An improved uniform star selection method based on orthogonal grid reference points

Abstract

The present invention discloses a method for uniform star selection using improved orthogonal grid reference points. The method includes screening a set of candidate stars based on the axis characteristics and pointing range of a horizontal telescope; initializing the positions of the orthogonal grid reference points; constructing a KD tree using the reference point positions; finding the nearest neighbor orthogonal grid reference point for each star and calculating the comprehensive evaluation weight of the star; calculating the contribution of each orthogonal grid reference point and the overall evaluation weight; using a particle swarm algorithm to find the maximum value of the overall evaluation weight to obtain the orthogonal grid reference point position that best fits the candidate star set; and selecting stars based on the distance-magnitude weighting method based on the optimal orthogonal grid reference point position to obtain a uniform star selection result. The uniform star selection method of the present invention improves the traditional orthogonal grid method, resulting in a more uniform distribution of selected stars, which facilitates telescope pointing accuracy correction and is also applicable to the selection of reference points for pointing correction of other multi-axis devices.

Description

Technical Field

[0001] The present invention belongs to the field of astronomical telescope control methods, and specifically relates to a star selection method for telescope pointing correction, and more particularly to a uniform star selection method for improving orthogonal grid reference points. Background Art

[0002] The pointing accuracy of an astronomical telescope is a key factor in determining the quality and accuracy of astronomical observations. The ability to accurately point a telescope at a specific target is crucial for obtaining clear and detailed images of celestial bodies. Currently, professional telescopes generally use a horizontal structure. The telescope has two rotation axes, azimuth and altitude. The mechanical structure of the telescope inevitably has systematic errors such as vertical axis error, horizontal axis error, collimation axis error, and code disk zero point error. The effects of these errors remain generally stable and repeatable, and pointing corrections can be made through modeling. Currently, there are three widely used pointing correction models: the basic parameter model, the spherical harmonic function model, and the turntable model. The correction process of these models is to select stars evenly distributed in the upper half of the sky, measure the deviation between the telescope's calibrated observation position and the position calculated by the star catalog, and use the pointing model to calculate the correction coefficient to correct the telescope's pointing.

[0003] The quality of the telescope pointing error correction model is closely related to the distribution of selected stars. The distribution of selected stars should be as uniform as possible across the upper half of the sky. The currently commonly used star selection method is the magnitude filter method, which selects stars with magnitudes less than or equal to a threshold. However, this method produces significantly uneven selection of stars, leading many researchers to propose improvements. Vedder proposed the orthogonal grid method, which generates an orthogonal grid of reference points within the pointing range of the azimuth and altitude axes and selects the nearest stars around them. This method quickly generates a uniform distribution of stars. However, the positions of the traditional orthogonal grid reference points may not be optimal, resulting in poor overall uniformity in star selection. The invention patent with patent number ZL 202310245507.2 proposes a uniform star selection method based on maximizing the Kozachenko-Leonenko entropy, using a simulated annealing algorithm to solve the optimal KL entropy of the selected star distribution. However, the multiple iterations of this method make the frequency of deleting and constructing the KD tree too high. Even the delayed deletion strategy cannot cope with dynamic scenarios. The KD tree rebalancing operation can only delete the original tree and recreate a new balanced binary tree, so the calculation is very time-consuming. Summary of the Invention

[0004] In response to the above-mentioned problems existing in the prior art, the present invention proposes a uniform star selection method for telescope pointing correction using an improved orthogonal grid reference point. This method can select stars within the pointing range of the telescope, and the selected stars are more uniform. The method is also applicable to the correction reference point selection problem of other multi-axis devices.

[0005] The technical solutions for achieving the purpose of the present invention are:

[0006] An improved uniform star selection method for orthogonal grid reference points includes the following steps:

[0007] Step 1: Based on the pointing range of the horizontal telescope used, select a set of candidate stars that meet the position and magnitude requirements;

[0008] Step 2: Initialize the positions of the orthogonal grid reference points of the correction stars;

[0009] Step 3: Construct a KD tree using the orthogonal grid reference point positions in step 2;

[0010] Step 4: Find the nearest neighbor orthogonal grid reference point of each star in the candidate star set and calculate the comprehensive evaluation weight;

[0011] Step 5: Calculate the contribution and overall evaluation weight of each orthogonal grid reference point;

[0012] Step 6: Use the particle swarm algorithm to solve the optimal grid point offset.

