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WO2021135161A1 - Real-time celestial positioning and metering method for space debris based on automatic pointing measurement - Google Patents

Real-time celestial positioning and metering method for space debris based on automatic pointing measurement Download PDF

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Publication number
WO2021135161A1
WO2021135161A1 PCT/CN2020/102323 CN2020102323W WO2021135161A1 WO 2021135161 A1 WO2021135161 A1 WO 2021135161A1 CN 2020102323 W CN2020102323 W CN 2020102323W WO 2021135161 A1 WO2021135161 A1 WO 2021135161A1
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star
stars
theoretical
space debris
image
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PCT/CN2020/102323
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French (fr)
Chinese (zh)
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张晓祥
高昕
李希宇
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中国科学院紫金山天文台
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Publication of WO2021135161A1 publication Critical patent/WO2021135161A1/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
    • G01C21/025—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means with the use of startrackers

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  • the invention relates to the technical field of space debris positioning, in particular to a method for real-time astronomical positioning and photometry of space debris based on automatic pointing determination.
  • Absolute positioning is the use of the telescope shaft system to achieve space debris measurement, which is affected by the processing accuracy of the telescope shaft system, the accuracy of atmospheric refraction correction, and temperature deformation. , It does not rely on background stars.
  • Relative positioning is based on the relative position of space debris and background stars to achieve space debris measurement.
  • the telescope pointing accuracy does not directly affect the measurement results, but when the telescope pointing and image plane installation errors are large, it will cause the theoretical coordinates of the stars on the image.
  • absolute measurement there are also two methods for precise photometric measurement of space debris: absolute measurement and relative measurement.
  • multiple standard photometric calibration stars in different fields of view are used to obtain a photometric model, which is called absolute measurement model, also called absolute photometry; using multiple photometric calibration stars in the same field of view,
  • the obtained metering model is called a relative pair measurement model, also known as relative metering.
  • the light metering method it is based on the successful matching of the actual gray scale of the star and the theoretical magnitude of the star, which also requires more accurate station temperature, relative humidity, and atmospheric pressure. Even so, in areas with low elevation angles, the accuracy of the correction of the telescope's pointing error is low due to the correction accuracy of atmospheric refraction.
  • the present invention provides a real-time astronomical positioning method for space targets based on automatic pointing determination, which can automatically optimize the film model according to the size of the observation field of view, and according to the given time on the image and the orientation of the image center, There is no need to input pointing information, and the image center orientation and image plane rotation angle are automatically determined, so as to realize the automatic matching of the theoretical coordinates of stars and the actual measured coordinates, thereby realizing real-time astronomical positioning and photometry of space debris.
  • the purpose of the present invention is to provide a real-time astronomical positioning and photometric method for space debris based on automatic orientation determination, which can automatically select the film model according to the size of the observation field of view, and automatically determine the image center orientation and image plane rotation angle according to a given time on the image , To realize the automatic matching of the theoretical coordinates of the stars and the actual measured coordinates, to realize the automatic matching of the gray value of the star on the image and its theoretical magnitude, so as to realize the real-time astronomical positioning and photometry of the space debris.
  • this method reduces the requirements for telescope shafting accuracy, reduces the requirements for telescope field installation and commissioning, reduces the requirements for inputting environmental temperature parameters at the station, and reduces the need for pointing calibration before observation. Requirements.
  • this method can automatically determine the zero point difference of the telescope's two axes without precise astronomical latitude and longitude, and can also realize real-time astronomical positioning and relative photometry of space debris. More importantly, this method can achieve high-precision astronomical positioning and relative photometry on mobile sites without astronomical latitude and longitude (only geographic latitude and longitude).
  • the present invention proposes a real-time astronomical positioning and photometric method for space debris based on automatic orientation determination.
  • the real-time astronomical positioning and photometric method includes the following steps:
  • S1 Generate the astronomical positioning star library and the first index data used to express the information of all the stars contained in the astronomical positioning star library; based on the astronomical positioning star library, generate a theoretical star map of the whole sky and use it for presentation The second index data of the angular distance information between the stars contained in the theoretical star map of the whole sky;
  • S2 Receive at least one frame of image including space debris and background stars, and obtain star information of stars and space debris within the preset detection threshold on the image; based on the obtained star information, calculate the angle between any two stars Distance, generate the star map of the star;
  • S3 Determine the upper and lower bounds of the measured star map of stars according to the theoretical star map and the second index data of the whole sky area, and obtain the maximum angular distance Minimum angular distance Intermediate angular distance Combined maximum angular distance Minimum angular distance Intermediate angular distance According to the preset matching rules, several stellar images included in the actual star map that match the theoretical star map of the entire sky are calculated;
  • the metering model is:
  • G i is the gray value of the i-th matched star after subtracting the background
  • i 1, 2,..., N 3
  • N 3 is the total number of matched star images
  • a and B are calculated by the least square method Relative metering model coefficients.
  • step S2 the process of generating an actual star map of stars includes the following steps:
  • N 1 star images from the image and define it as the first candidate star.
  • f is the focal length of the telescope
  • (x j , y j ) are the two-dimensional plane coordinates of the j-th first candidate star
  • (x k , y k ) are the two-dimensional plane coordinates of the k-th first candidate star.
  • step S1 the generation of the astronomical positioning stellar library and the first index data used to express the self-information of all stars contained in the astronomical positioning stellar library refer to:
  • step S1 the astronomically positioned star database is used to generate a theoretical star map of the entire sky region, and a second index for expressing the angular distance information between the stars contained in the theoretical star map of the entire sky region Data refers to:
  • N 2 stars in the whole sky area and define them as the second candidate star.
  • select three second candidate stars to form a triangular star map generate a theoretical star map of the whole sky area, and sort according to the angular distance of each triangle, and generate the corresponding index data.
  • step S1 the following formula is used to calculate the angular distance between any two second candidate stars:
  • ( ⁇ u , ⁇ u ) are the right ascension and declination of the u-th second candidate star
  • ( ⁇ v , ⁇ v ) are the right ascension and declination of the v-th second candidate star
  • step S3 according to the preset matching rules, calculating and obtaining several stellar image information of the stars included in the actual measured constellation map that matches the theoretical constellation map of the entire sky region includes the following steps:
  • ⁇ 1 and ⁇ 2 are both preset angular distance thresholds
  • step S4 the process of calculating the center pointing deviation and the image plane rotation angle based on the information of a number of successfully matched stars includes the following steps:
  • step S4 the process of obtaining the film constant model includes the following steps:
  • the related information of the star meeting the given magnitude threshold includes its corresponding two-dimensional plane coordinate theoretical values (X, Y), ascension and declination theoretical values ( ⁇ s , ⁇ s ), ideal coordinates
  • the shooting information corresponding to the image includes the shooting time of the image, pointing information, station latitude and longitude, station altitude, station temperature, station humidity, atmospheric pressure, and given field of view size;
  • the constant model calculation is performed, and the film constant model is automatically selected according to the positioning accuracy of the star, and the selected film constant model is automatically stored.
  • the calculation of the constant model includes:
  • the six-constant model, the twelve-constant model, and the fourteen-constant model are respectively selected for constant model calculations, among which:
  • the six-constant model corresponds to at least 3 calibration stars:
  • the twelve-constant model corresponds to at least 6 calibration stars:
  • the fourteen constant model corresponds to at least 7 calibration stars:
  • the real-time astronomical positioning method further includes:
  • ( ⁇ T , ⁇ T ) are the ideal coordinates of the space debris, which are obtained by substituting (x T , y T ) into the six-constant, twelve-constant or fourteen-constant model.
