enabling the two-dimensionalization of spatial target information. Then, based on the two-dimensional target features, optimization algorithms are designed for K-means clustering, including initial value selection, outlier detection, and single-point detection. Finally, an improved genetic algorithm is designed to combine multiple feasible solutions to derive an optimal field of view pointing scheme.

[0035] The method of this invention can quickly obtain target group cluster classification when a low-Earth orbit early warning constellation faces a large number of ballistic targets, thereby improving the target coverage capability of the early warning constellation. Specific Implementation Example 10: The only difference between Embodiment 10 and Embodiment 9 of the present invention is that: The present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement a k-means clustering method for early warning constellations oriented towards multiple targets.

[0037] The method includes the following steps: Step 1: Obtain target information, transform the three-dimensional spatial coordinate information to two dimensions through view plane projection, and establish a projected coordinate system; Step 2: Design an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers; Step 3: Design an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions; Step 4: Obtain the independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection and center detection.

[0038] This invention proposes a fast two-dimensional clustering method within the field of view plane of an early warning constellation sensor, based on the K-means clustering algorithm. First, based on the target observation geometry constructed using the Walker constellation, a method for projecting spatial targets onto the field of view plane is proposed, enabling the two-dimensionalization of spatial target information. Then, based on the two-dimensional target features, optimization algorithms are designed for K-means clustering, including initial value selection, outlier detection, and single-point detection. Finally, an improved genetic algorithm is designed to combine multiple feasible solutions to derive an optimal field of view pointing scheme.

[0039] The method of this invention can quickly obtain target group cluster classification when a low-Earth orbit early warning constellation faces a large number of ballistic targets, thereby improving the target coverage capability of the early warning constellation. Specific Implementation Example Eleven: The only difference between Embodiment Eleven and Embodiment Ten of this invention is that: This invention proposes a fast two-dimensional clustering method within the field of view plane of an early warning constellation sensor, based on the K-means clustering algorithm. First, based on the target observation geometry constructed using the Walker constellation, a method for projecting spatial targets onto the field of view plane is proposed, enabling the two-dimensionalization of spatial target information. Then, based on the two-dimensional target features, optimization algorithms are designed for K-means clustering, including initial value selection, outlier detection, and single-point detection. Finally, an improved genetic algorithm is designed to combine multiple feasible solutions to derive an optimal field of view pointing scheme.

[0041] The method includes the following steps: Step 1: Obtain target information, transform the three-dimensional spatial coordinate information to two dimensions through view plane projection, and establish a projected coordinate system; Step 2: Design an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers; Step 3: Design an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions; Step 4: Obtain the independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection and center detection.

[0042] This invention proposes a fast two-dimensional clustering method within the field of view plane of an early warning constellation sensor, based on the K-means clustering algorithm. First, based on the target observation geometry constructed using the Walker constellation, a method for projecting spatial targets onto the field of view plane is proposed, enabling the two-dimensionalization of spatial target information. Then, based on the two-dimensional target features, optimization algorithms are designed for K-means clustering, including initial value selection, outlier detection, and single-point detection. Finally, an improved genetic algorithm is designed to combine multiple feasible solutions to derive an optimal field of view pointing scheme.

[0043] The method of this invention can quickly obtain target group cluster classification when a low-Earth orbit early warning constellation faces a large number of ballistic targets, thereby improving the target coverage capability of the early warning constellation.

[0044] The specific steps are as follows: A view plane projection method is used to transform three-dimensional spatial coordinate information to two dimensions. The projected coordinate system is defined as follows: J2000 inertial coordinate system: with the Earth's center of mass as the origin, and the mean vernal equinox at epoch J2000 as... x axis, z The axis points towards the celestial pole of Beiping. y shaft and x , z The axes form a right-handed rectangular coordinate system.

[0045] Projected coordinate system: The line of intersection between the plane passing through the origin and perpendicular to the centroid-satellite vector and the equatorial plane points outwards from the Earth. y The axis, the direction of the centroid-satellite vector is... z axis, x shaft and y , z The axes form a right-handed rectangular coordinate system.

