Satellite formation space display method and system based on adaptive template matching

Abstract

The application provides a satellite formation space display method and system based on adaptive template matching, and relates to the technical field of satellite formation. By introducing pattern type recognition, foreground point set, skeleton point set and contour point set are extracted from a binary image, and pattern types are recognized according to distribution ratios, so that point sets most representing the structures of patterns with different geometric features can be selected to generate template point sets. By adopting coarse search screening and fine search screening mechanisms, the optimal rotation angle, scaling ratio and translation vector can be efficiently found in a wide geometric transformation parameter space, and adaptive lighting radii are determined according to the nearest distances of each satellite to other satellites. The adaptive radii can be dynamically adjusted according to the actual density of the satellite formation, so that when the final satellite lighting set is determined, the continuity of the pattern can be ensured, and the waste of satellite resources can be avoided, and the application potential and effect of the satellite formation space display are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of satellite formation technology, and more specifically, to a method and system for displaying satellite formations in space based on adaptive template matching. Background Technology

[0002] With the development of satellite formation flight, on-orbit collaborative control, space optical payloads and high-precision attitude control technologies, the use of multiple satellites to form discrete luminous arrays in specific observation directions, and the presentation of text, graphics, logos or dynamic patterns by controlling the switching, brightness or color state of the satellite luminous payloads, has become an important direction for exploration in satellite formation applications.

[0003] Existing pattern display methods typically binarize the image to be displayed first, and then map foreground pixels, edge pixels, or contour points to display units. For example, a regular LED array can map image pixels to LED coordinates at a fixed ratio; drone formation displays can directly form pattern outlines or filled areas by pre-planning the positions of each drone. These methods usually rely on conditions such as freely adjustable display unit positions, high array density, or relatively regular array structures, making them difficult to directly apply to satellite formations whose positions are constrained by orbits.

[0004] If a simple nearest-neighbor mapping method of "directly finding the nearest satellite" is used in satellite formation display, multiple pattern points may be mapped to the same satellite simultaneously, resulting in satellites being repeatedly occupied in some areas while other areas lack satellites for display. This problem is more pronounced for patterns composed of continuous lines, sharp corners, slender structures, or multiple independent areas, easily leading to excessive concentration of bright spots, uneven line thickness, local breaks, shift in the center of gravity of the pattern, and distortion of the overall outline. Summary of the Invention

[0005] The problem this invention aims to solve is that satellite formation display using the simple nearest neighbor mapping method is prone to duplicate occupation and uneven display.

[0006] To address the aforementioned problems, in a first aspect, the present invention provides a satellite formation space display method based on adaptive template matching, comprising: Obtain the pattern to be displayed and the position information of each satellite in the satellite formation on the display plane; The pattern to be displayed is preprocessed to obtain a binary image; Extract the foreground point set, skeleton point set, and contour point set from the binary image respectively, and determine the distribution ratio, which includes the skeleton ratio, contour ratio, and skeleton-contour ratio. Pattern types are identified based on distribution ratios. Pattern types include line patterns, outline patterns, and filled patterns. Based on the pattern type, extract points from the corresponding point set to generate a template point set; Based on the template points in the template point set, the rotation angle, the scaling ratio, and the translation vector, the transformed template points are obtained; Based on the distance from each transformed template point to the nearest satellite point and the coarse search cost, a coarse search is performed on the candidate transformation parameters in the parameter space consisting of the rotation angle range, scaling ratio range, and translation vector range, and a preset number of candidate transformation parameters are selected. Based on the distance cost between the transformed template points and satellite points and the total matching cost, a fine search and screening is performed on the candidate transformation parameters after coarse screening to obtain the final template point set and the optimal geometric transformation parameters. The adaptive illumination radius is determined based on the nearest neighbor distance between each satellite and other satellites; The final set of illuminated satellites is determined based on the minimum distance of each satellite from the final template point in the final template point set and the adaptive illumination radius.

[0007] Secondly, the present invention also provides a satellite formation space display system based on adaptive template matching, comprising: The information acquisition module is used to acquire the pattern to be displayed and the position information of each satellite in the satellite formation on the display plane; The pattern preprocessing module is used to preprocess the pattern to be displayed to obtain a binary image; The pattern analysis module is used to extract the foreground point set, skeleton point set, and contour point set from the binary image, and determine the distribution ratio, which includes the skeleton ratio, contour ratio, and skeleton-contour ratio; it is also used to identify the pattern type based on the distribution ratio, which includes line patterns, contour patterns, and filled patterns. The template point processing module is used to extract points from the corresponding point set according to the pattern type and generate a template point set; it is also used to obtain the transformed template points based on the template points in the template point set, the rotation angle, the scaling ratio, and the translation vector. The template point coarse search module is used to perform a coarse search and screening of candidate transformation parameters in the parameter space consisting of the rotation angle range, scaling ratio range, and translation vector range, based on the distance of each transformed template point to the nearest satellite point and the coarse search cost, and select a preset number of candidate transformation parameters. The template point fine search module is used to perform fine search and screening on the candidate transformation parameters after coarse screening based on the distance cost and total matching cost between the transformed template points and satellite points, so as to obtain the final template point set and the optimal geometric transformation parameters. The satellite illumination analysis module is used to determine the adaptive illumination radius based on the nearest neighbor distance of each satellite to other satellites; it is also used to determine the final set of illuminated satellites based on the minimum distance of each satellite from the final template point in the final template point set and the adaptive illumination radius.

[0008] This invention provides a method and system for space-based display of satellite formations based on adaptive template matching. Compared with existing technologies, it has the following advantages: By introducing pattern type recognition, foreground point sets, skeleton point sets, and contour point sets are extracted from binary images. Pattern types are then identified based on their distribution ratios. This allows for the selection of the point set most representative of the structure of patterns with different geometric features to generate template point sets, avoiding the problem of traditional methods that treat all patterns indiscriminately, leading to insufficient capture of complex pattern features. Furthermore, the use of coarse and fine search screening mechanisms efficiently finds the optimal rotation angle, scaling ratio, and translation vector within a broad geometric transformation parameter space, significantly improving matching efficiency and accuracy. This method introduces a mechanism to determine the adaptive lighting radius based on the nearest neighbor distance from each satellite to other satellites. This adaptive radius can be dynamically adjusted according to the current actual density of the satellite formation, ensuring pattern continuity while avoiding waste of satellite resources when determining the final set of illuminated satellites. This significantly improves the uniformity and visual effect of the pattern display, effectively solving problems such as excessive concentration of bright spots, uneven line thickness, and local breaks. By employing structured pattern analysis, efficient template matching search, and adaptive satellite illumination strategies, this paper presents a technical solution that can effectively address satellite formation position constraints and achieve high-quality space pattern display, significantly enhancing the application potential and effectiveness of satellite formation space display. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the 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.

[0010] Figure 1 A flowchart illustrating a satellite formation space display method based on adaptive template matching, provided in an embodiment of the present invention; Figure 2 A schematic diagram of a satellite formation space display system based on adaptive template matching is provided for an embodiment of the present invention; Figure 3 This is a schematic diagram of the distribution of a regular hexagonal lattice satellite array in the virtual primary star LVLH coordinate system provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the projection of a regular hexagonal lattice satellite array in the yz plane provided in an embodiment of the present invention; Figure 5 A geometric topological diagram of the observer and the formation satellites provided in an embodiment of the present invention; Figure 6 A schematic diagram of the LVLH coordinate system provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the relative orbital parameters in the LVLH coordinate system provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of the spatial configuration of a regular hexagonal lattice satellite array provided in an embodiment of the present invention; Figure 9 This is a schematic diagram of letter images provided in an embodiment of the present invention; Figure 10 This is a ground-based actual line-of-sight projection diagram provided for an embodiment of the present invention at an observation time; Figure 11 This is a ground-based actual line-of-sight projection diagram provided for another observation moment according to an embodiment of the present invention; Figure 12 A set of standard digital character patterns provided for embodiments of the present invention; Figure 13 This is a visual projection effect diagram of the actual ground line of sight provided in an embodiment of the present invention; Figure 14 This is a schematic diagram of an interlaced complex graphic identifier pattern provided in an embodiment of the present invention; Figure 15 This is an actual perspective projection diagram of a three-layer formation provided in an embodiment of the present invention; Figure 16 The actual perspective projection effect of the four-layer formation provided in the embodiment of the present invention. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application are described clearly and completely. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0012] Unlike ground-based LED arrays, projection displays, and drone light formations, the luminous units in satellite formation space displays are not fixedly arranged in a regular grid. Satellite positions are influenced by factors such as orbital dynamics, formation configuration, relative motion, orbital perturbations, attitude control errors, and observation time. Therefore, their projections on the display plane typically exhibit circular, annular, hexagonal, elliptical, layered nested, or other irregular discrete distributions. Even if satellites initially adopt a regular configuration, their relative positions may change during actual operation. Therefore, traditional image mapping methods using regular pixel arrays cannot be directly applied.