[0013] Step 7: Select evenly distributed stars based on the distance-magnitude weighting method.

[0014] Furthermore, step 1 specifically includes:

[0015] Step 1.1: Based on the axis characteristics of the azimuth and altitude axes of the horizontal telescope being used, the altitude axis ranges from 0 to 90°. The azimuth and altitude axes are perpendicular to each other and range from 0 to 360°, with 0° and 360° coinciding and forming a closed circular trajectory. Therefore, it is necessary to ensure that the calibration star to be selected is within the pointing range of the telescope's azimuth and altitude axes, that is, in the observer's upper half of the sky.

[0016] Step 1.2: Select the Hipparcos catalog and, based on the observation capabilities of the horizontal telescope being used, select stars brighter than magnitude 5. Perform astronomical calculations to convert the equatorial positions of the stars in the catalog to horizontal positions, and further select a set of candidate stars, the number of which is N.

[0017] Furthermore, in step 2, the orthogonal grid reference point positions of the correction stars are initialized, taking into account the number of orthogonal grid reference points, i.e., the number in the azimuth axis direction and the altitude axis direction, the grid spacing, and the offset of the grid points as a whole compared to the position zero point.

[0018] Furthermore, step 3 specifically includes:

[0019] Step 3.1: Construct the root node of the orthogonal grid reference point KD tree with a depth of 0, corresponding to the two-dimensional space formed by the telescope's two axes pointing to the upper half of the sky, where the azimuth axis ranges from 0° to 360° and the altitude axis ranges from 0° to 90°;

[0020] Step 3.2: Select the azimuth or height axis dimension based on the parity of the tree depth;

[0021] Step 3.3: Select the median of the axis dimension as the root node to construct the KD tree;

[0022] Step 3.4: Create node node and its left and right child nodes based on median, and divide the point set T into T1 and T2, where the left child node T1 contains points whose axis dimension is less than or equal to median, and T2 contains other points.

[0023] Furthermore, step 4 specifically includes:

[0024] Step 4.1: Find the leaf node containing the selected star point p in the KD tree: Starting from the root node, recursively visit downwards. If p is less than the current dimension coordinate of the node, move to the left child node, otherwise move to the right child node, until a leaf node is found. The path from the root node to the leaf node needs to be recorded and placed in a stack.

[0025] Step 4.2: Take the leaf node as the current nearest neighbor and recursively backtrack to the root node. If the node is closer to the selected star point p than the current nearest neighbor, then take the node as the current nearest neighbor.

[0026] Step 4.3: After finding the nearest neighbor orthogonal grid reference point, calculate the comprehensive evaluation weight w of each star according to the distance-magnitude weighting method i , the calculation method of the weight can be expressed as:

[0027] w i =-c1d i -c2m i (1)

[0028] Where i = 1, 2, ..., N, d i is the distance between the candidate star i and its nearest neighbor orthogonal grid reference point, c1 is the distance coefficient, and c1>0, the smaller the distance, the greater the comprehensive evaluation weight w of the candidate star i The higher; m i is the magnitude, the smaller the magnitude, the brighter the brightness, c2 is the magnitude coefficient, and c2>0, the brighter the brightness, the comprehensive evaluation weight of the candidate star w i The higher.

[0029] Furthermore, step 5 specifically includes:

[0030] Step 5.1: Measure the contribution of each grid point to the whole j , which can be expressed as:

[0031] v j =max(w k ) (2)

[0032] Among them, the orthogonal grid reference point j = 1, 2, ..., n, k is the candidate star within the jurisdiction of grid point j. Its contribution v j Depends on the maximum comprehensive evaluation weight of the candidate stars within the grid point's jurisdiction. Each candidate star has its nearest grid point, so it can be considered to belong to the jurisdiction of the corresponding grid point. The higher the contribution of each grid point, the greater the comprehensive evaluation weight within the jurisdiction, indicating that the candidate star is more valuable to the overall uniformity and observation convenience;

[0033] Step 5.2: In order to measure the overall fit between the orthogonal grid points and the candidate star set and the convenience of observation, consider introducing an overall evaluation weight V. The larger the value, the better the selection result. V can be expressed as:

[0034]

[0035] That is, the contribution of all grid points to the whole v j sum.