[0046] Based on the above rules, when a low-Earth orbit early warning satellite obtains the target's coordinate information from a ground station or a high-Earth orbit satellite, it will confirm and improve the accuracy of the information using its onboard scanning detectors before projecting it into the projected coordinate system. xy Projecting the target group onto the plane yields a two-dimensional projection. The coordinate transformation matrix is ​​calculated as follows: Since satellite coordinates can be given by ephemeris, and the target group centroid can be calculated, the centroid-satellite vector is: (1) The direction vector pointing outwards from the Earth's surface along the intersection of the plane passing through the origin and perpendicular to the centroid-satellite vector with the equatorial plane can be obtained by the cross product of the centroid-satellite vector and the unit vector along the z-axis of the J2000 coordinate system: (2) The coordinate transformation matrix is (3) in: (4) The coordinate transformation matrix is (5) After coordinate transformation, the coordinates of the target group in the J2000 system are converted to coordinates in the projected system. x , y The coordinates are the two-dimensional coordinates of the target on the projection plane.

[0047] The following design proposes an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers.

[0048] 1. From the target group coordinates x A target is randomly selected uniformly from the sample, and the coordinates of the selected target are taken as the first center, denoted as: .

[0049] 2. Calculate the distances to the remaining target locations. The distance. (Using) express and target coordinates The distance between them.

[0050] 3. In x The second center is randomly selected according to the following probability formula. , (6) 4. To further select a center j Perform the following two steps: a. Calculate the distance from each target location to each center, and assign the target to the nearest center.

[0051] b. For and ,exist x The centroid is randomly selected according to the following probability distribution. j , (7) in, The closest to the center The set of all target coordinates, In other words, when selecting each subsequent cluster center, the probability of selecting a target is proportional to the distance between that target and the nearest already selected cluster center.

[0052] 5. Repeat step 4, selecting the number of cluster centers as... k Stop when the time comes.

[0053] Next, we will design an outlier detection mechanism for clustering targets to reduce the occurrence of a small number of outliers occupying a single cluster.

[0054] Calculation parameter definition: No. i Locally attainable density at each point ( LRD ) (8) in, kN(i) It is a point of The nearest neighbor, It is a point i Time j distance, It is a point i To its first distance.

[0055] Outlier ( LOF ) (9) The LOF algorithm calculates the first LOF value according to the following process. i Outlier factors at a single point: 1. Calculate the first... i The Euclidean distance from one point to other points.

[0056] 2. Sort the distances from the previous step in ascending order and select the closest one. k A close neighbor.

[0057] 3. Calculate the local reachability density of all points according to the LDR calculation formula.

[0058] 4. Calculate the first LOF value according to the LOF calculation formula. i Outlier factors at each point.

[0059] Then, when most targets are evenly distributed and outliers are not prominent, the number of targets at the center of the cluster is small and the distribution of targets around the cluster is denser. By detecting whether the number of covered targets increases when the center of the field of view moves to the target position, the coverage can be effectively improved with almost no increase in computing time.

[0060] By using methods such as planar projection, optimized k-means clustering, outlier detection, and center detection, we can obtain an independent clustering of each satellite in the constellation for the target group. We call this partitioning a feasible solution for that satellite in the constellation. However, early warning missions require the overall constellation to cover the target group. The feasible solutions of each satellite are not optimal as a whole. Therefore, we generate 5 feasible solutions for each early warning satellite and design a genetic algorithm to optimize the overall coverage as follows, so as to generate a relatively optimal solution in a short time.

[0061] 1) Coding Design Number of observations num_observations The number of visible satellites for the target group is 10 here. Number of observation schemes. options for k The value is 5 here. Individual initialization is... Row vectors represent the clustering schemes selected from 10 observations. Clustering schemes are stored as cell arrays, with each scheme representing the target index that can be observed by the satellite in a single observation. Population fitness is the number of targets observed two or more times.

[0062] 2) Genetic manipulation design Initial solution generation: Since the solutions are relatively independent, random generation is sufficient.