  • the film model can be automatically selected according to the size of the observation field of view, and the image center direction and the image plane rotation angle can be automatically determined according to the given time and image center direction on the image, so as to realize the automatic matching of the theoretical and measured coordinates of the star, thus realizing the space Real-time astronomical positioning and photometry of debris.
  • this method reduces the requirements for the machining accuracy of the telescope shafting system, reduces the requirements for the installation and commissioning of the telescope field, reduces the input requirements for the ambient temperature parameters of the station, and reduces the need for pre-observation Point to the requirements of the standard school.
  • this method can also realize real-time astronomical positioning and relative photometry of space debris when the telescope pointing calibration cannot be achieved without precise astronomical latitude and longitude. Therefore, this method is a very good real-time astronomical positioning and photometric method for space debris.
  • This method can achieve high-precision astronomical positioning and relative photometry on mobile sites without astronomical latitude and longitude (only geographic latitude and longitude), and has good actual processing effects, and can be widely used in scientific research and engineering fields.
  • the computer system can provide real-time space debris astronomical positioning results, stellar astronomical positioning results, pointing image rotation measurement results, and star retrieval results on the image. These results can be used in a wide range of applications. For example, they can be displayed by the display system and stored in the storage medium of the computer system. They can also be used for orbit determination and precise orbit determination for space debris cataloging, and they can also be used to modify the space based on the results of the pointing measurement. The predicted location of the debris is conducive to improving the success rate of space debris capture and tracking.
  • Fig. 1 is a flowchart of the real-time astronomical positioning and photometric method of space debris based on automatic pointing determination of the present invention.
  • the real-time astronomical positioning and photometric method includes the following steps:
  • S1 Generate the astronomical positioning star library and the first index data used to express the information of all the stars contained in the astronomical positioning star library; based on the astronomical positioning star library, generate a theoretical star map of the whole sky and use it for presentation The second index data of the angular distance information between the stars contained in the all-sky theoretical star map.
  • S2 Receive at least one frame of image including space debris and background stars, and obtain star information of stars and space debris within the preset detection threshold on the image; based on the obtained star information, calculate the angle between any two stars Distance to generate the measured star map of the star.
  • S3 Determine the upper and lower bounds of the measured star map of stars according to the theoretical star map and the second index data of the whole sky area, and obtain the maximum angular distance Minimum angular distance Intermediate angular distance Combined maximum angular distance Minimum angular distance Intermediate angular distance According to the preset matching rules, a number of stellar images contained in the actual star map that match the theoretical star map of the entire sky area are calculated.
  • the metering model is:
  • G i is the gray value of the i-th matched star after subtracting the background
  • i 1, 2,..., N 3
  • N 3 is the total number of matched star images
  • a and B are calculated by the least square method Relative metering model coefficients.
  • the stars in the entire sky area of a given magnitude are stored in regions in the order of increasing right ascension and increasing declination, and indexing is formed to generate astronomical positioning star database and first index data for use in star retrieval.
  • indexing is formed to generate astronomical positioning star database and first index data for use in star retrieval.
  • select N 2 stars in the whole sky area and use the following formula to calculate the angular distance between any two stars according to the star’s right ascension and declination information:
  • ( ⁇ u , ⁇ u ) are the right ascension and declination of the u-th second candidate star
  • ( ⁇ v , ⁇ v ) are the right ascension and declination of the v-th second candidate star
  • the given threshold such as the minimum and maximum angular distance
  • choose three stars to form a triangular star map generate a theoretical star map of the whole sky, and sort according to the angular distance of each triangle.
  • the star information of the stars and space debris within the detection threshold on the image is obtained, including its two-dimensional plane coordinates (x, y), the number of pixels, the gray scale sum, and the image is compared in the order of decreasing the number of pixels. put in order.
  • any space debris acquisition method in the prior art can be used to obtain the star information of stars and space debris within the detection threshold on the image.
  • the right side of the image is the increasing direction of the x axis
  • the lower side of the image is the increasing direction of the y axis
  • x is the distance between the position of the star in the image and the origin of the coordinate on the x axis
  • Distance, y is the distance between the position of the star in the image and the origin of the coordinate in the y-axis direction.
  • N 1 stellar constellations According to the given threshold, select N 1 stellar constellations. According to the two-dimensional plane coordinates (x, y) of the stellar constellations, the focal length of the telescope is f.
  • the following formula is used to calculate the angular distance between any two stars, and three stars are selected to form a triangular star chart to generate the actual star chart of the star. Use the following formula to calculate the angular distance between any two first candidate stars:
  • (x j , y j ) are the two-dimensional plane coordinates of the j-th second candidate star
  • (x k , y k ) are the two-dimensional plane coordinates of the k-th second candidate star.
  • the order of angular distance is According to the index of the theoretical star map, the upper and lower bounds n of the candidate star map can be quickly realized.
  • the order of the corresponding angular distances of the triangles in the upper and lower bounds is Perform matching judgments.
  • Star information for a given magnitude threshold including theoretical values of two-dimensional plane coordinates (X, Y), theoretical values of right ascension and declination ( ⁇ s , ⁇ s ), theoretical values of ideal coordinates ( ⁇ s , ⁇ s ), theoretical values
  • the magnitude is M and sorted in the order of increasing theoretical magnitude.
  • the ideal coordinates ( ⁇ s , ⁇ s ) satisfy the following formula:
  • the film constant model is automatically selected according to the positioning accuracy of the star (only need to be selected once, and the optimization result is automatically stored).
  • ( ⁇ T , ⁇ T ) are the ideal coordinates of the space debris, which are obtained by substituting (x T , y T ) into the six-constant, twelve-constant or fourteen-constant model.
  • the computer system Based on the above input data, the computer system provides real-time space debris astronomical positioning and photometric results, stellar astronomical positioning and photometric results, pointing image rotation measurement results, and star retrieval results on the image in real time. These results can be displayed by the display system and stored in the storage medium of the computer system. They can be used for orbit determination of space debris cataloging and precise orbit determination. The predicted position of space debris can be corrected according to the pointing measurement results, which is beneficial to improve The success rate of space debris capture and tracking; it can be used for space debris identification and evaluation of the working status and rotation status of space targets with attitude control.

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Abstract

A real-time celestial positioning and metering method for the space debris based on automatic pointing measurement. The method comprises: generating a theoretical star chart; obtaining the astrology of a star and the space debris; generating an actually detected star chart; matching the theoretical star chart and the actually detected star chart; measuring the pointing and image surface rotation; retrieving the star; preferably selecting a film model; calculating a metering model; and performing celestial positioning and metering of the space debris. The method can automatically preferably select the film model according to the observation field of view size, and automatically measure an image center pointing and image surface angle of rotation according to the time given on an image to automatically match the theoretical coordinate and the actually measured coordinate of the star, and automatically match the gray scale value of the star on the image and the theoretical magnitude of the star, thereby achieving real-time celestial positioning and metering of the space debris.

Description

基于指向自动测定的空间碎片实时天文定位和测光方法Real-time astronomical positioning and photometric method of space debris based on automatic pointing determination 技术领域Technical field
本发明涉及空间碎片定位技术领域，具体而言涉及一种基于指向自动测定的空间碎片实时天文定位和测光方法。The invention relates to the technical field of space debris positioning, in particular to a method for real-time astronomical positioning and photometry of space debris based on automatic pointing determination.