[0036] Furthermore, in step 6, the offset of the orthogonal grid reference point (x0, y0) is regarded as a particle, and the particle swarm algorithm is used to update the velocity and position of the particle to solve the most appropriate orthogonal grid reference point offset (x0, y0) so that the overall evaluation weight V is maximized, and the orthogonal grid reference point position that best fits the candidate star set is obtained.

[0037] Furthermore, in step 7, the optimal orthogonal grid reference point positions obtained in step 6 are combined with the distance-magnitude weighted method to select stars, thereby obtaining the final uniform star selection result.

[0038] Compared with the existing technology, the present invention has significant advantages: (1) By optimizing the overall offset of the orthogonal grid points, the present invention can achieve uniform selection of stars for horizontal telescope correction. Compared with the traditional orthogonal grid method, the selection results are more uniform, which helps to correct the telescope's pointing accuracy. (2) The uniform star selection method of the present invention uses a particle swarm algorithm for optimization. Compared with other intelligent optimization methods, it is easier to implement and takes less computation time. It is also applicable to the selection of reference points for pointing correction of other multi-axis devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 4 is an overall flow chart of the method of the present invention.

[0040] Figure 2 Schematic diagram of the pointing range and screened star set of a horizontal telescope.

[0041] Figure 3 Sets the schematic for the orthogonal grid reference point locations.

[0042] Figure 4 Schematic diagram of the initial positions of the orthogonal grid reference points and the distribution results of 27 stars selected from the candidate star set.

[0043] Figure 5 The positions of the orthogonal grid reference points obtained by the uniform star selection method for the improved orthogonal grid reference points provided by the present invention, as well as the uniform distribution result diagram of 27 stars selected from the candidate star set. DETAILED DESCRIPTION

[0044] The present invention will be described in further detail below with reference to the accompanying drawings.

[0045] Figure 1 This is the overall flow chart of the method of the present invention. First, the candidate star set is screened according to the axis characteristics and pointing range of the horizontal telescope, and the orthogonal grid reference point position is initialized. Then the reference point position is used to construct a KD tree, find the nearest neighbor orthogonal grid reference point of each star, and calculate the comprehensive evaluation weight of the star, calculate the contribution of each orthogonal grid reference point, and calculate the overall evaluation weight. Then the particle swarm algorithm is used to solve the maximum value of the overall evaluation weight to obtain the orthogonal grid reference point position that best fits the candidate star set. Finally, based on the optimal orthogonal grid reference point position, stars are selected according to the distance-magnitude weighted method to obtain a uniform star selection result. Combined with Figure 1 The present invention provides an improved uniform star selection method for orthogonal grid reference points, comprising the following steps:

[0046] Step 1: Based on the pointing range of the horizontal telescope used, select a set of candidate stars that meet the position and magnitude requirements.

[0047] Step 1.1: Based on the axis characteristics of the azimuth and altitude axes of the horizontal telescope used, Figure 2 As shown, the altitude axis ranges from 0 to 90°; the azimuth axis and the altitude axis are perpendicular to each other and range from 0 to 360°. Therefore, it is necessary to consider that the correction star to be selected is within the pointing range of the telescope's azimuth axis and altitude axis, that is, in the observer's upper half of the sky.

[0048] Step 1.2: Use the Hipparcos catalog and select stars brighter than magnitude 5 based on the observation capability of the horizontal telescope used. Perform astronomical calculations to convert the equatorial positions of the stars in the catalog to horizontal positions, and further select a set of candidate stars, the number of which is N, such as Figure 2 The star points shown.

[0049] Step 2: Initialize the positions of the orthogonal grid reference points of the calibration stars.

[0050] Consider the number of orthogonal grid reference points, i.e. the number in the azimuth and altitude axes, the grid spacing, and the overall offset of the grid points relative to the zero position. Figure 3 As shown, assuming that the number of orthogonal grid reference points in the azimuth axis direction is 9 and the number in the altitude axis direction is 3, the number of orthogonal grid reference points is 27; assuming that the orthogonal grid is evenly distributed and equidistant on the azimuth axis, the interval is 360 / 9=40°, the interval on the altitude axis is also 40°, and the overall offset of the grid points relative to the zero position is (20°, 10°).

