A star map matching method based on star pair statistical features

Abstract

This invention discloses a star map matching method based on the statistical features of star pairs, comprising the following steps: constructing star pairs; searching for similar stars from an image star pair list and a star catalog star pair list; determining the rotation angles of the image and the star catalog; initially determining matching parameters; and precisely determining the matching parameters. This invention's method can achieve a relatively high correct matching rate even with star position errors, false star images, missing star images, and high-density star fields.

Description

Technical Field

[0001] This invention belongs to the field of astronomical observation technology and astronomical positioning of space targets. Specifically, it relates to a star map matching method based on the statistical characteristics of star pairs. Background Technology

[0002] Star image matching involves matching stars in astronomical observation images with stars in a reference star catalog to establish the correspondence between the measurement coordinate system of the measured image and the celestial coordinate system of the star catalog. Star image matching technology is fundamental to modern astronomical observation, astronomical positioning of space targets, and attitude control of star sensor satellites in aerospace engineering. It is a necessary preliminary step in determining the model of astrometric film. With the widespread application of EMCCD and SCMOS cameras in astronomical observations, the demand for fast and robust star image matching algorithms is increasingly prominent.

[0003] Common methods for star map matching include triangle or polygon matching based on corner features, and pattern recognition based on primary and companion star features, such as the grid algorithm. Triangle matching based on corner features has high computational complexity and suffers from redundant matching and long matching times. Compared to classic triangle matching methods, pattern matching methods like the grid algorithm suffer from the presence of missing or pseudo-stars, leading to incorrect selection of primary and companion star patterns and affecting matching accuracy and efficiency.

[0004] In astronomical observation, errors in star positions caused by field distortion, centering, etc., mismatch between the magnitudes of the stars detected by the star catalog and astronomical images, or noise such as cosmic rays can all lead to a large number of missing stars or false stars during the star map matching process. Inconsistencies in the filters and star catalogs used in astronomical observation, as well as magnitude errors caused by various noises, can all reduce the accuracy of star map matching.

[0005] Therefore, it is necessary to provide a new star map matching method based on the statistical features of star pairs. Summary of the Invention

[0006] In view of this, the present invention addresses the problems of redundant matching, long time consumption, sensitivity to position and magnitude errors, and low matching rate caused by sensitivity to missing or false stars in traditional and improved star map recognition methods based on triangles. It provides a star map matching method based on the statistical features of star pairs, which can be used to match small field-of-view astronomical CCD images and star catalogs.

[0007] To address the aforementioned technical problems, this invention discloses a star map matching method based on star pair statistical features, comprising the following steps:

[0008] Step 1: Construct star pairs;

[0009] Step 2: Search for similar stars from the image star pair list and the star catalog star pair list;

[0010] Step 3: Determine the rotation angle of the image and star catalog;

[0011] Step 4: Initially determine the matching parameters;

[0012] Step 5: Determine the matching parameters precisely.

[0013] Optionally, constructing the star pair in step 1 specifically involves:

[0014] Step 1.1: Flatten and bias the images captured by the astronomical camera;

[0015] Step 1.2: Perform star detection and centering operations on the flattened and bias-corrected images, using Gaussian fitting or the moment method to achieve a centering accuracy of 0.1 pixels or higher. Sort the stars by grayscale value from largest to smallest, and select the m brightest stars to construct list I from brightest to darkest. The list records the position and grayscale value (x, y, H) of the stars on the film. Sort the stars by magnitude from smallest to largest, and select the n brightest stars from the star list to construct list R, recording their positions and magnitude information (α, δ, M). Transform the position information of the selected stars from spherical coordinates to tangent plane coordinates. The transformation method is shown in the following formula:

[0016]

[0017]

[0018] Where α and δ are the right ascension and declination of the star, respectively; α0 and δ0 are the coordinates of the center of the tangent plane, and ξ and η are the ideal coordinates of the tangent plane of the star, respectively; pairing is performed in the image list and the star catalog list using the method of permutation and combination. The image list can construct m(m-1) / 2 star pairs, and the star catalog list can construct n(n-1) / 2 star pairs.