背景技术Background technique
在科研、军事等许多领域，都需要对空间碎片进行监视，一方面测定空间碎片的每一个观测时刻在天空中的位置及其变化，确定空间碎片的运行轨道，从而获取空间碎片精确的信息。基于此需求，空间碎片的精确测量是非常重要的基础环节，没有空间碎片的精确测量，空间碎片轨道识别，编目定轨，及精密定轨都无法实现。In many fields such as scientific research and military affairs, it is necessary to monitor space debris. On the one hand, the position and change of space debris in the sky are determined at each observation moment of space debris, and the orbit of space debris is determined, so as to obtain accurate information on space debris. Based on this demand, accurate measurement of space debris is a very important basic link. Without accurate measurement of space debris, space debris orbit identification, cataloging orbit determination, and precise orbit determination cannot be achieved.
空间碎片的位置精确测量有两种方法：绝对定位和相对定位，其中绝对定位就是利用望远镜的轴系实现空间碎片测量，它受到望远镜轴系加工精度、大气折射修正精度、温度变形等因素的影响，它不依赖背景恒星。相对定位是根据空间碎片和背景恒星的相对位置实现空间碎片的测量，望远镜指向精度不直接影响测量结果，但是当望远镜指向及像面安装误差大的情况下，就会造成恒星在图像上理论坐标和恒星在图像上实测坐标相差较大，尤其对于有像面误差的图像，边缘部分误差更大，无法满足给定匹配门限，因此造成恒星理论星图和实测星图匹配失败，无法实现相对定位。There are two methods to accurately measure the position of space debris: absolute positioning and relative positioning. Absolute positioning is the use of the telescope shaft system to achieve space debris measurement, which is affected by the processing accuracy of the telescope shaft system, the accuracy of atmospheric refraction correction, and temperature deformation. , It does not rely on background stars. Relative positioning is based on the relative position of space debris and background stars to achieve space debris measurement. The telescope pointing accuracy does not directly affect the measurement results, but when the telescope pointing and image plane installation errors are large, it will cause the theoretical coordinates of the stars on the image. There is a big difference between the actual measured coordinates of the star and the star on the image, especially for the image with image error, the edge part error is larger, and the given matching threshold cannot be met. Therefore, the matching of the theoretical star map and the measured star map of the star fails, and the relative positioning cannot be achieved. .
空间碎片的光度精确测量也有两种方法：绝对测量和相对测量。其中利用不同视场中的多个标准测光定标星，得到的测光模型，称之为绝对测量模型，也称为绝对测光；利用同一视场中的多个测光定标星，得到的测光模型，称之为相对对测量模型，也称为相对测光。无论是哪一种测光方式，它都是建立在恒星实测灰度和与恒星理论星等匹配成功的基础上，而这同样需要较为精确的测站温度、相对湿度、及大气压强。即使如此，在仰角较低的天区，受大气折射改正精度影响，望远镜指向误差修正精度偏低。There are also two methods for precise photometric measurement of space debris: absolute measurement and relative measurement. Among them, multiple standard photometric calibration stars in different fields of view are used to obtain a photometric model, which is called absolute measurement model, also called absolute photometry; using multiple photometric calibration stars in the same field of view, The obtained metering model is called a relative pair measurement model, also known as relative metering. Regardless of the light metering method, it is based on the successful matching of the actual gray scale of the star and the theoretical magnitude of the star, which also requires more accurate station temperature, relative humidity, and atmospheric pressure. Even so, in areas with low elevation angles, the accuracy of the correction of the telescope's pointing error is low due to the correction accuracy of atmospheric refraction.
基于现有天文定位方法的不足，本发明给出一种基于指向自动测定的空间目标实时天文定位方法，它能够根据观测视场大小自动优选底片模型，按照图像上给定时间和图像中心指向，无需指向信息输入，自动测定图像中心指向及像面旋转角，实现恒星理论坐标和实测坐标的自动匹配，从而实现空间碎片的实时天文定位及测光。Based on the shortcomings of existing astronomical positioning methods, the present invention provides a real-time astronomical positioning method for space targets based on automatic pointing determination, which can automatically optimize the film model according to the size of the observation field of view, and according to the given time on the image and the orientation of the image center, There is no need to input pointing information, and the image center orientation and image plane rotation angle are automatically determined, so as to realize the automatic matching of the theoretical coordinates of stars and the actual measured coordinates, thereby realizing real-time astronomical positioning and photometry of space debris.
发明内容Summary of the invention
本发明目的在于提供一种基于指向自动测定的空间碎片实时天文定位和测光方法，能够根据观测视场大小自动优选底片模型，按照图像上给定时间，自动测定图像中心指向及像面旋转角，实现恒星理论坐标和实测坐标的自动匹配，实现图像上恒星灰度值和其理论星等的自动匹配，从而实现空间碎片的实时天文定位及测光。对于固定站址(有精密的天文经纬度)的望远镜，该方法降低了望远镜轴系加工精度要求，降低望远镜外场安装调试要求，减少了测站环境温度参输入要求，减少了观测前需要指向标校的要求。对于可移动望远镜，该方法在无精密天文经纬度不能实现望远镜指向标校的情况下，能够自动测定望远镜两轴零点差， 也能实现空间碎片实时天文定位及相对测光。更重要的是该方法能够在没有天文经纬度的移动站址上(只有地理经纬度)上实现高精度天文定位及相对测光。The purpose of the present invention is to provide a real-time astronomical positioning and photometric method for space debris based on automatic orientation determination, which can automatically select the film model according to the size of the observation field of view, and automatically determine the image center orientation and image plane rotation angle according to a given time on the image , To realize the automatic matching of the theoretical coordinates of the stars and the actual measured coordinates, to realize the automatic matching of the gray value of the star on the image and its theoretical magnitude, so as to realize the real-time astronomical positioning and photometry of the space debris. For telescopes with fixed sites (with precise astronomical latitudes and longitudes), this method reduces the requirements for telescope shafting accuracy, reduces the requirements for telescope field installation and commissioning, reduces the requirements for inputting environmental temperature parameters at the station, and reduces the need for pointing calibration before observation. Requirements. For mobile telescopes, this method can automatically determine the zero point difference of the telescope's two axes without precise astronomical latitude and longitude, and can also realize real-time astronomical positioning and relative photometry of space debris. More importantly, this method can achieve high-precision astronomical positioning and relative photometry on mobile sites without astronomical latitude and longitude (only geographic latitude and longitude).