[0051] Step 3: Construct a KD tree based on the orthogonal grid reference point positions in step 2.

[0052] Step 3.1. Construct the root node of the KD tree of orthogonal grid reference points, with a depth of 0, corresponding to the two-dimensional space formed by the telescope's two axes pointing to the upper half of the sky, where the azimuth axis ranges from 0° to 360° and the altitude axis ranges from 0° to 90°;

[0053] Step 3.2, select the azimuth axis or height axis dimension according to the parity of the tree depth;

[0054] Step 3.3, select the median of the axis dimension as the root node to construct the KD tree;

[0055] Step 3.4: Create node node and its left and right child nodes based on median, and divide the point set T into T1 and T2, where the left child node T1 contains points whose axis dimension is less than or equal to median, and T2 contains other points.

[0056] Step 4: Find the nearest neighbor orthogonal grid reference point of each star in the candidate star set and calculate the comprehensive evaluation weight.

[0057] Step 4.1. Find the leaf node containing the selected star point p in the KD tree: Starting from the root node, recursively visit downward. If p is less than the current dimension coordinate of the node, move to the left child node, otherwise move to the right child node until a leaf node is found. The path from the root node to the leaf node needs to be recorded and placed in a stack.

[0058] Step 4.2: Take the leaf node as the current nearest neighbor and recursively backtrack to the root node. If the node is closer to the selected star point p than the current nearest neighbor, then take the node as the current nearest neighbor.

[0059] Step 4.3: After finding the nearest neighbor orthogonal grid reference point, calculate the comprehensive evaluation weight w of each star according to the distance-magnitude weighting method. i, the calculation method of the weight can be expressed as:

[0060] w i =-c1d i -c2m i

[0061] Where i = 1, 2, ..., N, d i is the distance between the candidate star i and its nearest neighbor orthogonal grid reference point, c1 is the distance coefficient, and c1>0, the smaller the distance, the greater the comprehensive evaluation weight w of the candidate star i The higher; m i is the magnitude, the smaller the magnitude, the brighter the brightness, c2 is the magnitude coefficient, and c2>0, the brighter the brightness, the comprehensive evaluation weight of the candidate star w i The higher.

[0062] Step 5: Calculate the contribution and overall evaluation weight of each orthogonal grid reference point.

[0063] Step 5.1: Measure the contribution of each grid point to the overall j , which can be expressed as:

[0064] v j =max(w k )

[0065] Among them, the orthogonal grid reference point j = 1, 2, ..., n, k is the candidate star within the jurisdiction of grid point j. Its contribution v j Depends on the maximum comprehensive evaluation weight of the candidate stars within the grid point's jurisdiction. Each candidate star has its nearest grid point, so it can be considered to belong to the jurisdiction of the corresponding grid point. The higher the contribution of each grid point, the greater the comprehensive evaluation weight within the jurisdiction, indicating that the candidate star is more valuable to the overall uniformity and observation convenience;

[0066] Step 5.2: In order to measure the overall fit between the orthogonal grid points and the candidate star set and the convenience of observation, consider introducing an overall evaluation weight V. The larger the value, the better the selection result. V can be expressed as:

[0067]

[0068] That is, the contribution of all grid points to the whole v j sum.

[0069] Step 6: Use the particle swarm algorithm to solve the optimal grid point offset.

[0070] The offset of the orthogonal grid reference point (x0, y0) is regarded as a particle, and the particle swarm algorithm is used to update the velocity and position of the particle to solve the most appropriate orthogonal grid reference point offset (x0, y0) so that the overall evaluation weight V is maximized, and the orthogonal grid reference point position that best fits the candidate star set is obtained.

[0071] Step 7: Select evenly distributed stars based on the distance-magnitude weighting method.

[0072] Based on the optimal orthogonal grid reference point position obtained in step 6, the distance-magnitude weighted method is combined to select stars, and the final uniform star selection result is obtained.