[0019] Optionally, the search for similar stars from the image star pair list and the star catalog star pair list in step 2 specifically involves:

[0020] Let the imaging focal length be denoted as F, and the camera's pixel size be denoted as... The distance scale relationship (ρ) between the image brightness coordinates and the ideal coordinate tangent plane coordinates is expressed as:

[0021]

[0022] The distances between star pairs in List I are represented as follows:

[0023]

[0024] Where, x i and y iFor the position measurement information of star i in the star pair constructed for the image list, x j and y j Position measurement information of star j in the star pair constructed for the image list;

[0025] The distances between star pairs in list R are represented as follows:

[0026]

[0027] Among them, (x p y p ) represents the positional information of star p in the star pair constructed in the star catalog list, (x q y q ) represents the positional information of star q in the star pair constructed from the star list;

[0028] The constraints for matching star pairs in the star pair lists constructed from images and star pair lists constructed from star catalogs are as follows:

[0029] |I ij -R pq |≤δF / F (6)

[0030]

[0031] Where δF is the focal length error of the measurement system, δM is the magnitude difference between the photometric systems of the measurement system and the star catalog system, and M p and M q The apparent magnitudes of the two stars in the star pair are H and H, respectively. i and H j Given the grayscale values ​​of two stars in the star pair in the image, candidate matching star pairs are selected according to the matching constraints mentioned above.

[0032] Optionally, determining the rotation angle of the image and star catalog in step 3 specifically involves:

[0033] For star pairs that meet the conditions, calculate their rotation angle, defined as follows: Figure 1 As shown, the bright star is labeled A, and the faint star is labeled B. Using the bright star as the center, the azimuth of the faint star relative to the bright star is calculated from north to east. The value range is 0°-360°.

[0034] Then calculate the relative rotation angle of the star pair:

[0035]

[0036] Where (xA, yA) represents the position information of bright star A, and (xB, yB) represents the position information of dark star B;

[0037] Then calculate the relative rotation angle of the star pair:

[0038] δθ=θI -θ R (9)

[0039] Where, θ I θ is the azimuth angle of the star pair in the image. R For the azimuth angle of the star pair in the star catalog, if δθ is less than 0, add 360° to the calculated relative rotation angle to ensure that the relative rotation angle is always between 0° and 360°; then divide δθ into 360 parts in 1° intervals and count the number of rotation angles appearing in each interval.

[0040] Then, the rotation angle information that meets the conditions is statistically analyzed.

[0041] |δθ-mode(round(δθ))|<1° (10)

[0042] The `round()` function is used to round down the integer part of the rotation angle, and `mode()` is used to take the mode of the rounded-down rotation angle.

[0043] The angles that meet the above conditions are averaged, and then the values ​​that are more than 3 standard deviations from the average are removed by an iterative method. After the iteration is completed, the average value is taken to obtain the relative rotation angle δθ2. This rotation angle is the approximate rotation angle.

[0044] Optionally, the preliminary determination of matching parameters in step 4 specifically involves:

[0045] The projection mapping relationship between the measuring coordinate system and the ideal tangent plane coordinate system is determined by the following four constant formula.

[0046] ξ=ρcosθx-ρsinθy+c (11)

[0047] η=ρsinθx+ρcosθy+d (12)

[0048] Where θ is the rotation angle between the two coordinate systems and ρ is the scale, substituting the candidate matching star into the above formula yields the coordinate center translations c and d; the average translations c and d are obtained using iteration and the 3-times standard deviation principle.