[0063] Crossover operation: This part uses a two-point crossover method, which greatly increases population diversity while ensuring the rationality of offspring.

[0064] The execution process for the intersection of two points is as follows: Step 1: Randomly select two points located inside the array, denoted as... .

[0065] Step 2: middle left side and The gene segments on the right were copied to... .

[0066] Step 3: The gene segments between the two parts were copied to respectively. .

[0067] Mutation operations: By inserting or replacing individual gene loci in individuals within a population, mutations can be made, which can maintain population diversity to a certain extent and optimize the problem of algorithms easily getting trapped in local optima.

[0068] Insertion mutations have the following execution process: 1. Randomly select a gene locus from the individuals to be operated on.

[0069] 2. Randomly insert the gene locus from the previous step into another gene locus, leaving the other gene loci unchanged.

[0070] Using the genetic algorithm described above, the optimal combination of solutions with relatively high overall coverage can be obtained from the five feasible solutions for each early warning satellite in a relatively short time.

[0071] In summary, the clustering method designed in this invention enables low-Earth orbit early warning constellations to quickly obtain target group clusters corresponding to early warning satellites when facing multiple ballistic targets.

[0072] This invention is verified through numerical simulation. The numerical simulation problem, simulation design process, and simulation results are described below as an implementation method and technical evidence of this invention.

[0073] Numerical simulation problem description A Walker constellation with circular orbital parameters of 30 / 6 / 1 was constructed, with an orbital altitude of 1600 km and an orbital inclination of 102.49°. The simulation time was Time (UTCG) 8 Mar 2024 04:25:00. A ballistic missile was used to simulate the target group's center of mass, with the launch point at 47°N 122.9°W and the target point at 35.7°N 139.7°E, both at sea level. The launch time was Time (UTCG) 8 Mar 2024 04:00:00. Around the target group's center of mass, n=30 random points were randomly generated within a cube with a side length of 550 km to simulate the known ballistic missile target position information.

[0074] Through simulation steps including visual plane projection, k-means clustering, outlier detection, and center detection, five feasible solutions were obtained for each of the ten visible satellites in the target group. Examples of feasible solutions for each satellite are shown below. Figure 2-11 As shown.

[0075] The genetic algorithm designed above is used to combine and optimize the feasible solutions for each star, resulting in a relatively optimal cluster partition. The fitness value (number of successfully observed targets) of the genetic algorithm changes with the number of iterations as follows: Figure 12 As shown.

[0076] The results of the genetic algorithm calculation are as follows: Global Best Fitness: 21.00 Global Best Individual: [5 1 4 3 4 2 3 3 2 2] Successfully observed points: [1;2;4;6;7;9;10;11;12;13;14;15;16;17;18;19;22;23;24;25;26] Under this scheme, 21 targets were successfully observed. The clustering scheme selected by each satellite is [5 1 43 4 2 3 3 2 2]. The targets that were successfully observed by two or more satellites are numbered [1;2;4;6;7;9;10;11;12;13;14;15;16;17;18;19;22;23;24;25;26].

[0077] The algorithm takes an average of about 2 seconds, and the early warning constellation can effectively track 21 out of 30 ballistic targets, achieving a coverage rate of 70%.

[0078] The above description is merely a preferred embodiment of a multi-target early warning constellation k-means clustering method. The scope of protection for this method is not limited to the above embodiments; all technical solutions falling within this framework are within the protection scope of this invention. It should be noted that for those skilled in the art, any improvements and variations made without departing from the principles of this invention should also be considered within the protection scope of this invention.

Claims

1. A multi-target-oriented k-means clustering method for early warning constellations, characterized by: The method includes the following steps: Step 1: Obtain target information, transform the three-dimensional spatial coordinate information to two dimensions through view plane projection, and establish a projected coordinate system; Step 2: Design an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers; Step 3: Design an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions; Step 4: Obtain the independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection and center detection.