[0073] This example specifically uses the Hipparcos catalog and the NOVAS (Naval Observatory Vector Astrometry Software) package provided by the U.S. Naval Observatory to calculate the horizontal coordinates of stars. The Julian day is set to 2459924, and the observation location is (117.287°E, 31.864°N). Taking into account the detection capabilities of telescopes of different apertures and the observation conditions at the observation site, N = 708 stars with a magnitude of 5.0 or less and located in the upper half of the sky above the horizon are selected.

[0074] Experiments were conducted to simulate the situation. Initialize the orthogonal grid reference point positions of the correction star. Set the number of orthogonal grid reference points to 27, the number in the azimuth axis direction to 3, the number in the altitude axis direction to 9, the interval between the azimuth axis and the altitude axis direction to 40°, and the offset of the azimuth altitude axis to (20°, 10°). Figure 3 and Figure 4 shown.

[0075] Calculate as Figure 4 The overall evaluation weight at the initial moment is -247.6. The particle swarm algorithm is used to optimize the orthogonal grid reference point offset to (x0, y0), and the optimal orthogonal grid reference point position is (19.8°, 1.6°). The maximum overall evaluation weight after optimization is -200.3. The larger the overall evaluation weight, the closer the orthogonal grid reference point position is to the selected star set, that is, the more the selected stars form an orthogonal grid distribution. According to the optimal orthogonal grid reference point position obtained in step 6, the distance-magnitude weighted method is combined to select stars, and the final uniform star selection result is obtained, as shown in the figure below. Figure 5 shown.

[0076] Compared with the uniform star selection method (MKLE) based on maximizing the Kozachenko-Leonenko entropy of patent No. ZL 2023 1 0245507.2, the running time of the two methods for solving the optimal distribution is compared. As shown in Table 1, it can be seen that the uniform star selection method with an improved orthogonal grid reference point proposed in the present invention takes only 1 / 27 of the time of the MKLE method, indicating the rapidity of the present invention.

[0077] Table 1 Time (seconds) for selecting n stars using different uniform selection methods

[0078]

[0079] As can be seen from the above, this embodiment simulates and experiments a uniform star selection method using an improved orthogonal grid reference point. First, a candidate star set is selected based on the axis characteristics and pointing range of the horizontal telescope, and the orthogonal grid reference point positions are initialized. A KD tree is then constructed using the reference point positions to find the nearest neighboring orthogonal grid reference point for each star. A comprehensive evaluation weight for each star is calculated, along with the contribution of each orthogonal grid reference point and the overall evaluation weight. A particle swarm algorithm is then used to maximize the overall evaluation weight, obtaining the orthogonal grid reference point position that best matches the candidate star set. Finally, based on the optimal orthogonal grid reference point position, stars are selected using a distance-magnitude weighting method to achieve a uniform star selection result. This improved uniform star selection method using orthogonal grid reference points is suitable for uniformly selecting stars during pointing correction of horizontal telescopes and achieves greater uniformity than traditional orthogonal grid methods.

[0080] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. An improved uniform star selection method for orthogonal grid reference points, characterized in that: The following steps are involved: Step 1: Based on the pointing range of the telescope used, select a set of candidate stars that meet the position and magnitude requirements; Step 2: Initialize the orthogonal grid reference point positions of the calibration stars; Step 3: Construct a KD tree using the orthogonal grid reference point positions in step 2; Step 4: Find the nearest neighbor orthogonal grid reference point of each star in the candidate star set and calculate the comprehensive evaluation weight; Step 5: Calculate the contribution and overall evaluation weight of each orthogonal grid reference point; Step 6: Use the particle swarm algorithm to solve the optimal grid point offset; Step 7: Select evenly distributed stars based on the distance-magnitude weighting method.

2. The improved uniform star selection method of orthogonal grid reference points according to claim 1, characterized in that: The step 1 comprises: Step 1.1: Based on the characteristics of the azimuth and altitude axes of the telescope being pointed, the altitude axis ranges from 0 to 90°. The azimuth and altitude axes are perpendicular to each other and range from 0 to 360°, with 0° and 360° coinciding and forming a closed circular trajectory. Therefore, it is necessary to ensure that the calibration star to be selected is within the pointing range of the telescope's azimuth and altitude axes, that is, in the observer's upper half of the sky. Step 1.2: Select the Hipparcos catalog and, based on the observation capabilities of the horizontal telescope being used, select stars brighter than magnitude 5. Perform astronomical calculations to convert the equatorial positions of the stars in the catalog to horizontal positions, and further select a set of candidate stars, the number of which is N.