[0049] Optionally, the precise determination of the matching parameters in step 5 specifically involves:

[0050] Based on the initial parameters obtained in step 4 All detected constellations are transformed to the celestial coordinate system, and the nearest matching star catalog target is found; the obtained star map and star catalog matching pairs are then used to solve for the film constant model parameters using the least squares method. This step can be performed twice to reduce the risk of matching errors caused by the coarse matching error in the fourth step. At this point, the entire matching process is complete.

[0051] Compared with the prior art, the present invention can achieve the following technical effects:

[0052] Compared to traditional triangulation matching algorithms, this invention has lower time complexity. The matching algorithm of this invention can be divided into two steps: coarse matching and fine matching. This method can achieve a relatively high correct matching rate even with errors in star positions, false star patterns, missing star patterns, and high-density star fields.

[0053] Of course, any product implementing this invention does not necessarily need to achieve all of the technical effects described above at the same time. Attached Figure Description

[0054] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0055] Figure 1 This invention defines the azimuth angles of fainter and brighter stars;

[0056] Figure 2 This is a flowchart of the star map matching method based on star pair statistical features of the present invention;

[0057] Figure 3 This is a star map obtained by the present invention with the target being the open star cluster M35;

[0058] Figure 4 The present invention obtains a rough matching rotation angle by taking the mode of bin counting for the relative rotation angle;

[0059] Figure 5 This is a diagram showing the effect of the matching completed by the present invention. Detailed Implementation

[0060] The following will describe the implementation of the present invention in detail with reference to the embodiments, so as to fully understand how the present invention uses technical means to solve technical problems and achieve technical effects and to implement it accordingly.

[0061] This invention discloses a star map matching method based on the statistical features of star pairs, comprising the following steps:

[0062] Step 1, Construct star pairs:

[0063] Step 1.1: Flatten and bias the images captured by the astronomical camera;

[0064] Step 1.2: Perform star detection and centering operations on the flattened and bias-corrected image. Centering accuracy using Gaussian fitting or the moment method is generally 0.1 pixels or higher. Select m of the brightest stars in descending order of brightness (star grayscale values ​​sorted from largest to smallest) to construct list I, recording the star's position and grayscale value (x, y, H) on the film. Select n stars in the star list in ascending order of brightness (star magnitudes sorted from smallest to largest) to construct list R, recording their positions and magnitude information (α, δ, M). Transform the selected stars' position information from spherical coordinates to tangent plane coordinates. The transformation method is shown in the following formula:

[0065]

[0066]

[0067] Where α and δ are the right ascension and declination of the star, respectively; α0 and δ0 are the coordinates of the center of the tangent plane; and ξ and η are the ideal coordinates of the tangent plane of the star.

[0068] By using permutations and combinations, pairing stars in both the image list and the star list can be performed. The image list can construct m(m-1) / 2 star pairs, and the star list can construct n(n-1) / 2 star pairs.

[0069] Step 2: Search for similar stars from the image star pair list and the star catalog star pair list:

[0070] Let the imaging focal length be denoted as F, and the camera's pixel size be denoted as... The distance scale relationship (ρ) between the image brightness coordinates and the ideal coordinate tangent plane coordinates is expressed as:

[0071]

[0072] The distances between star pairs in List I are represented as follows:

[0073]

[0074] Where, x i and y i For the position measurement information of star i in the star pair constructed for the image list, x j and y j Position measurement information of star j in the star pair constructed for the image list;

[0075] The distances between star pairs in list R are represented as follows:

[0076]

[0077] Among them, (x p y p) represents the positional information of star p in the star pair constructed in the star catalog list, (x q y q ) represents the positional information of star q in the star pair constructed from the star list;

[0078] The constraints for matching star pairs in the star pair lists constructed from images and star pair lists constructed from star catalogs are as follows:

[0079] |I ij -R pq |≤δF / F (6)

[0080]

[0081] Where δF is the focal length error of the measurement system, δM is the magnitude difference between the photometric systems of the measurement system and the star catalog system, and Mp and M q The apparent magnitudes of the two stars in the star pair are H and H, respectively. i and H j Given the grayscale values ​​of two stars in the star pair in the image, candidate matching star pairs are selected according to the matching constraints mentioned above.