[0013] Furthermore, different patterns possess different structural features. For line-based patterns such as text strokes, five-pointed stars, arrows, and wireframe logos, visual features are mainly concentrated near the skeleton or center line; for outline-based patterns such as circles, hollow letters, and outline trademarks, visual features are mainly concentrated in the boundary area; for solid icons, solid symbols, and large-area filled patterns, visual features are distributed throughout the entire foreground area. If a uniform foreground pixel sampling method is used for different patterns, it can easily lead to thickened strokes or loss of detail in line-based patterns, incorrect filling of the interior of outline-based patterns, and localized voids in filled patterns. Therefore, it is necessary to adaptively generate discrete template point sets based on the skeleton, outline, and foreground area features of the pattern.

[0014] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0015] like Figure 1 As shown in the figure, an embodiment of this application provides a satellite formation space display method based on adaptive template matching, comprising: S1: Obtain the pattern to be displayed and the position information of each satellite in the satellite formation on the display plane.

[0016] Specifically, the pattern to be displayed can be text, numbers, symbols, trademarks, graphics, or other two-dimensional images; the satellite position can be obtained from the relative position of the satellite formation, orbital status, formation coordinate system, or projected coordinate system. The pattern to be displayed can be a digital image provided by the user through an image input device, such as an image file acquired by a scanner or camera, or a vector graphic directly exported from computer graphics software. The position information of each satellite in the satellite formation within the display plane can be obtained through a satellite navigation system (such as GPS or BeiDou) combined with measurement data from ground observation stations, or through real-time position sharing and calculation via inter-satellite links. For example, a fixed time interval can be set to periodically receive the real-time three-dimensional coordinates of all satellites participating in the display task from the satellite control center and project them onto a preset two-dimensional display plane.

[0017] S2: Preprocess the pattern to be displayed to obtain a binary image.

[0018] Specifically, the preprocessing step may include converting a color or grayscale image to a black and white image. For example, a fixed brightness threshold can be used, setting all pixels with brightness values ​​higher than the threshold to white (representing the background) and all pixels with brightness values ​​lower than or equal to the threshold to black (representing the foreground). This simple binarization method can simplify complex image information into binary data containing only the foreground and background, facilitating subsequent feature extraction and analysis.

[0019] S3: Extract the foreground point set, skeleton point set, and contour point set from the binary image respectively, and determine the distribution ratio, which includes the skeleton ratio, contour ratio, and skeleton-contour ratio.

[0020] Specifically, the foreground point set can be formed directly by traversing the binary image and collecting the coordinates of all pixels representing the foreground. The skeleton point set can be obtained by performing morphological thinning operations on the foreground point set, for example, repeatedly deleting pixels at the edges of the foreground point set until no more can be deleted, thus obtaining the skeleton of the pattern. The contour point set can be obtained through edge detection algorithms, for example, by detecting the boundary pixels between the foreground and background point sets. The distribution ratio can be determined by calculating the ratio of the number of points in each point set to the total number of points in the foreground point set. For example, the skeleton ratio can be simply defined as the number of points in the skeleton point set divided by the number of points in the foreground point set.

[0021] S4: Identify the pattern type based on the distribution ratio. Pattern types include line patterns, outline patterns, and filled patterns.

[0022] Specifically, the judgment can be made according to the preset empirical rules: if the skeleton ratio is high, it may be identified as a line pattern; if the outline ratio is high and the skeleton ratio is low, it may be identified as an outline pattern; if both the skeleton ratio and the outline ratio are relatively low, it may be identified as a filled pattern.

[0023] S5: Based on the pattern type, extract points from the corresponding point set to generate a template point set.

[0024] Specifically, if the pattern is identified as a line pattern, a subset of points can be selected from the skeleton point set as the template point set; if it is identified as a contour pattern, points are selected from the contour point set; if it is identified as a filled pattern, points are selected from the foreground point set. The point extraction method can be simple uniform sampling, for example, selecting a point at fixed intervals, or randomly selecting a preset number of points.

[0025] S6: Obtain the transformed template points based on the template points in the template point set, the rotation angle, the scaling ratio, and the translation vector.

[0026] Specifically, for each template point in the template point set, its coordinates can be multiplied by a rotation matrix, then by a scaling factor, and finally by a translation vector to obtain the coordinates of the template point in the new position and orientation. The initial values ​​of the rotation angle, scaling factor, and translation vector can be set to preset default values, such as a rotation angle of 0 degrees, a scaling factor of 1, and a translation vector of zero.

[0027] S7: Based on the distance from each transformed template point to the nearest satellite point and the coarse search cost, perform a coarse search and screening of candidate transformation parameters in the parameter space consisting of the rotation angle range, scaling ratio range, and translation vector range, and select a preset number of candidate transformation parameters.

[0028] Specifically, the Euclidean distance between each transformed template point and all satellite points can be calculated, and the nearest satellite point can be found. The coarse search cost can be simply defined as the sum of the distances from all transformed template points to their nearest satellite points. Then, several sets of candidate transformation parameters with the minimum coarse search cost are selected and retained.

[0029] S8: Based on the distance cost and total matching cost between the transformed template points and satellite points, a fine search is performed on the candidate transformation parameters after coarse screening to obtain the final template point set and the optimal geometric transformation parameters.

[0030] Specifically, for each set of candidate transformation parameters, the distance cost between each transformed template point and the satellite point can be calculated, and an attempt can be made to match the transformed template point with the satellite point one-to-one. The total matching cost can be simply defined as the sum of the distance costs of all matching pairs. By traversing a certain range of rotation angles, scaling ratios, and translation vectors, the candidate transformation parameters that minimize the total matching cost are found and determined as the optimal geometric transformation parameters.

[0031] S9: Determine the adaptive illumination radius based on the nearest neighbor distance of each satellite to other satellites.

[0032] Specifically, the distance between each satellite and all other satellites in the formation can be calculated, and the minimum distance can be found. Then, these minimum distances of all satellites are averaged to obtain an average nearest neighbor distance, which is used as the adaptive lighting radius. The determination of this radius is intended to reflect the current density of the satellite formation.

[0033] S10: Determine the final set of illuminated satellites based on the minimum distance of each satellite from the final template point in the final template point set and the adaptive illumination radius.

[0034] Specifically, for each satellite in the formation, the distance from it to all final template points in the final template point set is calculated, and the minimum value is taken. If this minimum value is less than or equal to the previously determined adaptive lighting radius, the satellite is considered to be lit; otherwise, the satellite is not lit. In this way, it is possible to flexibly determine which satellites participate in the display based on the shape of the pattern and the distribution of satellites, thereby forming the final pattern.

[0035] In this optional embodiment, by introducing pattern type recognition, foreground point sets, skeleton point sets, and contour point sets are extracted from the binary image. The pattern type is then identified based on the distribution ratio. This allows for the selection of the point set that best represents the structure of patterns with different geometric features (such as line-type, contour-type, and filled-type) to generate the template point set. This avoids the problem of traditional methods treating all patterns indiscriminately, leading to insufficient capture of complex pattern features. Furthermore, by employing a coarse-search and fine-search screening mechanism, and through a phased, coarse-to-fine matching strategy, the optimal rotation angle, scaling ratio, and translation vector can be efficiently found in a broad geometric transformation parameter space, significantly improving the efficiency and accuracy of matching. The coarse search can quickly eliminate a large number of unreasonable transformations, while the fine search performs precise matching within the narrowed range, ensuring the best fit between the final template point set and the satellite formation distribution. Further, this method introduces a mechanism to determine the adaptive illumination radius based on the nearest neighbor distance from each satellite to other satellites. This adaptive radius can be dynamically adjusted according to the actual density of the satellite formation, ensuring pattern continuity while avoiding waste of satellite resources when determining the final set of illuminated satellites. For example, when a "V" shaped pattern needs to be displayed in a relatively sparse satellite formation, the adaptive illumination radius will increase accordingly, allowing the gaps to be filled by illuminating satellites further away, ensuring the integrity of the lines, even with large satellite spacing. In dense formations, the radius will decrease to maintain pattern clarity and detail. This significantly improves the uniformity and visual effect of the pattern display, effectively solving problems such as excessive concentration of bright spots, uneven line thickness, and local breaks. In summary, through structured pattern analysis, efficient template matching search, and adaptive satellite illumination strategies, a technical solution is provided that can effectively address satellite formation position constraints and achieve high-quality space pattern display, significantly enhancing the application potential and effectiveness of satellite formation space displays.

[0036] The following is a detailed description of each step.

[0037] S1: Obtain the pattern to be displayed and the position information of each satellite in the satellite formation on the display plane.

[0038] Let the satellite point set be: in, The number of satellites participating in the display. Represents the position coordinates of the j-th satellite. and These represent the x-coordinate and y-coordinate values ​​of satellite j, respectively.

[0039] S2: Preprocess the pattern to be displayed to obtain a binary image. This step specifically includes the following:

[0040] S211: Scale the input pattern to be displayed to a preset canvas size. This canvas size can be preset according to the scale range of the satellite formation on the projection plane, the resolution requirements of the target pattern, or the accuracy requirements of subsequent template point sampling.

[0041] S212: Perform grayscale processing on the scaled pattern to be displayed to obtain a grayscale image.