为达成上述目的，结合图1，本发明提出一种基于指向自动测定的空间碎片实时天文定位和测光方法，所述实时天文定位和测光方法包括以下步骤：In order to achieve the above objective, in conjunction with FIG. 1, the present invention proposes a real-time astronomical positioning and photometric method for space debris based on automatic orientation determination. The real-time astronomical positioning and photometric method includes the following steps:
S1：生成天文定位恒星星库、和用于表述天文定位恒星星库所包含的所有恒星自身信息的第一索引数据；基于天文定位恒星星库，生成全天区理论星图、和用于表述全天区理论星图所包含的恒星之间角距信息的第二索引数据；S1: Generate the astronomical positioning star library and the first index data used to express the information of all the stars contained in the astronomical positioning star library; based on the astronomical positioning star library, generate a theoretical star map of the whole sky and use it for presentation The second index data of the angular distance information between the stars contained in the theoretical star map of the whole sky;
S2：接收至少一帧包括空间碎片和背景恒星的图像，获得图像上在预设检测门限内的恒星和空间碎片的星象信息；基于获取的恒星星象信息，计算得到任意两颗恒星之间的角距，生成恒星实测星图；S2: Receive at least one frame of image including space debris and background stars, and obtain star information of stars and space debris within the preset detection threshold on the image; based on the obtained star information, calculate the angle between any two stars Distance, generate the star map of the star;
S3：根据全天区理论星图和第二索引数据，确定恒星实测星图的上下界限，获取最大角距
Figure PCTCN2020102323-appb-000001
最小角距
Figure PCTCN2020102323-appb-000002
中间角距
Figure PCTCN2020102323-appb-000003
结合最大角距
Figure PCTCN2020102323-appb-000004
最小角距
Figure PCTCN2020102323-appb-000005
中间角距
Figure PCTCN2020102323-appb-000006
按照预设的匹配规则，计算得到恒星实测星图中所包含的与全天区理论星图相匹配的若干个恒星星象； S3: Determine the upper and lower bounds of the measured star map of stars according to the theoretical star map and the second index data of the whole sky area, and obtain the maximum angular distance
Figure PCTCN2020102323-appb-000001
Minimum angular distance
Figure PCTCN2020102323-appb-000002
Intermediate angular distance
Figure PCTCN2020102323-appb-000003
Combined maximum angular distance
Figure PCTCN2020102323-appb-000004
Minimum angular distance
Figure PCTCN2020102323-appb-000005
Intermediate angular distance
Figure PCTCN2020102323-appb-000006
According to the preset matching rules, several stellar images included in the actual star map that match the theoretical star map of the entire sky are calculated;
S4：以匹配成功的若干个恒星星象信息为基础，计算得到中心指向偏差、像面旋转角、底片常数模型、相对测光模型；S4: Based on the information of several stellar images that have been successfully matched, the center pointing deviation, the image surface rotation angle, the film constant model, and the relative metering model are calculated;
其中，测光模型为：Among them, the metering model is:
Figure PCTCN2020102323-appb-000007
Figure PCTCN2020102323-appb-000007
其中，G i是第i颗匹配成功的恒星星象扣除背景后的灰度值，
Figure PCTCN2020102323-appb-000008
是第i颗匹配成功的恒星星象对应的理论星等，i＝1，2，...，N 3，N 3是匹配成功的恒星星象的总数，A和B是采用最小二乘法计算得到的相对测光模型系数。 Among them, G i is the gray value of the i-th matched star after subtracting the background,
Figure PCTCN2020102323-appb-000008
Is the theoretical magnitude corresponding to the i-th successfully matched star image, i=1, 2,..., N 3 , N 3 is the total number of matched star images, A and B are calculated by the least square method Relative metering model coefficients.
进一步的实施例中，步骤S2中，所述生成恒星实测星图的过程包括以下步骤：In a further embodiment, in step S2, the process of generating an actual star map of stars includes the following steps:
按照给定门限，从图像中选择N 1颗恒星星象，定义成第一候选恒星，结合第一候选恒星在图像上的二维平面坐标和望远镜的焦距，计算得到任意两颗第一候选恒星之间的角距，选择三颗第一候选恒星组成三角形星图，生成恒星实测星图； According to a given threshold, select N 1 star images from the image and define it as the first candidate star. Combine the two-dimensional plane coordinates of the first candidate star on the image and the focal length of the telescope to calculate one of any two first candidate stars. Select the three first candidate stars to form a triangle star map, and generate a star map of the actual star;
其中，采用下述公式计算任意两颗第一候选恒星之间的角距：Among them, the following formula is used to calculate the angular distance between any two first candidate stars:
Figure PCTCN2020102323-appb-000009
Figure PCTCN2020102323-appb-000009
其中，f是望远镜的焦距，(x j，y j)是第j颗第一候选恒星的二维平面坐标，(x k，y k)是第k颗第一候选恒星的二维平面坐标。 Among them, f is the focal length of the telescope, (x j , y j ) are the two-dimensional plane coordinates of the j-th first candidate star, and (x k , y k ) are the two-dimensional plane coordinates of the k-th first candidate star.
进一步的实施例中，步骤S1中，所述生成天文定位恒星星库、和用于表述天文定位恒星星库所包含的所有恒星自身信息的第一索引数据是指：In a further embodiment, in step S1, the generation of the astronomical positioning stellar library and the first index data used to express the self-information of all stars contained in the astronomical positioning stellar library refer to:
将给定星等的全天区恒星按照赤经增加及赤纬增加的顺序分区存放，并形成索引，生成天文定位恒星星库及索引数据。Store the stars in the whole sky area of a given magnitude in the order of increasing right ascension and increasing declination, and form an index to generate astronomical positioning star database and index data.
进一步的实施例中，步骤S1中，所述基于天文定位恒星星库，生成全天区理论星图、和用于表述全天区理论星图所包含的恒星之间角距信息的第二索引数据是指：In a further embodiment, in step S1, the astronomically positioned star database is used to generate a theoretical star map of the entire sky region, and a second index for expressing the angular distance information between the stars contained in the theoretical star map of the entire sky region Data refers to:
按照给定星等门限，选择全天区N 2颗恒星星象，定义成第二候选恒星，结合第二候选恒星的赤经和赤纬，计算得到任意两颗第二候选恒星之间的角距，按照给定角距门限，任选三颗第二候选恒星组成三角形星图，生成全天区理论星图，并按照每个三角形的角距大小进行排序，生成相应的索引数据。 According to the given magnitude threshold, select N 2 stars in the whole sky area and define them as the second candidate star. Combine the ascension and declination of the second candidate star to calculate the angular distance between any two second candidate stars , According to the given angular distance threshold, select three second candidate stars to form a triangular star map, generate a theoretical star map of the whole sky area, and sort according to the angular distance of each triangle, and generate the corresponding index data.
进一步的实施例中，步骤S1中，采用下式计算任意两颗第二候选恒星之间的角距：In a further embodiment, in step S1, the following formula is used to calculate the angular distance between any two second candidate stars:
Figure PCTCN2020102323-appb-000010
Figure PCTCN2020102323-appb-000010
其中，(α u，δ u)是第u颗第二候选恒星的赤经和赤纬，(α v，δ v)是第v颗第二候选恒星的赤经和赤纬，
Figure PCTCN2020102323-appb-000011
是第u颗和第v颗第二候选恒星之间的角距。 Among them, (α u , δ u ) are the right ascension and declination of the u-th second candidate star, (α v , δ v ) are the right ascension and declination of the v-th second candidate star,
Figure PCTCN2020102323-appb-000011
Is the angular distance between the u-th and v-th second candidate stars.