[0082] Step 3: Determine the rotation angle of the image and star catalog:

[0083] For star pairs that meet the conditions, calculate their rotation angle, defined as follows: Figure 1 As shown, the bright star is labeled A, and the faint star is labeled B. Using the bright star as the center, the azimuth of the faint star relative to the bright star is calculated from north to east. The value range is 0°-360°.

[0084] Then calculate the relative rotation angle of the star pair:

[0085]

[0086] Where (xA, yA) represents the position information of bright star A, and (xB, yB) represents the position information of dark star B.

[0087] Then calculate the relative rotation angle of the star pair:

[0088] δθ=θ I -θ R (9) Where, θ I θ is the azimuth angle of the star pair in the image. R For the azimuth angle of the star pair in the star catalog, if δθ is less than 0, add 360° to the calculated relative rotation angle to ensure that the relative rotation angle is always between 0° and 360°. Then, divide δθ into 360 intervals of 1° each and count the number of rotation angles appearing in each interval.

[0089] Then, the rotation angle information that meets the conditions is statistically analyzed.

[0090] |δθ-mode(round(δθ))|<1° (10)

[0091] Here, round() is the rounding function, and mode() is the mode function for rotating the angle after rounding.

[0092] The angles that meet the above conditions are averaged, and then the values ​​that are more than 3 standard deviations from the average are removed by an iterative method. After the iteration is completed, the average value is taken to obtain the relative rotation angle δθ2. This rotation angle is the approximate rotation angle.

[0093] Step 4: Preliminary determination of matching parameters:

[0094] The projection mapping relationship between the measuring coordinate system and the ideal tangent plane coordinate system can be determined using the following four constant formula.

[0095] ξ=ρcosθx-ρsinθy+c (11)

[0096] η=ρsinθx+ρcosθy+d (12)

[0097] Where θ represents the rotation angle between the two coordinate systems, and ρ is the scale, substituting the candidate matching star into the above formula yields the coordinate center translations c and d. The average translations c and d are then calculated using iteration and the three-times-standard-deviation principle. Thus, the coarse mapping parameters for the coordinate transformation are obtained.

[0098] Step 5: Precisely determine the matching parameters:

[0099] Based on the initial parameters obtained in step 4 Transform all detected constellations into the celestial coordinate system and find the nearest matching constellation target;

[0100] The obtained star map and star catalog matching pairs are used to solve for the parameters of the film constant model using the least squares method. This step can be performed twice to reduce the risk of matching errors caused by the coarse matching error in the fourth step. At this point, the entire matching process is complete.

[0101] Example 1

[0102] To address the needs of astronomical observation and target positioning, a star map matching method based on the statistical characteristics of star pair rotation angles was invented. This method can detect stars in astronomical images, match the detected stars with star numbers in the star catalog, obtain the astronomical coordinates (right ascension, declination) values ​​of the stars in the image, and provide the film constant model of the captured star map.

[0103] The camera and telescope parameters used in the astronomical images of the examples are shown in Table 1:

[0104] Table 1 Telescope and Camera Parameters

[0105] focal length 1330cm Focal ratio 13 Primary mirror diameter 100cm CCD field of view 16 cents CCD pixel count 4096*4112 Pixel size 15μ

[0106] The night sky was photographed using a camera in Kunming, Yunnan Province, with the target being the open star cluster M35. The resulting star image is shown below. Figure 3 As shown, after bias and flat field preprocessing of the image, a total of 1402 stars were obtained using the star detection method. Among them, the two brightest stars were excluded because they were overexposed and exceeded the full width at half maximum (FWHM) threshold of star detection, resulting in limited centering accuracy.