[0042] Specifically, for a color input image, the pixel values ​​of each color channel are weighted and combined according to a preset grayscale conversion rule to obtain the corresponding grayscale image. The grayscale conversion rule can be determined based on the color space of the input image, the overall brightness distribution, display requirements, or preset parameters. In one embodiment, the position in the grayscale image... pixel value at It can be represented as: in, , , These represent the values ​​of the pixel in the corresponding red, green, and blue color channels. The grayscale conversion function can be a linear weighted function, a nonlinear conversion function, a conversion function based on the luminance component, or a conversion function adaptively determined by the image processing module based on the features of the input image.

[0043] S213: Determine the binarization threshold of the grayscale image according to the preset segmentation strategy, and generate a binary image.

[0044] Specifically, the threshold selection method can be a fixed threshold, an adaptive threshold determined based on grayscale histogram analysis, or a local threshold dynamically determined according to the local brightness distribution of the image. Further, based on the ratio of bright to dark pixels in the image, the pixel distribution characteristics of the boundary region, or a preset foreground polarity rule, it is determined whether the pattern to be displayed corresponds to a bright or dark region, and the polarity of the foreground and background pixels is determined accordingly. In the final generated binary image, foreground pixels are used to represent the area of ​​the pattern to be displayed, and background pixels are used to represent the non-display area.

[0045] Standardized and simplified preprocessing of the patterns to be displayed effectively solves the problems of inconsistent original pattern sizes, complex color information, and difficulty in distinguishing foreground and background. Scaling the input patterns to a preset canvas size ensures that subsequent matching algorithms operate at a uniform scale, avoiding computational complexity and matching errors caused by size differences. Grayscale processing removes redundant color information, reduces data dimensionality, and makes image processing more efficient. Binarization based on a preset segmentation strategy clearly separates the pattern foreground and background, providing high-quality input for subsequent accurate extraction of key features such as the pattern's skeleton and contour. This significantly improves the accuracy of pattern analysis and the reliability of template point set generation, ultimately ensuring the accuracy and visual effect of the satellite formation's space display patterns.

[0046] Since the number of satellites is usually limited, while the number of foreground pixels, contour pixels, or skeleton pixels in the original image may be far greater than the number of satellites, directly using all image pixels for matching would result in a large computational load and a large number of redundant template points. Simple random sampling, on the other hand, might leave key structures such as sharp corners, turning points, thin lines, and small independent regions without sufficient coverage. Therefore, how to generate a discrete set of template points that can simultaneously reflect the overall shape and local structural features of the pattern under the constraint of a limited number of satellites is a crucial problem for achieving high-quality space displays. The solution is presented in steps S3-S5 below.

[0047] S3: Extract the foreground point set, skeleton point set, and contour point set from the binary image respectively, and determine the distribution ratio, which includes the skeleton ratio, contour ratio, and skeleton-contour ratio.

[0048] Specifically, the number of attractions is set as follows: The number of skeleton points is The number of contour points is Constructing the skeleton proportions Outline proportions and the proportions of the skeleton and outline They are respectively: S4: Identify the pattern type based on the distribution ratio. Pattern types include line patterns, outline patterns, and filled patterns.

[0049] Specifically, when the skeleton ratio, outline ratio, or skeleton-outline ratio meets preset conditions, the pattern is identified as a line-type pattern; when the pattern does not meet the line-type conditions but the outline ratio is relatively high, the pattern is identified as a hollow outline-type pattern; all other patterns are identified as solid-filled patterns. For example, the preset conditions for a line-type pattern are: skeleton ratio > 0.20 and outline ratio > 0.35, or skeleton / outline ratio > 0.30 (slender curve); if the above preset conditions are not met, and the outline ratio > 0.50, the outline ratio is considered relatively high, and the pattern type is determined to be an outline-type pattern; except for the above cases, the patterns in other cases are filled patterns.

[0050] S5: Based on the pattern type, extract points from the corresponding point set to generate a template point set.

[0051] The line-type patterns correspond to the skeleton point set, the outline-type patterns correspond to the outline point set, and the filled patterns correspond to the foreground point set.

[0052] S511: Select the point closest to the centroid of the corresponding point set as the initial template point.

[0053] Specifically, for line patterns, template points are extracted from the skeleton point set; for contour patterns, template points are extracted from the contour point set; and for filled patterns, template points are extracted from the foreground point set. For patterns containing multiple independent regions, connected component analysis can be performed first to remove noise regions with areas smaller than a threshold, and the number of template points can be allocated according to the area ratio of each effective connected component to ensure that smaller but displayable independent regions can obtain sufficient template point coverage.

[0054] S512: Subsequently, each time, select the point with the largest minimum distance from the unselected points in the corresponding point set to the selected template point set, until the preset number of template points is reached, and the template point set is obtained.

[0055] Specifically, let the template point set be: in, This represents the number of template points; The coordinates of the template point, and These are the x and y coordinates of the template point, respectively. The number of template points can be adaptively set according to the number of satellites: in, This is a template number adaptive function. The template number adaptive function is determined based on the number of satellites participating in the display, the complexity of the target pattern, display accuracy requirements, or system computing resources, ensuring that the number of template points maintains a preset proportional relationship with the number of satellites; for example... ,in, To minimize the number of templates, This is the quantity ratio coefficient. The number of satellites to be displayed. This is to improve the ability to express continuous lines, boundary contours, and local details even with a limited number of satellites.

[0056] This application can selectively extract template points from the set of points that best represent the characteristics of the identified pattern type, avoiding unnecessary point set interference. Simultaneously, by first selecting the point with the nearest centroid as the initial point, and then iteratively selecting the point with the largest minimum distance from the selected template point set, it ensures that the generated template point set not only fully covers the key geometric features of the pattern but also has a uniform distribution among the points, avoiding local density and redundancy. This significantly improves the representativeness and quality of the template point set, thus providing more accurate input for subsequent coarse and fine search matching, effectively improving the accuracy and robustness of satellite formation matching with target patterns, and potentially reducing the number of template points required, optimizing the utilization efficiency of computational resources.

[0057] S601: The template point set is centered to obtain the centroid of the template point.

[0058] S602: Based on the template point and the template point centroid, obtain the centered template point.

[0059] Specifically, the template point set is centered, and the centroid of the template point is: The centralized template point is: in, and These represent the x-coordinate and y-coordinate values ​​of the centroid of the template point, respectively. This represents the coordinates of the centered template point. and These represent the x-coordinate and y-coordinate values ​​of the centered template point, respectively.

[0060] S603: Obtain the compensation template point based on the centered template point and the two-dimensional projection matrix.

[0061] Specifically, when the ground observation perspective needs to be considered, a two-dimensional projection matrix is ​​established between the satellite formation display plane and the observer's line-of-sight plane: in, , , , These are the element values ​​at the corresponding positions in the two-dimensional projection matrix.

[0062] When the projection matrix is ​​invertible, its inverse matrix is ​​calculated, and the centered template points are converted into compensated template points: The negative value for the ordinate is used to unify the ordinate direction between the image coordinate system and the display plane coordinate system. Enabling view compensation fixes the template rotation angle, preventing subsequent rotation searches from negating the applied projection compensation.

[0063] S604: When view compensation is not enabled, the centralized template point is used as the template point for matching, i.e., the template point for matching. Equal to the centralized template point .

[0064] S605: When view compensation is enabled, the compensation template point is used as the template point for matching, i.e., the template point for matching. Equal to compensation template point .

[0065] Centralized processing makes geometric transformations more stable and efficient, while viewpoint compensation ensures that the matching process fully considers the actual visual effects, thus significantly improving the accuracy and robustness of pattern matching. This allows satellite formations to more accurately present preset patterns, enhancing the effect and visual appeal of space displays.

[0066] S6: Obtain the transformed template points based on the template points in the template point set, the rotation angle, the scaling ratio, and the translation vector.

[0067] The transformed template points are: ; ; in, These are the transformed template points. For scaling ratio, The rotation angle; It is a translation vector. and These are the x and y coordinates of the translation vector, respectively. Template points for matching; It is a rotation matrix.

[0068] After generating the template point set, the spatial alignment between the pattern and the satellite formation configuration needs to be addressed. The target pattern and the satellite formation typically differ in scale, center position, and orientation, requiring geometric transformations such as rotation, scaling, and translation to make the pattern template fit the satellite point set as closely as possible. If transformation parameters are manually set, repeated adjustments are needed for different patterns, satellite configurations, and time periods. Performing highly complex global matching directly on all parameter combinations significantly increases computational overhead, hindering dynamic display and rapid evaluation of multiple schemes.

[0069] S7: Based on the distance from each transformed template point to the nearest satellite point and the coarse search cost, perform a coarse search and screening of candidate transformation parameters within the parameter space comprised of the rotation angle range, scaling ratio range, and translation vector range, and select a preset number of candidate transformation parameters. This step specifically includes the following:

[0070] After generating the template point set, the spatial alignment between the pattern and the satellite formation configuration needs to be addressed. The target pattern and the satellite formation typically differ in scale, center position, and orientation, requiring geometric transformations such as rotation, scaling, and translation to make the pattern template fit the satellite point set as closely as possible. If transformation parameters are manually set, repeated adjustments are needed for different patterns, satellite configurations, and time periods. Performing highly complex global matching directly on all parameter combinations significantly increases computational overhead, hindering dynamic display and rapid evaluation of multiple solutions. To balance matching accuracy and computational efficiency, a hierarchical matching approach combining coarse and fine search is adopted.