进一步的实施例中，步骤S3中，所述按照预设的匹配规则，计算得到恒星实测星图中所包含的与全天区理论星图相匹配的若干个恒星星象信息包括以下步骤：In a further embodiment, in step S3, according to the preset matching rules, calculating and obtaining several stellar image information of the stars included in the actual measured constellation map that matches the theoretical constellation map of the entire sky region includes the following steps:
S31：根据全天区理论星图和第二索引数据，确定候选星图的上下界限，获取最大角距
Figure PCTCN2020102323-appb-000012
最小角距
Figure PCTCN2020102323-appb-000013
中间角距
Figure PCTCN2020102323-appb-000014
S31: Determine the upper and lower bounds of the candidate star map according to the theoretical star map of the whole sky area and the second index data, and obtain the maximum angular distance
Figure PCTCN2020102323-appb-000012
Minimum angular distance
Figure PCTCN2020102323-appb-000013
Intermediate angular distance
Figure PCTCN2020102323-appb-000014
S32：依次计算上下界限中任意三颗定标星i，j，k组成的三角形的角距，设计算得到的角距由大到小顺序为
Figure PCTCN2020102323-appb-000015
根据下述匹配条件，将计算得到的角距
Figure PCTCN2020102323-appb-000016
对应
Figure PCTCN2020102323-appb-000017
Figure PCTCN2020102323-appb-000018
进行匹配判断，直至匹配成功N 3颗恒星： S32: Calculate the angular distances of triangles composed of any three calibration stars i, j, and k in the upper and lower bounds in sequence, and the calculated angular distances from large to small are in the order of
Figure PCTCN2020102323-appb-000015
According to the following matching conditions, the calculated angular distance
Figure PCTCN2020102323-appb-000016
correspond
Figure PCTCN2020102323-appb-000017
Figure PCTCN2020102323-appb-000018
Perform matching judgment until N 3 stars are successfully matched:
第j颗定标星和第k颗定标星之间满足下式：The following formula is satisfied between the j-th calibration star and the k-th calibration star:
Figure PCTCN2020102323-appb-000019
Figure PCTCN2020102323-appb-000019
任意三颗i，j，k定标星之间满足下式：Any three i, j, k calibration stars satisfy the following formula:
Figure PCTCN2020102323-appb-000020
Figure PCTCN2020102323-appb-000020
其中，ε 1和ε 2均为预设的角距门限； Among them, ε 1 and ε 2 are both preset angular distance thresholds;
进一步的实施例中，步骤S4中，所述以匹配成功的若干个恒星星象信息为基础，计算得到中心指向偏差、像面旋转角的过程包括以下步骤：In a further embodiment, in step S4, the process of calculating the center pointing deviation and the image plane rotation angle based on the information of a number of successfully matched stars includes the following steps:
设匹配成功的N 3颗恒星在图像上的二维平面坐标为(x i，y i)，i＝1，2，...N 3，对应的理论二维平面坐标坐标为(X i，Y i)，i＝1，2，...N 3； Suppose the two-dimensional plane coordinates of the successfully matched N 3 stars on the image are (x i , y i ), i=1, 2,...N 3 , and the corresponding theoretical two-dimensional plane coordinates are (X i , Y i ), i=1, 2,...N 3 ;
利用下式，采用最小二乘方法，计算出系数a，b，c，d，e，f，从而得到中心指向偏差及像面旋转角：Using the following formula, using the least square method to calculate the coefficients a, b, c, d, e, f, so as to obtain the center pointing deviation and the image rotation angle:
Figure PCTCN2020102323-appb-000021
Figure PCTCN2020102323-appb-000021
进一步的实施例中，步骤S4中，所述底片常数模型的获取过程包括以下步骤：In a further embodiment, in step S4, the process of obtaining the film constant model includes the following steps:
结合天文定位恒星星库和第一索引数据，根据图像对应的拍摄信息和全天区星图指向测定结果(α p，δ p)，检索出视场中满足给定星等门限的所有恒星的相关信息，所述满足给定星等门限的恒星的相关信息包括其所对应的二维平面坐标理论值(X，Y)、赤经和赤纬理论值(α s，δ s)、理想坐标理论值(ξ s，ζ s)、理论星等M，按照理论星等由小到大的顺序对检索出的恒星进行排序；其中，所述理想坐标(ξ s，ζ s)满足以下公式： Combining the astronomical positioning star database and the first index data, according to the corresponding shooting information of the image and the whole sky star map pointing measurement results (α p , δ p ), retrieve all the stars in the field of view that meet the given magnitude threshold Related information, the related information of the star meeting the given magnitude threshold includes its corresponding two-dimensional plane coordinate theoretical values (X, Y), ascension and declination theoretical values (α s , δ s ), ideal coordinates The theoretical value (ξ s , ζ s ), theoretical magnitude M, sort the retrieved stars according to the theoretical magnitude from small to large; wherein, the ideal coordinates (ξ s , ζ s ) satisfy the following formula:
Figure PCTCN2020102323-appb-000022
Figure PCTCN2020102323-appb-000022
其中，所述图像对应的拍摄信息包括图像的拍摄时间、指向信息、测站经纬度、测站海拔高度、测站温度、测站湿度、大气压强、给定视场大小；Wherein, the shooting information corresponding to the image includes the shooting time of the image, pointing information, station latitude and longitude, station altitude, station temperature, station humidity, atmospheric pressure, and given field of view size;
根据图像对应视场大小，结合匹配成功的N 3颗恒星在图像上的二维平面坐标(x i，y i)，及理想坐标
Figure PCTCN2020102323-appb-000023
i＝1，2，...N 3，进行常数模型计算，根据恒星的定位精度，自动优选底片常数模型，并且自动存储优选出的底片常数模型。 According to the size of the corresponding field of view of the image, combine the two-dimensional plane coordinates (x i , y i ) of the successfully matched N 3 stars on the image and the ideal coordinates
Figure PCTCN2020102323-appb-000023
i=1, 2,...N 3 , the constant model calculation is performed, and the film constant model is automatically selected according to the positioning accuracy of the star, and the selected film constant model is automatically stored.
进一步的实施例中，所述进行常数模型计算包括，In a further embodiment, the calculation of the constant model includes:
结合匹配成功的定标星数量，分别选用六常数模型、十二常数模型、十四常数模型进行常数模型计算，其中：Combined with the number of successfully matched calibration stars, the six-constant model, the twelve-constant model, and the fourteen-constant model are respectively selected for constant model calculations, among which:
所述六常数模型对应至少3个以上的定标星：The six-constant model corresponds to at least 3 calibration stars:
Figure PCTCN2020102323-appb-000024
Figure PCTCN2020102323-appb-000024
所述十二常数模型对应至少6个以上的定标星：The twelve-constant model corresponds to at least 6 calibration stars:
Figure PCTCN2020102323-appb-000025
Figure PCTCN2020102323-appb-000025
所述十四常数模型对应至少7个以上的定标星：The fourteen constant model corresponds to at least 7 calibration stars:
Figure PCTCN2020102323-appb-000026
Figure PCTCN2020102323-appb-000026
进一步的实施例中，所述实时天文定位方法还包括：In a further embodiment, the real-time astronomical positioning method further includes:
S5：根据空间碎片的二维平面坐标实测值(x T，y T)，采用以下公式获得空间碎片的赤经和赤纬(α T，δ T)： S5: According to the measured values of the two-dimensional plane coordinates of the space debris (x T , y T ), use the following formula to obtain the right ascension and declination (α T , δ T ) of the space debris:
Figure PCTCN2020102323-appb-000027
Figure PCTCN2020102323-appb-000027
其中，(ξ T，ζ T)为空间碎片的理想坐标，由(x T，y T)代入六常数、十二常数或者十四常数模型获得。 Among them, (ξ T , ζ T ) are the ideal coordinates of the space debris, which are obtained by substituting (x T , y T ) into the six-constant, twelve-constant or fourteen-constant model.