2. The method according to claim 1, characterized in that: Step 1 specifically involves: J2000 inertial coordinate system: with the Earth's center of mass as the origin, and the mean vernal equinox at epoch J2000 as... x axis, z The axis points towards the celestial pole of Beiping. y shaft and x , z The axes form a right-handed rectangular coordinate system; Projected coordinate system: The line of intersection between the plane passing through the origin and perpendicular to the centroid-satellite vector and the equatorial plane points outwards from the Earth. y The axis, the direction of the centroid-satellite vector is... z axis, x shaft and y , z The axes form a right-handed rectangular coordinate system; When a low-Earth orbit early warning satellite obtains the target's coordinate information from a ground station or a high-Earth orbit satellite, it will confirm and improve the accuracy of the information using its onboard scanning detectors before projecting it into the projected coordinate system. xy Projecting the target group onto the plane yields a two-dimensional projection. The coordinate transformation matrix is ​​calculated as follows: Since satellite coordinates can be given by ephemeris, and the target group centroid can be calculated, the centroid-satellite vector is: (1) The direction vector pointing outwards from the Earth's surface along the intersection of the plane passing through the origin and perpendicular to the centroid-satellite vector with the equatorial plane can be obtained by the cross product of the centroid-satellite vector and the unit vector along the z-axis of the J2000 coordinate system: (2) The coordinate transformation matrix is (3) in: (4) The coordinate transformation matrix is (5) After coordinate transformation, the coordinates of the target group in the J2000 system are converted to coordinates in the projected system. x , y The coordinates are the two-dimensional coordinates of the target on the projection plane.

3. The method according to claim 2, characterized in that: Step 2 specifically involves: Step 2.1: From the target group coordinates x A target is randomly selected uniformly from the sample, and the coordinates of the selected target are taken as the first center, denoted as: ; Step 2.2: Calculate the remaining target positions to The distance; using express and target coordinates The distance between them; Step 2.3: In x The second center is randomly selected according to the following probability formula. , (6) Step 2.4: To further select the center j Perform two steps; Step 2.5: Repeat step 2.4, selecting the number of cluster centers as... k Stop when the time comes.

4. The method according to claim 3, characterized in that: The two steps in step 2.4 include: Step 2.4.1: Calculate the distance from each target location to each center, and assign the target to the nearest center; Step 2.4.2: For and ,exist x The centroid is randomly selected according to the following probability distribution. j , (7) in, The closest to the center The set of all target coordinates, .

5. The method according to claim 4, characterized in that: Step 3 specifically involves: Calculation parameter definition, the first i Locally attainable density at each point LRD: (8) in, kN(i) It is a point of The nearest neighbor, It is a point i Time j distance, It is a point i To its first distance; Outlier LOF: (9)。 6. The method according to claim 5, characterized in that: The LOF algorithm calculates the first LOF value according to the following process. i Outlier factors at a single point; S1: Calculate the... i Euclidean distance from one point to other points; S2: Sort the distances from the previous step in ascending order and select the closest one. k A close neighbor; S3: Calculate the local reachability density of all points according to the LDR calculation formula; S4: Calculate the first according to the LOF calculation formula. i Outlier factors at each point.

7. The method according to claim 6, characterized in that: Step 4 specifically involves: Step 4.1: Coding design, number of observations num_observations To determine the number of visible satellites in the target group, the number of observation schemes options for k Value, individual initialization Row vectors represent the scheme selected from 10 observations; clustering schemes are stored in the form of cell arrays. Step 4.2: Genetic operation design, including the generation of initial solutions and crossover operations; Step 4.3: Mutation operation: Mutate individual gene loci in individuals of the population through insertion and replacement.

8. A multi-target early warning constellation k-means clustering system, characterized by: The system includes: The information acquisition module acquires target information and transforms the three-dimensional spatial coordinate information into two dimensions through a view plane projection method to establish a projection coordinate system. The design module designs an initial value selection method for k-means clustering to ensure a relatively uniform distribution of initial cluster centers. The detection module is designed with an outlier detection mechanism for clustering targets to reduce the number of outliers occupying cluster partitions. The partitioning module obtains an independent clustering of each satellite in the constellation for the target group by means of planar projection, optimized k-means clustering, outlier detection, and center detection.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the method as claimed in claims 1-7.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the method of claims 1-7.

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