[0071] S711: Determine the centroid of the satellite point set based on the satellite's position information.

[0072] Specifically, in the coarse search phase, the centroid of the satellite point set is first calculated: ; in, and These are the x-coordinate and y-coordinate values ​​of the centroid of the satellite point set, respectively.

[0073] S712: The scaling range is obtained based on the maximum radius of the satellite point set relative to the centroid of the satellite point set and the maximum radius of the template point participating in the matching relative to the origin.

[0074] Specifically, calculate the maximum radius of the satellite point set relative to the centroid: ; Calculate the maximum radius of the template point set relative to the origin: ; The scaling range is determined based on the scale relationship between the satellite point set and the template point set: ; ; in, This is the lower bound of the scaling range. This is the upper bound of the scaling range. , , This is the lower bound fluctuation coefficient. This is the upper bound floating coefficient.

[0075] Additionally, for rotation angles around a preset center angle Centered on, the rotation angle range is ,in, Set the preset center angle (for example, it can be 0°, which is fixed at 0° when view compensation is enabled). The search range is set to a preset angle (e.g., 30°). The translation vector is based on the centroid of the satellite point set. Centered on the maximum radius of the satellite point set As the boundary, the range of the x-coordinate of the translation vector is... The range of the ordinate of the translation vector is .

[0076] S713: Translate the satellite point set to a coordinate system centered on the translation vector to obtain the translated satellite point set.

[0077] Specifically, for each group of candidate translation vectors The satellite point set is translated to a coordinate system centered on the translation vector to obtain the translated satellite points. , Represents the position coordinates of the j-th satellite. It is a translation vector.

[0078] S714: Analyze the distances between the transformed template point and the satellite points in the translated satellite point set, and match the satellite point corresponding to the closest distance with the transformed template point. (The closest distance between the transformed template point and the satellite points in the translated satellite point set is then calculated.) .

[0079] S715: Based on the number of times each satellite is matched by its nearest neighbor and the duplicate matching penalty function, the duplicate matching penalty term is obtained.

[0080] S716: Obtain the coarse search cost based on the nearest distance, the duplicate matching penalty term, and the coarse search cost function.

[0081] S717: Based on the coarse search cost, a preset number of candidate transformation parameters are selected from the parameter space comprised of the rotation angle range, scaling ratio range, and translation vector range. The candidate transformation parameters are quadruples of data. .

[0082] In the coarse search phase, multiple template points are allowed to temporarily correspond to the same satellite. To avoid the candidate transformation parameters achieving a low distance cost due to excessive clustering of template points near a few satellites, the statistical analysis of the first phase is performed. The number of times a satellite is matched by its nearest neighbor And construct a duplicate match penalty term: ; The cost of a coarse search is: ; in, Indicates the template point after transformation. Indicates the translation of the satellite point. This indicates the number of times each satellite is matched with its nearest neighbor. Indicates the number of satellites participating in the display. This indicates the preset penalty coefficient. Indicates the number of template points. Indicates the range of vectors.

[0083] Based on the coarse search cost, a preset number of candidate transformation parameters are selected from smallest to largest to enter the fine search stage.

[0084] During the coarse search screening, the search space is effectively limited, avoiding calculations within unreasonable parameter ranges and significantly improving the efficiency of the coarse search. The introduction of a duplicate matching penalty mechanism ensures that the coarse search results are more evenly distributed across the satellite point set, avoiding the trap of local optima and providing higher-quality and more reasonable candidate transformation parameters for the subsequent fine search. This not only reduces the computational burden of the fine search but also improves the accuracy and robustness of the final matching, ensuring that the satellite formation can display the target pattern more accurately and stably.

[0085] Bipartite graph minimum weight matching can establish a one-to-one correspondence between template points and satellite points, making it suitable for evaluating the overall alignment under a certain geometric transformation parameter. However, if the one-to-one matching results are directly used as the list of satellites to be lit, it will be subject to the exclusive constraint of one-to-one matching: for multiple satellites near the same continuous line or the same contour, usually only some satellites can obtain a matching relationship, while the remaining satellites that are close to the pattern but have not been assigned will remain off, which can easily cause the displayed lines to become thinner, the bright spots to be discontinuous, and the contours to be discontinuous.

[0086] S8: Based on the distance cost and total matching cost between the transformed template points and satellite points, a fine search is performed on the candidate transformation parameters after coarse screening to obtain the final template point set and optimal geometric transformation parameters. This step specifically includes the following:

[0087] S811: Obtain the distance cost based on the transformed template points and satellite points.

[0088] In the fine search phase, a local refinement search is performed around the candidate parameters obtained from the coarse search, using smaller angle and scaling steps. For each set of refined candidate parameters, a distance cost is constructed between the transformed template point and the satellite point. .

[0089] S812: The minimum value between the number of satellites participating in the display and the number of template points will be used as the number of template points for the fine search. (Fine Search Template Point Count) .

[0090] S813: If the number of transformed template points exceeds the number of refined search template points, then select the number of transformed template points that are equal to the number of refined search template points from the transformed template points as the refined search template point set.

[0091] Since the minimum weight matching process of the bipartite graph used for fine search in the current implementation requires that the number of template points participating in the matching does not exceed the number of satellites, when the number of template points is greater than the number of satellites, a subset of templates with a number not exceeding the number of satellites is selected to participate in fine search.

[0092] S814: Using the bipartite graph minimum weight matching algorithm, a one-to-one matching relationship is established between the fine search template point set and the satellite point set. Among the candidate transformation parameters after coarse screening, the rotation angle, scaling ratio and translation vector that minimize the total matching cost are selected as the optimal geometric transformation parameters, and the final template point set is determined. The total matching cost is the sum of the distance costs between all matched fine search template points and satellite points.

[0093] In the fine search phase, the minimum weight matching algorithm of the bipartite graph is used to establish a one-to-one correspondence between the template subset and the satellite point set, so as to minimize the total matching cost: in, Indicates the relationship with the first The satellite number corresponding to each transformed template point; Represents the template point after transformation With the corresponding satellite points The distance cost between them. The candidate transformation parameters with the minimum search cost are selected as the optimal geometric transformation parameters. ,in, Indicates the optimal rotation angle. This indicates the optimal scaling ratio. and These represent the x and y coordinates of the optimal translation vector, respectively.

[0094] It should be noted that the minimum weight matching result of the bipartite graph in the fine search phase is used to determine the overall optimal spatial alignment attitude of the pattern relative to the satellite formation, rather than being directly used as the final list of illuminated satellites.

[0095] After obtaining the optimal geometric transformation parameters, all template points are transformed to obtain the final template point set. ,in, This represents the template point after transformation using the optimal geometric transformation parameters.

[0096] This application effectively overcomes the local optima problem that may exist in the coarse search stage through a refined matching strategy. By using a bipartite graph minimum weight matching algorithm to search in the parameter space, it can accurately find the optimal geometric transformation parameters and the final template point set, thereby ensuring that the satellite formation can present the target pattern with high precision, significantly improving the accuracy and visual quality of the space display effect.

[0097] S9: Determine the adaptive illumination radius based on the nearest neighbor distance of each satellite to other satellites. This step specifically includes the following:

[0098] S911: Determine the optimal translation satellite point based on the translation vector and satellite point in the optimal geometric transformation parameters. .

[0099] S912: Based on the nearest neighbor distance of each optimal translation satellite point to other optimal translation satellite points, select a preset number of nearest neighbor distances to obtain the median distance.

[0100] Calculate the minimum distance from each satellite to all final template points. .

[0101] To accommodate different satellite formation scales and local satellite densities, the nearest neighbor distance from each satellite to other satellites is calculated. ,in, This represents the k-th optimal translation satellite point.

[0102] Take the median distance of the nearest neighbors of several satellites. .

[0103] S913: The adaptive lighting radius is obtained based on the median distance and the preset distance coefficient.

[0104] Determine the adaptive lighting radius based on the median. ,in, This is the preset radius ratio coefficient.

[0105] This application can dynamically determine the adaptive illumination radius based on the actual distribution density of the satellite formation and the relative positions after geometric transformation. This avoids the poor display effect that may result from using a fixed illumination radius, such as blurring of the pattern due to an excessively large radius in densely populated satellite areas, or pattern breakage due to an excessively small radius in sparsely populated satellite areas. By introducing the median distance and a preset distance coefficient, the illumination radius can intelligently adapt to the local characteristics of the satellite formation, thereby ensuring the clarity and integrity of the pattern display under different satellite distribution conditions, significantly improving the adaptability and robustness of the space display effect.

[0106] Some existing solutions use a fixed distance threshold to determine whether a satellite should be lit, that is, the satellite is lit when the distance between the satellite and the pattern template point is less than a preset value. This threshold usually relies on human experience. When the overall scale of the satellite formation, the satellite spacing or local density changes, the fixed threshold is difficult to apply to different configurations: if the threshold is too small, it will result in insufficient satellite lighting and broken lines; if the threshold is too large, it will result in pattern edge expansion, adhesion of adjacent structures, and accidental lighting of satellites in non-target areas.