以上本发明的技术方案，与现有相比，其显著的有益效果在于，Compared with the prior art, the above technical solution of the present invention has significant beneficial effects in that:
(1)能够根据观测视场大小自动优选底片模型，按照图像上给定时间和图像中心指向，自动测定图像中心指向及像面旋转角，实现恒星理论坐标和实测坐标的自动匹配，从而实现空间碎片的实时天文定位及测光。(1) The film model can be automatically selected according to the size of the observation field of view, and the image center direction and the image plane rotation angle can be automatically determined according to the given time and image center direction on the image, so as to realize the automatic matching of the theoretical and measured coordinates of the star, thus realizing the space Real-time astronomical positioning and photometry of debris.
(2)对于固定站址(有精密的天文经纬度)的望远镜，该方法降低了望远镜轴系加工精度要求，降低望远镜外场安装调试要求，减少了测站环境温度参输入要求，减少了观测前需要指向标校的要求。对于可移动望远镜，该方法在无精密天文经纬度不能实现望远镜指向标校的情况下，也能实现空间碎片实时天文定位和相对测光。因此该方法是一种的非常好的空间碎片实时天文定位和测光方法。(2) For a telescope with a fixed site (with precise astronomical latitude and longitude), this method reduces the requirements for the machining accuracy of the telescope shafting system, reduces the requirements for the installation and commissioning of the telescope field, reduces the input requirements for the ambient temperature parameters of the station, and reduces the need for pre-observation Point to the requirements of the standard school. For movable telescopes, this method can also realize real-time astronomical positioning and relative photometry of space debris when the telescope pointing calibration cannot be achieved without precise astronomical latitude and longitude. Therefore, this method is a very good real-time astronomical positioning and photometric method for space debris.
(3)该方法能够在没有天文经纬度的移动站址上(只有地理经纬度)上实现高精度天文定位和相对测光，实际处理效果好，能够广泛地应用到科研、及工程领域中。(3) This method can achieve high-precision astronomical positioning and relative photometry on mobile sites without astronomical latitude and longitude (only geographic latitude and longitude), and has good actual processing effects, and can be widely used in scientific research and engineering fields.
(4)计算机系统能够实时给出图像上的空间碎片天文定位结果、恒星天文定位结果、指向像面旋转测定结果、恒星检索结果。这些结果应用场景广泛，例如，可以提供给可以通过显示系统显示出来，以及存储在计算机系统的存储介质中，也可以供空间碎片编目定轨及精密定轨使用，还可以根据指向测定结果修正空间碎片的预报位置，有利于提高空间碎片的捕获和跟踪成功率。(4) The computer system can provide real-time space debris astronomical positioning results, stellar astronomical positioning results, pointing image rotation measurement results, and star retrieval results on the image. These results can be used in a wide range of applications. For example, they can be displayed by the display system and stored in the storage medium of the computer system. They can also be used for orbit determination and precise orbit determination for space debris cataloging, and they can also be used to modify the space based on the results of the pointing measurement. The predicted location of the debris is conducive to improving the success rate of space debris capture and tracking.
应当理解，前述构思以及在下面更加详细地描述的额外构思的所有组合只要在这样的构思不相互矛盾的情况下都可以被视为本公开的发明主题的一部分。另外，所要求保护的主题的所有组合都被视为本公开的发明主题的一部分。It should be understood that all combinations of the aforementioned concepts and the additional concepts described in more detail below can be regarded as part of the inventive subject matter of the present disclosure as long as such concepts are not mutually contradictory. In addition, all combinations of the claimed subject matter are regarded as part of the inventive subject matter of the present disclosure.
结合附图从下面的描述中可以更加全面地理解本发明教导的前述和其他方面、实施例和特征。本发明的其他附加方面例如示例性实施方式的特征和/或有益效果将在下面的描述中显见，或通过根据本发明教导的具体实施方式的实践中得知。The foregoing and other aspects, embodiments and features of the teachings of the present invention can be more fully understood from the following description with reference to the accompanying drawings. Other additional aspects of the present invention, such as the features and/or beneficial effects of the exemplary embodiments, will be apparent in the following description, or learned from the practice of the specific embodiments taught in accordance with the present invention.
附图说明Description of the drawings
附图不意在按比例绘制。在附图中，在各个图中示出的每个相同或近似相同的组成部分可以用相同的标号表示。为了清晰起见，在每个图中，并非每个组成部分均被标记。现在，将通过例子并参考附图来描述本发明的各个方面的实施例，其中：The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component shown in each figure may be represented by the same reference numeral. For the sake of clarity, not every component is labeled in every figure. Now, embodiments of various aspects of the present invention will be described by way of examples and with reference to the accompanying drawings, in which:
图1是本发明的基于指向自动测定的空间碎片实时天文定位和测光方法的流程图。Fig. 1 is a flowchart of the real-time astronomical positioning and photometric method of space debris based on automatic pointing determination of the present invention.
具体实施方式Detailed ways
为了更了解本发明的技术内容，特举具体实施例并配合所附图式说明如下。In order to better understand the technical content of the present invention, specific embodiments are described in conjunction with the accompanying drawings as follows.
结合图1，本发明提及一种基于指向自动测定的空间碎片实时天文定位和测光方法，所述实时天文定位和测光方法包括以下步骤：With reference to Figure 1, the present invention mentions a real-time astronomical positioning and photometric method for space debris based on automatic orientation determination. The real-time astronomical positioning and photometric method includes the following steps:
S1：生成天文定位恒星星库、和用于表述天文定位恒星星库所包含的所有恒星自身信息的第一索引数据；基于天文定位恒星星库，生成全天区理论星图、和用于表述全天区理论星图所包含的恒星之间角距信息的第二索引数据。S1: Generate the astronomical positioning star library and the first index data used to express the information of all the stars contained in the astronomical positioning star library; based on the astronomical positioning star library, generate a theoretical star map of the whole sky and use it for presentation The second index data of the angular distance information between the stars contained in the all-sky theoretical star map.
S2：接收至少一帧包括空间碎片和背景恒星的图像，获得图像上在预设检测门限内的恒 星和空间碎片的星象信息；基于获取的恒星星象信息，计算得到任意两颗恒星之间的角距，生成恒星实测星图。S2: Receive at least one frame of image including space debris and background stars, and obtain star information of stars and space debris within the preset detection threshold on the image; based on the obtained star information, calculate the angle between any two stars Distance to generate the measured star map of the star.
S3：根据全天区理论星图和第二索引数据，确定恒星实测星图的上下界限，获取最大角距
Figure PCTCN2020102323-appb-000028
最小角距
Figure PCTCN2020102323-appb-000029
中间角距
Figure PCTCN2020102323-appb-000030
结合最大角距
Figure PCTCN2020102323-appb-000031
最小角距
Figure PCTCN2020102323-appb-000032
中间角距
Figure PCTCN2020102323-appb-000033
按照预设的匹配规则，计算得到恒星实测星图中所包含的与全天区理论星图相匹配的若干个恒星星象。 S3: Determine the upper and lower bounds of the measured star map of stars according to the theoretical star map and the second index data of the whole sky area, and obtain the maximum angular distance
Figure PCTCN2020102323-appb-000028
Minimum angular distance
Figure PCTCN2020102323-appb-000029
Intermediate angular distance
Figure PCTCN2020102323-appb-000030
Combined maximum angular distance
Figure PCTCN2020102323-appb-000031
Minimum angular distance
Figure PCTCN2020102323-appb-000032
Intermediate angular distance
Figure PCTCN2020102323-appb-000033
According to the preset matching rules, a number of stellar images contained in the actual star map that match the theoretical star map of the entire sky area are calculated.