[0107] The five brightest stars were selected for matching, and an appropriate number of data points were chosen based on the area ratio between the star catalog and the CCD field of view. In this implementation case, we used several star catalogs of different sizes with magnitudes less than 19 downloaded from the GaiaDr2 catalog for testing. The selected area for the star catalogs was circular, and the number of stars selected in the catalogs is shown in Table 2.

[0108] Table 2 shows the number of stars selected.

[0109]

[0110] Using the first group as an example, there are 4 pairs that meet the requirements for star pair distance and magnitude threshold, and their relative rotation angles are shown in Table 3 below.

[0111] Table 3 Relative Rotation Angle

[0112] Eligible star pairs Relative rotation angle 1 10.1278° 2 178.1574° 3 178.1577° 4 178.1580°

[0113] The relative rotation angle is counted using bin counting, such as Figure 4 As shown, taking the mode yields a rough matching rotation angle of 178°. Several different star catalogs of varying sizes were used for correct matching, with 1296 stars successfully matched, such as... Figure 5 As shown, circles represent successful matches, while triangles represent unsuccessful matches. The main reason for the unsuccessful matches is that these targets are very faint, resulting in poor accuracy of apparent magnitude measurements, exceeding the specified magnitude difference threshold.

[0114] The foregoing description illustrates and describes several preferred embodiments of the invention. However, as previously stated, it should be understood that the invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the invention should be within the protection scope of the appended claims.

Claims

1. A star map matching method based on star pair statistical characteristics, characterized in that, The method comprises the following steps: Step 1, constructing star pairs; Step 2, searching similar stars from the image star pair list and the catalogue star pair list; Step 3, determining the rotation angle of the image and the catalogue; Step 4, preliminarily determining the matching parameters; Step 5, accurately determining the matching parameters; The step 2 of searching similar stars from the image star pair list and the catalogue star pair list specifically comprises: Let the imaging focal length be F, and the camera's pixel size be The distance scale relationship (p) between the image brightness coordinates and the ideal coordinate tangent plane coordinates is expressed as: The star pair distance in the list I is expressed as: where x i and y i are the position measurement information of star image i in the star pair constructed by the image list, and x j and y j are the position measurement information of star image j in the star pair constructed by the image list. The star pair distance in the list R is expressed as: where (x p ,y p ) is the position information of the constant star p in the constructed star pair of the star catalog list, and (x q ,y q ) is the position information of the star image q in the constructed star pair of the star catalog list. The matching limitation of the star pairs in the image constructed star pair list and the catalogue constructed star pair list is: |I ij -R pq |≤δF / F (6) wherein, δF is the focal length error of the measuring system, δM is the photometric system magnitude difference between the measuring system and the catalogue system, M p and M q are the apparent magnitudes of the two stars in the catalogue star pair, H i and H j are the gray scale values of the two star images in the image star pair, and the candidate matching star pair is selected according to the matching restriction condition described above; The step 4 of preliminarily determining the matching parameters specifically comprises: The projection mapping relationship between the measurement coordinate system and the ideal tangent plane coordinate system is determined by the following four constant formulae: ξ = ρcosθx - ρsinθy + c (11) η = ρsinθx + ρcosθy + d (12) Wherein θ is the rotation angle of the two coordinate systems, ρ is the scale, the candidate matching star is brought into the formulae to obtain the coordinate center translation c and d; the average translation c and d are obtained by iteration and 3 times standard deviation principle; Wherein x, y are the measurement coordinates of the star image on the CCD; The step 5 of accurately determining the matching parameters specifically comprises: Initial parameters from step 4 Convert all detected star images to the celestial coordinate system and find the nearest matching catalog object; use the resulting star catalog match pair to solve for the plate constant model parameters using least squares This step is performed twice to reduce the risk of matching errors due to the coarse matching errors in step 4. At this point, the entire matching process is complete. where c, d represent the offset of two directions in the ideal tangent plane coordinate system respectively; p, respectively represent the scaling and rotation between the metric coordinate system and the ideal tangent plane coordinate system.

Images