[0107] S10: Determine the final set of illuminated satellites based on the minimum distance of each satellite from the final template point in the final template point set and the adaptive illumination radius.

[0108] Specifically, when the minimum distance between each satellite and the final template point in the final template point set is less than or equal to the adaptive lighting radius, the satellite is determined to be lit; otherwise, the satellite is determined not to be lit. That is, the... The illumination status of a satellite is defined as follows: in, Indicates lighting up the first One satellite, Indicates the extinguishing of the first One satellite.

[0109] The optimal mapping relationship obtained by the bipartite graph minimum weight matching algorithm in the fine search phase is only used to lock the best spatial alignment attitude parameters (i.e., the optimal geometric transformation parameters) between the overall pattern and the satellite formation. And finally, the satellite array was illuminated. This breaks the one-to-one exclusive constraint, and its mathematical expression is defined as: ,in, This indicates the coordinates of the illuminated satellite.

[0110] Through the above decoupling design, the lighting decision is entirely based on the reverse nearest neighbor determination distance from each satellite to the final transformed template point set. This allows multiple spatially adjacent satellites to be mapped simultaneously to the same final template point or the vicinity of the same local continuous contour, thereby significantly improving the visual continuity and topological integrity of continuous lines, slender curves, and large filled areas under discrete irregular configuration constraints.

[0111] The direction of a satellite formation relative to the ground observer's line of sight may change at different display times. Even if the satellites form a correct pattern in their own coordinate system, the ground observer may still see a rotated, stretched, compressed, tilted, or mirrored pattern after projection along the observation direction. Especially when the observer is not near the normal direction of the satellite formation, the projection relationship between the formation display plane and the observation plane introduces significant scaling distortion. Without considering this projection relationship, the matching result achieved in the satellite formation coordinate system may not necessarily present the correct visual effect in the ground observation direction.

[0112] S11: Periodically acquire the real-time position of the satellite formation and the line-of-sight parameters of ground observers.

[0113] S12: If the dynamic drift deviation of the ground observer's line of sight parameters exceeds the preset drift threshold, reanalyze the two-dimensional projection matrix and re-perform the coarse search, fine search, and spot matching.

[0114] In dynamic display scenarios, the system periodically obtains the current time. The real-time position of the satellite formation and the line-of-sight parameters of the ground observer. Let the reference time for the last global full-scale matching be... The observer's real-time azimuth and elevation angles relative to the satellite formation at the current moment are respectively and The real-time azimuth and elevation angles of the observer relative to the satellite formation at the reference time are respectively... and The dynamic drift deviation of the viewpoint is defined as: in, and These represent the dynamic drift deviation of the azimuth angle and the dynamic drift deviation of the elevation angle, respectively, when the triggering condition is met. (in When the preset angle drift threshold is reached, or when the geometric distortion of the satellite formation configuration or the amount of display quality degradation exceeds the preset criteria, the system triggers a full rematch, recalculates the two-dimensional projection matrix at the current moment, and performs a global hierarchical grid search.

[0115] S13: If the dynamic drift deviation of the ground observer's line of sight parameters is less than or equal to the preset drift threshold, maintain the fine search results, update the adaptive illumination radius, and redetermine the final set of illuminated satellites.

[0116] During the incremental period when a full rematch was not triggered (i.e.) The system enters the incremental matching process and directly inherits the reference time. The optimal spatial alignment translation vector is obtained. With scaling And fix the transformation angle. At this time, the optimal translation satellite point at time t in the aligned coordinate system for each satellite is represented as: in, Let represent the position coordinates of the j-th satellite. Based on the dynamically updated optimal translation satellite point coordinates, the system updates the nearest neighbor distances of each satellite to other satellites in real time at time t. And by taking the median, the adaptive lighting radius at time t is dynamically adjusted: Finally, based on the real-time minimum distance from the satellite to the final template point at time t... Refresh the illumination status of each satellite at time t: This mechanism avoids highly complex repetitive global grid searches during long-term dynamic display by decoupling and inheriting parameters, thus significantly reducing the computational overhead of spaceborne or ground-based systems while ensuring visual fidelity for ground observation.

[0117] This application effectively addresses the dynamic changes in line-of-sight parameters for ground observers, resolving the issue of potential distortion or inaccuracy in satellite formation display patterns under dynamic observation environments. When line-of-sight parameters drift significantly, the system can promptly perform comprehensive re-matching and re-illumination to ensure the accuracy of the displayed pattern. Conversely, when the drift is small, by maintaining the refined search results and updating only the adaptive illumination radius, the system significantly reduces the computational burden while maintaining display quality, thereby improving real-time response and resource utilization efficiency. This makes the satellite formation space display method more robust and adaptable in practical applications, continuously providing ground observers with stable, accurate, and high-quality space display effects.

[0118] like Figure 2 As shown in the figure, an embodiment of this application provides a satellite formation space display system based on adaptive template matching, comprising: The information acquisition module 10 is used to acquire the pattern to be displayed and the position information of each satellite in the satellite formation on the display plane.

[0119] The pattern preprocessing module 20 is used to preprocess the pattern to be displayed to obtain a binary image.

[0120] The pattern analysis module 30 is used to extract the foreground point set, skeleton point set, and contour point set from the binary image respectively, and determine the distribution ratio, which includes the skeleton ratio, contour ratio, and skeleton-contour ratio; it is also used to identify the pattern type based on the distribution ratio, which includes line pattern, contour pattern, and filled pattern.

[0121] The template point processing module 40 is used to extract points from the corresponding point set according to the pattern type and generate a template point set; it is also used to obtain the transformed template points according to the template points in the template point set, the rotation angle, the scaling ratio, and the translation vector.

[0122] The template point coarse search module 50 is used to perform a coarse search and screening of candidate transformation parameters in the parameter space consisting of the rotation angle range, scaling ratio range, and translation vector range, based on the distance of each transformed template point to the nearest satellite point and the coarse search cost, and select a preset number of candidate transformation parameters.

[0123] The template point fine search module 60 is used to perform fine search and screening on the candidate transformation parameters after coarse screening based on the distance cost and total matching cost between the transformed template points and satellite points, so as to obtain the final template point set and the optimal geometric transformation parameters.

[0124] The satellite illumination analysis module 70 is used to determine the adaptive illumination radius based on the nearest neighbor distance of each satellite to other satellites; it is also used to determine the final set of illuminated satellites based on the minimum distance of each satellite from the final template point in the final template point set and the adaptive illumination radius.

[0125] By combining the pattern analysis module and the template point processing module in a collaborative manner, the system selects the point set that best represents the structure of patterns with different geometric features, avoiding the problem of insufficient feature capture caused by the indiscriminate application of all patterns in traditional methods. At the same time, by introducing a two-stage screening mechanism of template point coarse search module and template point fine search module, the system efficiently finds the optimal transformation parameters in a broad geometric transformation parameter space, significantly improving matching efficiency and accuracy. In addition, the satellite lighting analysis module dynamically determines the adaptive lighting radius based on the nearest neighbor distance between satellites, enabling the lighting strategy to adapt to the real-time density of satellite formations and effectively ensuring the continuity and uniformity of the pattern. Because the pattern analysis module can accurately identify line patterns, outline patterns, or filled patterns based on distribution ratios, and correspond them to skeleton point sets, outline point sets, or foreground point sets respectively, it avoids the defect of multiple pattern point sets mapping to the same satellite in simple nearest neighbor mapping. The template point coarse search module quickly eliminates unreasonable transformation parameters through coarse search screening, while the template point fine search module establishes a one-to-one correspondence in the fine search stage using a bipartite graph minimum weight matching algorithm, thereby ensuring the rational allocation of satellite resources. The satellite illumination analysis module dynamically adjusts the illumination range according to the actual density of the satellite formation through an adaptive illumination radius mechanism, ensuring the pattern continuity in sparse areas while avoiding excessive concentration of bright spots in dense areas. Through the above technical solutions, this application achieves high-quality space pattern display under the condition that the satellite position is constrained by the orbit, effectively overcoming technical defects such as excessive concentration of bright spots, uneven line thickness, and local breaks, and significantly improving the practicality and visual effect of satellite formation space display.