S4：以匹配成功的若干个恒星星象信息为基础，计算得到中心指向偏差、像面旋转角、底片常数模型、相对测光模型。S4: Based on the information of several stellar images that have been successfully matched, the center pointing deviation, the image rotation angle, the film constant model, and the relative metering model are calculated.
其中，测光模型为：Among them, the metering model is:
Figure PCTCN2020102323-appb-000034
Figure PCTCN2020102323-appb-000034
其中，G i是第i颗匹配成功的恒星星象扣除背景后的灰度值，
Figure PCTCN2020102323-appb-000035
是第i颗匹配成功的恒星星象对应的理论星等，i＝1，2，...，N 3，N 3是匹配成功的恒星星象的总数，A和B是采用最小二乘法计算得到的相对测光模型系数。 Among them, G i is the gray value of the i-th matched star after subtracting the background,
Figure PCTCN2020102323-appb-000035
Is the theoretical magnitude corresponding to the i-th successfully matched star image, i=1, 2,..., N 3 , N 3 is the total number of matched star images, A and B are calculated by the least square method Relative metering model coefficients.
简单来说，本发明的技术方案包括以下几个工作步骤：In short, the technical scheme of the present invention includes the following working steps:
(1)理论星图生成。(1) Theoretical star map generation.
(2)恒星及空间碎片星象。(2) Astrology of stars and space debris.
(3)实测星图生成。(3) The measured star map is generated.
(4)理论星图及实测星图匹配。(4) Matching of theoretical star map and measured star map.
(5)指向及像面旋转测定。(5) Pointing and image rotation measurement.
(6)恒星检索。(6) Stellar retrieval.
(7)底片模型优选。(7) Optimum film model.
(8)测光模型计算。(8) Photometric model calculation.
(9)空间碎片天文定位。(9) Astronomical positioning of space debris.
在实际应用中，针对采集到连续的观测图像，通过空间目标检测获得每一帧图像上恒星及空间碎片的星象信息之后，依次采用上述9个步骤，获得空间碎片的天文定位及测光数据。更优化和更具体描述以上各步骤如下：In practical applications, after the continuous observation images are collected, the astrological information of stars and space debris on each frame of image is obtained through space target detection, and the above 9 steps are used in sequence to obtain the astronomical positioning and photometric data of the space debris. A more optimized and more detailed description of the above steps are as follows:
一、理论星图生成1. Theoretical star map generation
按照给定星等的全天区恒星按照赤经增加及赤纬增加的顺序，分区存放，并形成索引，生成天文定位恒星星库及第一索引数据，用于恒星检索使用。按照给定星等门限，选择全天区N 2颗恒星星象，根据恒星的赤经和赤纬信息，采用下式计算任意两颗恒星之间的角距： The stars in the entire sky area of a given magnitude are stored in regions in the order of increasing right ascension and increasing declination, and indexing is formed to generate astronomical positioning star database and first index data for use in star retrieval. According to the given magnitude threshold, select N 2 stars in the whole sky area, and use the following formula to calculate the angular distance between any two stars according to the star’s right ascension and declination information:
Figure PCTCN2020102323-appb-000036
Figure PCTCN2020102323-appb-000036
其中，(α u，δ u)是第u颗第二候选恒星的赤经和赤纬，(α v，δ v)是第v颗第二候选恒星的赤经和赤纬 Among them, (α u , δ u ) are the right ascension and declination of the u-th second candidate star, and (α v , δ v ) are the right ascension and declination of the v-th second candidate star
按照给定门限，比如最小及最大角距，任选三颗恒星组成三角形星图，生成全天区理论星图，并按照每个三角形的角距大小进行排序。生成全天区理论星图库及相应的第二索引数 据，供星图检索使用。According to the given threshold, such as the minimum and maximum angular distance, choose three stars to form a triangular star map, generate a theoretical star map of the whole sky, and sort according to the angular distance of each triangle. Generate an all-sky area theoretical star database and corresponding second index data for star map retrieval.
二、恒星及空间碎片星象2. Astrology of stars and space debris
按照空间碎片检测方法，获得图像上在检测门限内恒星及空间碎片的星象信息，包括其二维平面坐标(x，y)、像素个数、灰度和，按照像素个数减少的顺序对图像进行排序。优选的，可以采用现有技术中的任意一种空间碎片获取方法来获得图像上在检测门限内恒星及空间碎片的星象信息。其中，设图像的左上角为坐标原点(0，0)，图像右侧为x轴增加方向，图像下侧为y轴增加方向，x为图像中星象所在位置在x轴方向上与坐标原点的距离，y为图像中星象所在位置在y轴方向上与坐标原点的距离。According to the space debris detection method, the star information of the stars and space debris within the detection threshold on the image is obtained, including its two-dimensional plane coordinates (x, y), the number of pixels, the gray scale sum, and the image is compared in the order of decreasing the number of pixels. put in order. Preferably, any space debris acquisition method in the prior art can be used to obtain the star information of stars and space debris within the detection threshold on the image. Among them, suppose the upper left corner of the image is the origin of coordinates (0, 0), the right side of the image is the increasing direction of the x axis, the lower side of the image is the increasing direction of the y axis, and x is the distance between the position of the star in the image and the origin of the coordinate on the x axis. Distance, y is the distance between the position of the star in the image and the origin of the coordinate in the y-axis direction.
三、实测星图生成3. Measured star map generation
按照给定门限，选择N 1颗恒星星象，根据恒星星象的二维平面坐标(x，y)，望远镜的焦距为f。采用下式计算任意两颗恒星之间的角距，人选三颗恒星组成三角形星图，生成恒星实测星图。采用下述公式计算任意两颗第一候选恒星之间的角距： According to the given threshold, select N 1 stellar constellations. According to the two-dimensional plane coordinates (x, y) of the stellar constellations, the focal length of the telescope is f. The following formula is used to calculate the angular distance between any two stars, and three stars are selected to form a triangular star chart to generate the actual star chart of the star. Use the following formula to calculate the angular distance between any two first candidate stars:
Figure PCTCN2020102323-appb-000037
Figure PCTCN2020102323-appb-000037
其中，(x j，y j)是第j颗第二候选恒星的二维平面坐标，(x k，y k)是第k颗第二候选恒星的二维平面坐标。 Among them, (x j , y j ) are the two-dimensional plane coordinates of the j-th second candidate star, and (x k , y k ) are the two-dimensional plane coordinates of the k-th second candidate star.
四、理论星图及实测星图匹配4. Theoretical star map and actual star map matching
对于图像上任意三颗定标星i，j，k组成角距大小顺序为
Figure PCTCN2020102323-appb-000038
的三角形，根据理论星图的索引，快速实现候选星图的上下界n，对上下界限中三角形对应角距大小顺序为
Figure PCTCN2020102323-appb-000039
Figure PCTCN2020102323-appb-000040
进行匹配判断。 For any three calibrated stars i, j, k in the image, the order of angular distance is
Figure PCTCN2020102323-appb-000038
According to the index of the theoretical star map, the upper and lower bounds n of the candidate star map can be quickly realized. The order of the corresponding angular distances of the triangles in the upper and lower bounds is
Figure PCTCN2020102323-appb-000039
Figure PCTCN2020102323-appb-000040
Perform matching judgments.