3. The improved uniform star selection method of orthogonal grid reference points according to claim 1, characterized in that: In step 2, the orthogonal grid reference point positions of the correction star are initialized, taking into account the number of orthogonal grid reference points, i.e., the number in the azimuth and altitude axis directions, the grid spacing, and the offset of the grid points as a whole compared to the position zero point.

4. The improved uniform star selection method of orthogonal grid reference points according to claim 1, characterized in that: The step 3 comprises: Step 3.1: Construct the root node of the orthogonal grid reference point KD tree with a depth of 0, corresponding to the two-dimensional space formed by the telescope's two axes pointing to the upper half of the sky, where the azimuth axis ranges from 0° to 360° and the altitude axis ranges from 0° to 90°; Step 3.2: Select the azimuth or height axis dimension based on the parity of the tree depth; Step 3.3: Select the median of the axis dimension as the root node to construct the KD tree; Step 3.4: Create node node and its left and right child nodes based on median, and divide the point set T into T1 and T2, where the left child node T1 contains points whose axis dimension is less than or equal to median, and T2 contains other points.

5. The improved uniform star selection method of orthogonal grid reference points according to claim 1, characterized in that: The step 4 comprises: Step 4.1: Find the leaf node containing the selected star point p in the KD tree: Starting from the root node, recursively visit downwards. If p is less than the current dimension coordinate of the node, move to the left child node, otherwise move to the right child node, until a leaf node is found. The path from the root node to the leaf node needs to be recorded and placed in a stack. Step 4.2: Take the leaf node as the current nearest neighbor and recursively backtrack to the root node. If the node is closer to the selected star point p than the current nearest neighbor, then take the node as the current nearest neighbor. Step 4.3: After finding the nearest neighbor orthogonal grid reference point, calculate the comprehensive evaluation weight w of each star according to the distance-magnitude weighting method i , the calculation method of the weight can be expressed as: In i =-c1d i -c2m i (1) Where i = 1, 2, ..., N, d i is the distance between the candidate star i and its nearest neighbor orthogonal grid reference point, c1 is the distance coefficient, and c1>0, the smaller the distance, the greater the comprehensive evaluation weight w of the candidate star i The higher; m i is the magnitude, the smaller the magnitude, the brighter the brightness, c2 is the magnitude coefficient, and c2>0, the brighter the brightness, the comprehensive evaluation weight of the candidate star w i The higher.

6. The improved uniform star selection method of orthogonal grid reference points according to claim 1, characterized in that: The step 5 comprises: Step 5.1: Measure the contribution of each grid point to the whole j , expressed as: v j =max(w k ) (2) Among them, the orthogonal grid reference point j = 1, 2, ..., n, k is the candidate star within the jurisdiction of grid point j, and its contribution v j It depends on the maximum comprehensive evaluation weight of the candidate stars within the grid point's jurisdiction. Each candidate star has its nearest grid point, so the candidate star is considered to belong to the jurisdiction of the corresponding grid point. The higher the contribution of each grid point, the greater the comprehensive evaluation weight within the jurisdiction, indicating that the candidate star is more valuable to the overall uniformity and observation convenience. Step 5.2: In order to measure the overall fit between the orthogonal grid points and the candidate star set and the convenience of observation, an overall evaluation weight V is introduced. The larger the value, the better the selection result. V can be expressed as: That is, the contribution of all grid points to the whole v j sum.

7. The improved uniform star selection method of orthogonal grid reference points according to claim 1, characterized in that: In step 6, the offset of the orthogonal grid reference point (x0, y0) is regarded as a particle, and the particle swarm algorithm is used to update the velocity and position of the particle to solve the most appropriate orthogonal grid reference point offset (x0, y0) so that the overall evaluation weight V is maximized, and the orthogonal grid reference point position that best fits the candidate star set is obtained.

8. The improved uniform star selection method of orthogonal grid reference points according to claim 1, characterized in that: In step 7, the optimal orthogonal grid reference point positions obtained in step 6 are combined with the distance-magnitude weighted method to select stars, thereby obtaining the final uniform star selection result.

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