[0126] Experimental tests were conducted using the above method, taking a three-layer hexagonal formation of 37 satellites as an example. The formation includes one central satellite, six inner-layer satellites, twelve middle-layer satellites, and eighteen outer-layer satellites. A space display system was constructed based on a regular hexagonal lattice satellite array, consisting of multiple actively emitting satellites in low Earth orbit. Each satellite, as a single display unit of the space display system, carries a light-emitting device, which can be an LED lamp payload, enabling low-power, high-brightness illumination. The brightness and color of the light-emitting device are controllable. To meet the needs of ground-based naked-eye observation, the brightness of the light-emitting device must be less than magnitude 6; the lower the magnitude, the brighter the celestial body. The satellite carries an LED lamp array, which can be observed from the ground when lit. This technology has been implemented and verified on the Ladybeetle-I satellite. The Ladybeetle-I satellite operates at an altitude of 547 km, and its light-emitting payload consists of an LED array and a lens combination. It was launched into orbit in December 2018 and completed flashing tests in orbit, with its light-emitting payload flashing according to Morse code rules. Ground-based testing showed that the Ladybeetle-I beacon light provides at least [illumination value] within a divergence angle range of ±3°. Illumination higher than that of a zero magnitude star ( The illuminance of the beacon light, even in its scattered areas, is easily visible to the naked eye. Therefore, laboratory measurements show that when the Ladybeetle-I satellite is in orbit, the beacon light can be directly observed with the naked eye, and its flight path is visible on clear nights in most Chinese cities (such as Xi'an, Beijing, and Shenzhen). Furthermore, the Ladybeetle-I satellite's on-orbit test report also measured the actual illumination range and brightness of the beacon light. Below the satellite, within a 25km diameter radius centered on the satellite's vertical projection onto the Earth, its light is visible to the human eye; directly below the satellite, the beacon light's illuminance is estimated to be -0.6829 magnitude. In conclusion, the Ladybeetle-I satellite, through this example, demonstrates the technical feasibility of ground-based visible light payloads.

[0127] All satellite display units together form a configuration-self-stabilizing regular hexagonal lattice display array. The regular hexagonal lattice display array consists of one virtual master star and multiple orbiting slave stars. The slave stars orbit the virtual master star in relative orbital motion. All slave stars are positioned along the orbital-normal direction of the virtual master star. - The virtual master star is arranged in a tightly packed hexagonal lattice structure within the plane. This lattice, centered on a virtual master star, is composed of multiple nested hexagonal layers sharing a common center point. The virtual master star can exist objectively or serve solely as the virtual center point for the hexagonal lattice display array design. Several slave stars are uniformly distributed on each hexagonal ring layer, with strictly equal spacing between adjacent satellites. In the LVLH coordinate system of the virtual master star, the distribution of the hexagonal lattice satellite array is as follows: Figure 3 As shown. The mapping of a regular hexagonal lattice satellite array on the yz plane is as follows. Figure 4 As shown, the ground-based observation effect presents a honeycomb-like uniform dot matrix, with strictly equal spacing between adjacent pixels and no visual unevenness. The image includes one virtual master star and three layers of regular hexagonal lattice rings sharing a common center point. From the inside out, each layer of the ring has 6, 12, and 18 slave stars (excluding the center point) evenly distributed, respectively, forming a closely arranged, equally spaced honeycomb-like display array in space.

[0128] In the SEZ coordinate system of the ground observer, the three-dimensional spatial geometric topology of the ground station and the observed target satellite formation is as follows: Figure 5 As shown in the diagram. The origin represents the ground observer, and the three axes correspond to the south, east, and zenith directions, respectively.

[0129] To complete the orbital parameter design of the space display system, the orbital design method for the virtual primary and secondary satellites is presented step by step here. The orbital parameters of the satellite in the geocentric inertial frame are calculated using the semi-major axis. eccentricity Track inclination Right ascension of ascending node Near the arch point angle , and the near point angle To describe. In a space display system, the orbital eccentricity of the virtual primary star should be taken as... This means the virtual primary satellite is located in a circular orbit. To improve the satellite's luminous display effect, minimize light pollution in space, and extend the satellite's lifespan, the virtual primary satellite is located in a near-Earth circular orbit at an altitude of [missing information]. A range of 300km-500km is preferred, and the semi-major axis of the virtual primary star's orbit should be taken as... ,in, The radius is the Earth's radius. The orbital inclination of the virtual primary star. This will affect the range of latitudes at which the space display system is visible from Earth, and its orbital inclination. and coverage of the highest latitude Approximately satisfy Right ascension of the ascending node Near the arch point angle , and the near point angle The value only needs to be in Within the specified range.

[0130] Next, we design the configuration parameters of the relative orbital trajectory of the slave star with respect to the virtual master star. Under the influence of gravity, both the master star and the slave star revolve around the Earth in Keplerian motion. Projecting the trajectory of the slave star onto the LVLH coordinate system of the master star, we can obtain the relative orbital trajectory of the slave star with respect to the master star. The LVLH coordinate system is defined as follows: the origin c is located at the center of mass of the virtual master star. The axis points in the direction of the position vector r of the virtual master star. The axis points in the direction of the virtual primary star's velocity. The axis points in the direction of the normal vector of the virtual primary star's orbit, forming a right-handed coordinate system, such as... Figure 6 As shown. When the primary star is directly overhead for a ground-based observer, the direction of visual observation is opposite to that of the LVLH. Since the axes are aligned, the images observed from the ground are essentially derived from the relative motion trajectories of the stars with respect to the primary star. Projection onto a plane.

[0131] Let the configuration parameters of the relative orbital trajectory of the secondary star with respect to the virtual primary star be: A geometrical diagram of the configuration parameters in the LVLH coordinate system, as shown below. Figure 7 As shown. For relative flight trajectory in The semi-major axis of the plane projection ellipse is located at On the axis, Let be the semi-minor axis of the projected ellipse, located at . On the axis, the coordinates of the center point relative to the orbital trajectory are: , for Amplitude in direction, and They are respectively from the stars plane and Phase in the direction. The plane normal vector relative to the flight trajectory is... ,in In conclusion, and This determines the size of the relative orbital trajectory. and The relative position of the center point of the flight trajectory is determined. and The direction of the relative orbital trajectory is determined. and This determines the phase of the star in its relative orbital trajectory.

[0132] Theoretically, configuration parameters can be set. The values ​​of the parameters are used to obtain a space display system with a regular hexagonal lattice array and specific geometric characteristics. The values ​​of the configuration parameters should follow the following principles: (1) They must satisfy the following conditions. To ensure that the relative flight trajectory does not diverge. (2) and Positive real numbers should be taken, and and The maximum value should not exceed 10km to ensure the accuracy of the relative motion model. (3) Real numbers should be taken, and The absolute value should not exceed 10km to ensure the accuracy of the relative motion model. (4) ,when and At that time, the relative trajectory is The planar projection is a perfect circle. In the regular hexagonal lattice array of this invention, take... and This ensures that the relative trajectory of each slave star is circular and that the overall lattice rotates with the rigid body of the master star. (5) For a regular hexagonal lattice array, the number of slave stars on the same layer (ring) The angles are not evenly spaced, but rather determined by the satellite's desired position in the lattice. The only certainty: ,in, The initial latitude argument of the main star, It is the arctangent function in the fourth quadrant. The perigee argument of the virtual primary star. This is the approximate angle of the hypothetical primary star. The angles of each secondary star... and All are equal to their distance from the center point And to ensure the rigid body rotates, take (Right now (6) The value of is related to the apparent diameter observed from the ground. The relevant condition should satisfy the following formula: Finally, the orbital parameters of the secondary star are determined. This is based on the orbital parameters of the virtual primary star. and from star configuration parameters The difference in orbital elements between the secondary star and the virtual primary star can be calculated using the following formula. : in, This represents the correlation difference between the semi-major axes. This indicates the correlation difference in orbital eccentricity. This indicates the correlation difference in orbital inclination angle. This represents the correlation difference between the ascending nodes and the right ascension. This represents the correlation difference between the near and near angles. This indicates the correlation difference between the near-arch point angles. Represents the arctangent function with quadrants.

[0133] Based on this, the orbital parameters of each satellite are: Completed the design of a satellite array for a space display system.

[0134] Using a virtual primary star as the reference center, the remaining secondary stars are arranged in a regular hexagonal lattice structure along the orbital-normal plane of the primary star. The lattice consists of multiple nested layers of regular hexagons sharing a common central point. layer( )Include Each slave star has a set of 364 slave stars, and the distance between adjacent slave stars is strictly equal. All slave stars satisfy the following condition: , And phase coupling condition This ensures that the lattice rotates with the rigid body of the host star. The resulting satellite array is projected onto the LVLH coordinate system. The plane presents a honeycomb-like regular hexagonal dot matrix with a constant spacing between adjacent dots, and there is no visual unevenness in density.

[0135] The orbital parameters of the primary star are shown in Table 1 below. The Earth's radius is 6378.13 km, and the orbital altitude H is 500 km.

[0136] Table 1. Orbital parameters of the primary satellite in the hexagonal lattice satellite array. A total of three hexagonal lattice arrays are arranged, with one satellite at the center, six satellites evenly distributed in the first ring (one distance from the center), twelve satellites evenly distributed in the second ring (twelve distances from the center), and eighteen satellites evenly distributed in the third ring (three distances from the center). To ensure a common center point, [the following is taken]. To ensure a fixed distance between adjacent satellites, the distance between satellites within and between each ring is equal; to ensure coplanarity, all satellites move in the orbit-normal plane, and the distance from the satellite to the center of each layer is... The ring number increases linearly; to ensure that the ground observations are in the shape of a regular hexagonal lattice, a phase coupling condition is adopted. (Right now This ensures that the configuration maintains rigid body rotation from the perspective of the primary star. The values ​​of the star configuration parameters are shown in Table 2 below.

[0137] Table 2 Configuration parameters of regular hexagonal lattice satellite arrays The initial latitude argument of the primary star; For each satellite in The lattice coordinates (in meters) in the plane are generated by the axial coordinate method; the distance between adjacent satellites is d = 1 km.

[0138] The orbital parameters of the satellite, obtained from the configuration parameters, are shown in Table 3 below. This represents the value calculated from the orbital eccentricity of the star. Very small, approximately 0; Indicates the semi-major axis of the star's orbit. Indicates the inclination of a star's orbit. Indicates the right ascension from the ascending node of the star. Indicates the angle from the near-circumference point of the star. This indicates the angle from the star's level anterior point.

[0139] Table 3. Slave orbital parameters of the hexagonal lattice satellite array In the LVLH coordinate system of the virtual master star, the hexagonal lattice satellite array is distributed as follows: Figure 3 As shown. The mapping of a regular hexagonal lattice satellite array on the yz plane is as follows. Figure 4 As shown, the ground observation effect presents a honeycomb-shaped uniform dot matrix, with strictly equal spacing between adjacent pixels, and no visual unevenness in density.

[0140] The generated satellite array orbital parameters are input into satellite simulation software, and the resulting spatial configuration changes over time, as shown below. Figure 8 As shown, the designed hexagonal lattice display array always rotates around the virtual host star, maintaining a constant distance between adjacent satellites within the lattice. The overall arrangement is regular and orderly, unaffected by orbital motion or perturbations. By rationally planning the on / off state and color of the LED lights on each satellite, relatively complex text, patterns, and video information can be displayed on the lattice points.

[0141] Will Figure 9 The letter images shown are input into spatial dynamic simulation software for quantitative visual verification, yielding the actual line-of-sight (LOS) projection effects at different observation times, as shown below. Figure 10 and Figure 11 As shown.

[0142] The results show that, Figure 10 As shown, when the real-time azimuth and elevation angles of the formation center relative to the ground station are (-65.2°, 54.8°), although the low elevation angle observation causes obvious axial shearing and three-dimensional fitting distortion in the spatial array projection, through the perspective inverse projection compensation in this embodiment of the invention, the illuminated luminous satellite array presents a target character pattern with high topological fidelity and continuous outline (taking the uppercase letter 'B' as an example) from the perspective of a ground observer.

[0143] As the satellite formation moves at high speed along its orbit, such as Figure 11 As shown, when the relative azimuth and elevation angles dynamically drift to (-226.9°, 68.5°), the projected attitude of the space constellation in the line-of-sight plane undergoes significant dynamic rotation and scaling. At this point, the fast path adaptive control mechanism proposed in this invention is triggered, dynamically adjusting and switching the list of individual satellites performing the lighting task. During this highly dynamic transformation, the final geometric contour of the target presented in the line-of-sight plane by the ground observer does not undergo any morphological drift or projection distortion, maintaining a highly stable, upright, and faithful visual presentation. This fully verifies the spatiotemporal robustness and adaptive decoupling compensation capability of this invention in handling high-dynamic, large-angle distortion space display scenarios.

[0144] To further verify the broad adaptability and versatility of this invention for diverse display content, the number and styles of input source images are expanded. For example... Figure 12 A set of standard numeric characters and graphic symbols with different topological shapes (such as patterns of numeric characters 2, 3, 4 and 5) are input into the system of this application, and the dynamic lighting control instruction set generated therefrom is synchronously injected into the space dynamic simulation software for multi-scene quantitative visual verification.

[0145] Under the constraints of high-speed satellite formation orbiting along its orbit and long-term, highly dynamic drift of the ground observation perspective (including azimuth, elevation, and line-of-sight shear deformation), the full-process reconstructed visual projection effects within the actual line-of-sight (LOS) plane are as follows: Figure 13 As shown.

[0146] Full-scale quantitative verification results demonstrate that the proposed matching and lighting decoupling control architecture exhibits extremely high reconstruction quality for various types of digital and graphic identifiers. Under different dynamic observation times and complex star array rotation geometry, each set of simulation experiments can present a high-fidelity visual shape with smooth boundaries, no perspective shrinkage, and no shearing distortion in the ground-based line-of-sight projection plane. This fully confirms that the proposed scheme possesses excellent engineering universality, fully automatic feature perception capability, and spatiotemporal robustness in graphic space display missions.

[0147] The foregoing Figure 12 and Figure 13 The single-character or conventional geometric pattern shown already achieves good baseline display results in a three-layer hexagonal lattice formation composed of 37 satellites. To further test the fine topological reconstruction and detail resolution capabilities of this application for highly complex multi-connected domain combination patterns with high-frequency geometric details, intersecting line segments, and multiple closed hollow structures under different satellite formation sizes and spatial pixel densities, this embodiment introduces a larger-scale formation configuration for comparative generalization verification.

[0148] The experiment employs a large-scale expansion using a four-layer hexagonal lattice formation of 61 satellites, which is distributed in space. Specifically, it includes one virtual central master star, six first-layer slave stars, twelve second-layer slave stars, eighteen third-layer slave stars, and twenty-four fourth-layer slave stars.

[0149] Will Figure 14 The complex graphic pattern (taking the interlaced pattern as an example), featuring interlocking double rings, typical multi-connected domain topology, and multiple acute-angle intersections, is input into the system. Because the pattern's lines overlap and contain multiple independent hollow connected domains, the algorithm automatically initiates a connected domain-aware sampling strategy, precisely allocating sampling points according to the area ratio of each effective region, generating a high-density target template point set, and performing hierarchical geometric matching. The calculated dynamic lighting control commands are run at different formation sizes, and multi-dimensional quantitative visual reconstruction is performed using spatial dynamic simulation software. The final actual perspective projection effects in the ground observer's line-of-sight (LOS) plane are shown below. Figure 15 and Figure 16 As shown. Among them, Figure 15 The display effect of 37 satellites in a three-layer formation. Figure 16 This is a display effect of 61 satellites arranged in a four-layer formation.

[0150] The full quantitative comparison results show that, under the constraints of this highly complex multi-connected pattern, due to... Figure 15 The corresponding three-layer satellite formation has a small number of discrete pixels and insufficient spatial sampling rate, which leads to severe geometric aliasing at the sharp overlap of the double ring intersection during adaptive judgment. The contour edges are locally filled and stuck, resulting in poor image recognition during ground observation.

[0151] In stark contrast, such as Figure 16 As shown, when using a four-layer formation scheme with 61 satellites, the spatial discrete pixel density is significantly improved. The algorithm successfully achieves fine spatial resolution at the acute angles of the intersecting double-C graphics, perfectly stripping and depicting the geometric boundaries of each independent hollow connected domain. The lines are smooth and the contours are completely closed, without any morphological drift or visual breaks. This strongly verifies that the proposed solution is not only effective for simple characters, but also possesses excellent scale-adaptive generalization ability, dynamic graphic robustness, and high-fidelity lossless reconstruction capability when facing highly complex, high-spectral-detail multi-connected domain commercial trademarks and logos.

[0152] In summary, compared with existing technologies, it has the following beneficial effects: 1. This application generates templates by using skeleton points, contour points, and foreground points for line-type, outline-type, and filled-type patterns, respectively. It can also combine connected component analysis to allocate template points to multiple independent regions, so that the template point set can more accurately reflect the key visual structure of different patterns and improve the pattern expression capability with a limited number of satellites.

[0153] 2. This application uses the farthest point sampling method to generate discrete template points, so that the template points are relatively evenly distributed within the pattern range, reducing problems such as excessively dense local point sets, omission of sharp corners, missing fine lines and loss of small areas caused by random sampling.

[0154] 3. This application enables the target pattern to automatically adapt to different numbers of satellites, different satellite formation scales, and different satellite spatial configurations by searching for rotation, scaling, and translation parameters, without the need for repeated manual parameter adjustments for each pattern and configuration.

[0155] 4. This application employs a hierarchical matching mechanism combining coarse search and fine search. In the coarse search stage, candidate parameters that are not matched globally or are overly clustered locally are quickly eliminated through nearest neighbor distance and duplicate matching penalties; in the fine search stage, the minimum weight matching of bipartite graphs is used to further determine the optimal geometric transformation parameters, thus balancing computational efficiency and matching accuracy.

[0156] 5. This application decouples the solution of geometric matching parameters from the final satellite lighting decision. The bipartite graph minimum weight matching is only used to determine the optimal spatial alignment of the overall pattern, and the final satellite lighting state is determined by the reverse nearest neighbor method. This method avoids the problems of thinning continuous lines, discontinuous bright spots, and discontinuous contours caused by directly using one-to-one matching results, and allows multiple adjacent satellites to jointly express the same line or contour area, which can improve the visual continuity and integrity of the pattern.

[0157] 6. This application adaptively determines the illumination radius based on the median of the local nearest neighbor distance of the satellites, enabling the illumination threshold to be adjusted according to changes in the overall scale of the satellite formation, satellite spacing, and local density. Compared to a fixed distance threshold, this reduces the risk of pattern breakage due to an excessively small threshold or pattern expansion, structural adhesion, and accidental illumination due to an excessively large threshold.

[0158] 7. This application can compensate for the template points based on the projection relationship between the satellite formation display plane and the ground observation line of sight plane, thereby reducing the pattern rotation, stretching, compression, tilting or mirror distortion caused by changes in the observation angle, so that ground observers can obtain a display effect that is more in line with expectations.

[0159] 8. This application is applicable to circular, ring, hexagonal, elliptical, rectangular, grid-shaped, layered nested, and other irregular satellite formation configurations. It is also applicable to different light emission control methods such as binary illumination, multi-level brightness, color control, flashing control, and time-division multiplexing, and has strong versatility and scalability.

[0160] An electronic device provided in this application includes a memory and a processor; the memory is used to store a computer program; the processor is used to implement the satellite formation space display method based on adaptive template matching as described above when the computer program is executed.

[0161] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the satellite formation space display method based on adaptive template matching as described above.

[0162] In this embodiment, the beneficial effects of the electronic device and the computer-readable storage medium are similar to those of the satellite formation space display method based on adaptive template matching described above, and will not be repeated here.

[0163] The present invention describes electronic devices that can serve as servers or clients of this application, which are examples of hardware devices that can be applied to various aspects of this application. Electronic devices are intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices can also represent various forms of mobile devices, such as personal digital assistant devices, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the application described and / or claimed herein.

[0164] Electronic devices include a computing unit that can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM can also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0165] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc. In this application, the separately described modules may or may not be physically separate. Some or all of the modules can be selected to achieve the purpose of the embodiments of this application according to actual needs. Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0166] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0167] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A satellite formation space display method based on adaptive template matching, characterized in that, include: Obtain the pattern to be displayed and the position information of each satellite in the satellite formation on the display plane; The pattern to be displayed is preprocessed to obtain a binary image; Extract the foreground point set, skeleton point set, and contour point set from the binary image respectively, and determine the distribution ratio, which includes the skeleton ratio, contour ratio, and skeleton-contour ratio. Pattern types are identified based on distribution ratios. Pattern types include line patterns, outline patterns, and filled patterns. Based on the pattern type, extract points from the corresponding point set to generate a template point set; Based on the template points in the template point set, the rotation angle, the scaling ratio, and the translation vector, the transformed template points are obtained; Based on the distance from each transformed template point to the nearest satellite point and the coarse search cost, a coarse search is performed on the candidate transformation parameters in the parameter space consisting of the rotation angle range, scaling ratio range, and translation vector range, and a preset number of candidate transformation parameters are selected. Based on the distance cost between the transformed template points and satellite points and the total matching cost, a fine search and screening is performed on the candidate transformation parameters after coarse screening to obtain the final template point set and the optimal geometric transformation parameters. The adaptive illumination radius is determined based on the nearest neighbor distance between each satellite and other satellites; The final set of illuminated satellites is determined based on the minimum distance of each satellite from the final template point in the final template point set and the adaptive illumination radius.

2. The satellite formation space display method based on adaptive template matching as described in claim 1, characterized in that, The line-type patterns correspond to the skeleton point set, the outline-type patterns correspond to the outline point set, and the filled patterns correspond to the foreground point set. The step of extracting points from the corresponding point set according to the pattern type and generating a template point set includes: Select the point closest to the centroid of the corresponding point set as the initial template point; Then, each time, the point with the largest minimum distance to the selected template point set is selected from the unselected points in the corresponding point set, until the preset number of template points is reached, and the template point set is obtained.

3. The satellite formation space display method based on adaptive template matching as described in claim 1, characterized in that, Before obtaining the transformed template points based on the template points in the template point set, rotation angle, scaling ratio, and translation vector, the process also includes: The template point set is centered to obtain the centroid of the template point; Based on the template point and the template point centroid, the centered template point is obtained; Based on the centered template points and the two-dimensional projection matrix, the compensation template points are obtained; When view compensation is not enabled, the centralized template point is used as the template point for matching; When view compensation is enabled, the compensation template point is used as the template point for matching.

4. The satellite formation space display method based on adaptive template matching as described in claim 3, characterized in that, The transformed template points are: ； ； in, These are the transformed template points. For scaling ratio, The rotation angle; It is a translation vector. and These are the x and y coordinates of the translation vector, respectively. Template points for matching; It is a rotation matrix.

5. The satellite formation space display method based on adaptive template matching as described in claim 1, characterized in that, The process involves coarsely searching and filtering candidate transformation parameters within a parameter space comprised of the rotation angle range, scaling ratio range, and translation vector range, based on the distance from each transformed template point to the nearest satellite point and the coarse search cost. A preset number of candidate transformation parameters are selected, including: Determine the centroid of the satellite point set based on the satellite's position information; The scaling range is obtained based on the maximum radius of the satellite point set relative to the centroid of the satellite point set and the maximum radius of the template point participating in the matching relative to the origin. The satellite point set is translated to a coordinate system centered on the translation vector to obtain the translated satellite point set; Analyze the distance between the transformed template point and the satellite points in the translated satellite point set, and match the satellite point corresponding to the closest distance with the transformed template point; The duplicate matching penalty term is obtained based on the number of times each satellite is matched by its nearest neighbor and the duplicate matching penalty function; The coarse search cost is obtained based on the nearest distance, the duplicate matching penalty term, and the coarse search cost function; Based on the coarse search cost, a preset number of candidate transformation parameters are selected from the parameter space consisting of the rotation angle range, scaling ratio range, and translation vector range.

6. The satellite formation space display method based on adaptive template matching as described in claim 5, characterized in that, The closest distance between the transformed template point and the satellite points in the translated satellite point set is: The duplicate matching penalty term is: The cost of the coarse search is: in, Indicates the template point after transformation. Indicates the translation of the satellite point. This indicates the number of times each satellite is matched with its nearest neighbor. Indicates the number of satellites participating in the display. This indicates the preset penalty coefficient. Indicates the number of template points. Indicates the range of vectors.

7. The satellite formation space display method based on adaptive template matching as described in claim 5, characterized in that, The step of performing a fine search and screening on the candidate transformation parameters after coarse screening, based on the distance cost and total matching cost between the transformed template points and satellite points, to obtain the final template point set and optimal geometric transformation parameters includes: The distance cost is obtained based on the transformed template points and satellite points; The minimum of the number of satellites and the number of template points displayed will be used as the number of template points for fine-tuning. If the number of transformed template points exceeds the number of refined search template points, then select the number of transformed template points that are equal to the number of refined search template points from the transformed template points as the refined search template point set; Using the bipartite graph minimum weight matching algorithm, a one-to-one matching relationship is established between the fine search template point set and the satellite point set. Among the candidate transformation parameters after coarse screening, the rotation angle, scaling ratio and translation vector that minimize the total matching cost are selected as the optimal geometric transformation parameters, and the final template point set is determined. The total matching cost is the sum of the distance costs between all matched fine search template points and satellite points.

8. The satellite formation space display method based on adaptive template matching as described in claim 1, characterized in that, The process of determining the adaptive illumination radius based on the nearest neighbor distance from each satellite to other satellites includes: Determine the optimal translation satellite point based on the translation vector and satellite point in the optimal geometric transformation parameters; Based on the nearest neighbor distance of each optimal translation satellite point to other optimal translation satellite points, a preset number of nearest neighbor distances are selected to obtain the median distance; The adaptive lighting radius is obtained based on the median distance and the preset distance coefficient.

9. The satellite formation space display method based on adaptive template matching as described in claim 1, characterized in that, Also includes: Periodically acquire the real-time position of the satellite formation and the line-of-sight parameters of ground observers; If the dynamic drift deviation of the ground observer's line of sight parameters exceeds the preset drift threshold, the two-dimensional projection matrix is ​​re-analyzed, and the coarse search, fine search, and spot matching are performed again. If the dynamic drift deviation of the ground observer's line-of-sight parameters is less than or equal to the preset drift threshold, maintain the fine search results, update the adaptive illumination radius, and redetermine the final set of illuminated satellites.

10. A satellite formation space display system based on adaptive template matching, characterized in that, include: The information acquisition module is used to acquire the pattern to be displayed and the position information of each satellite in the satellite formation on the display plane; The pattern preprocessing module is used to preprocess the pattern to be displayed to obtain a binary image; The pattern analysis module is used to extract the foreground point set, skeleton point set, and contour point set from the binary image, and determine the distribution ratio, which includes the skeleton ratio, contour ratio, and skeleton-contour ratio; it is also used to identify the pattern type based on the distribution ratio, which includes line patterns, contour patterns, and filled patterns. The template point processing module is used to extract points from the corresponding point set according to the pattern type and generate a template point set; It is also used to obtain the transformed template points based on the template points in the template point set, the rotation angle, the scaling ratio, and the translation vector; The template point coarse search module is used to perform a coarse search and screening of candidate transformation parameters in the parameter space consisting of the rotation angle range, scaling ratio range, and translation vector range, based on the distance of each transformed template point to the nearest satellite point and the coarse search cost, and select a preset number of candidate transformation parameters. The template point fine search module is used to perform fine search and screening on the candidate transformation parameters after coarse screening based on the distance cost and total matching cost between the transformed template points and satellite points, so as to obtain the final template point set and the optimal geometric transformation parameters. The satellite illumination analysis module is used to determine the adaptive illumination radius based on the nearest neighbor distance of each satellite to other satellites; It is also used to determine the final set of illuminated satellites based on the minimum distance of each satellite from the final template point in the final template point set and the adaptive illumination radius.

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