由于f可能不是太准，但是第j颗定标星和第k颗定标星之间依然能够满足下式：Since f may not be too accurate, the following formula can still be satisfied between the j-th calibration star and the k-th calibration star:
Figure PCTCN2020102323-appb-000041
Figure PCTCN2020102323-appb-000041
任意三颗i，j，k定标星之间满足下式：
Figure PCTCN2020102323-appb-000042
和
Figure PCTCN2020102323-appb-000043
Any three i, j, k calibration stars satisfy the following formula:
Figure PCTCN2020102323-appb-000042
with
Figure PCTCN2020102323-appb-000043
五、指向及像面旋转测定。5. Pointing and image rotation measurement.
假设匹配成功了N 3颗恒星，图像上星象二维平面坐标(x i，y i)，i＝1，2，...N 3，星象的理论二维平面坐标坐标(X i，Y i)，i＝1，2，...N 3。 Assuming that N 3 stars are successfully matched, the two-dimensional plane coordinates of the star image on the image (x i , y i ), i=1, 2,...N 3 , the theoretical two-dimensional plane coordinates of the star image (X i , Y i) ), i=1, 2,...N 3 .
利用下式，采用最小二乘方法，计算出系数a，b，c，d，e，f，从而得到中心指向偏差及像面旋转角：Using the following formula, using the least square method to calculate the coefficients a, b, c, d, e, f, so as to obtain the center pointing deviation and the image rotation angle:
Figure PCTCN2020102323-appb-000044
Figure PCTCN2020102323-appb-000044
六、恒星检索。6. Stellar retrieval.
根据图像对应的时间和全天区星图指向测定结果(α p，δ p)，测站经纬度、海拔高度，测站温度、湿度、大气压强，给定视场大小，检索出视场中满足给定星等门限的恒星信息，包括二维平面坐标理论值(X，Y)、赤经和赤纬理论值(α s，δ s)、理想坐标理论值(ξ s，ζ s)、理论星等M，并按照理论星等增加的顺序进行排序。所述理想坐标(ξ s，ζ s)满足以下公式： According to the time corresponding to the image and the measurement results of the star map orientation in the whole sky (α p , δ p ), the longitude and latitude of the station, the altitude, the temperature, humidity, and atmospheric pressure of the station, the size of the field of view is given, and the satisfying field of view is retrieved Star information for a given magnitude threshold, including theoretical values of two-dimensional plane coordinates (X, Y), theoretical values of right ascension and declination (α s , δ s ), theoretical values of ideal coordinates (ξ s , ζ s ), theoretical values The magnitude is M and sorted in the order of increasing theoretical magnitude. The ideal coordinates (ξ s , ζ s ) satisfy the following formula:
Figure PCTCN2020102323-appb-000045
Figure PCTCN2020102323-appb-000045
七、底片模型优选。Seven, the film model is optimized.
根据图像对应视场大小，假设匹配成功了N 3颗恒星，图像上星象二维平面坐标(x i，y i)，及理想坐标
Figure PCTCN2020102323-appb-000046
i＝1，2，...N 3。采用以下六常数、十二常数、十四常数模型计算，根据恒星的定位精度，自动优选底片常数模型(只需优选一次，自动存储优选结果)。 According to the size of the corresponding field of view of the image, assuming that N 3 stars are successfully matched, the two-dimensional plane coordinates (x i , y i ) of the star image on the image, and the ideal coordinates
Figure PCTCN2020102323-appb-000046
i=1, 2,...N 3 . Using the following six-constant, twelve-constant, and fourteen-constant model calculation, the film constant model is automatically selected according to the positioning accuracy of the star (only need to be selected once, and the optimization result is automatically stored).
六常数模型(需要3个以上的定标星)Six-constant model (requires more than 3 calibration stars)
Figure PCTCN2020102323-appb-000047
Figure PCTCN2020102323-appb-000047
十二常数模型(需要6个以上的定标星)Twelve-constant model (requires more than 6 calibration stars)
Figure PCTCN2020102323-appb-000048
Figure PCTCN2020102323-appb-000048
十四常数模型(需要7个以上的定标星)Fourteen constant model (requires more than 7 calibration stars)
Figure PCTCN2020102323-appb-000049
Figure PCTCN2020102323-appb-000049
八、测光模型计算8. Calculation of photometric model
假设匹配成功了N 3颗恒星，星象扣除背景的灰度值为G i，以及对应的理论星等为
Figure PCTCN2020102323-appb-000050
i＝1，2，...，N 3。利用下式，采用最小二乘方法，获得相对测光模型系数A和B： Assuming that N 3 stars are successfully matched, the gray value of the star image after subtracting the background is G i , and the corresponding theoretical magnitude is
Figure PCTCN2020102323-appb-000050
i=1, 2,..., N 3 . Using the following formula, the least square method is used to obtain the relative metering model coefficients A and B:
Figure PCTCN2020102323-appb-000051
LOG有10下标
Figure PCTCN2020102323-appb-000051
LOG has 10 subscripts
九、空间碎片天文定位。9. Astronomical positioning of space debris.
根据空间碎片的二维平面坐标实测值(x T，y T)，采用以下公式获得空间碎片的赤经和赤纬(α T，δ T)： According to the measured values of the two-dimensional plane coordinates of the space debris (x T , y T ), use the following formula to obtain the right ascension and declination (α T , δ T ) of the space debris:
Figure PCTCN2020102323-appb-000052
Figure PCTCN2020102323-appb-000052
其中，(ξ T，ζ T)为空间碎片的理想坐标，由(x T，y T)代入六常数、十二常数或者十四常数模型获得。 Among them, (ξ T , ζ T ) are the ideal coordinates of the space debris, which are obtained by substituting (x T , y T ) into the six-constant, twelve-constant or fourteen-constant model.
计算机系统根据上述输入数据，实时给出了图像上的空间碎片天文定位及测光结果、恒星天文定位及测光结果、指向像面旋转测定结果、恒星检索结果。这些结果可以提供给可以通过显示系统显示出来，以及存储在计算机系统的存储介质中，可以供空间碎片编目定轨及 精密定轨使用，可以根据指向测定结果修正空间碎片的预报位置，有利于提高空间碎片的捕获和跟踪成功率；可以供空间碎片识别使用，评估有姿控空间目标的工作状态及旋转状态等。Based on the above input data, the computer system provides real-time space debris astronomical positioning and photometric results, stellar astronomical positioning and photometric results, pointing image rotation measurement results, and star retrieval results on the image in real time. These results can be displayed by the display system and stored in the storage medium of the computer system. They can be used for orbit determination of space debris cataloging and precise orbit determination. The predicted position of space debris can be corrected according to the pointing measurement results, which is beneficial to improve The success rate of space debris capture and tracking; it can be used for space debris identification and evaluation of the working status and rotation status of space targets with attitude control.
在本公开中参照附图来描述本发明的各方面，附图中示出了许多说明的实施例。本公开的实施例不必定义在包括本发明的所有方面。应当理解，上面介绍的多种构思和实施例，以及下面更加详细地描述的那些构思和实施方式可以以很多方式中任意一种来实施，这是因为本发明所公开的构思和实施例并不限于任何实施方式。另外，本发明公开的一些方面可以单独使用，或者与本发明公开的其他方面的任何适当组合来使用。In this disclosure, various aspects of the present invention are described with reference to the accompanying drawings, in which numerous illustrated embodiments are shown. The embodiments of the present disclosure are not necessarily defined to include all aspects of the present invention. It should be understood that the various concepts and embodiments introduced above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed in the present invention are not Limited to any implementation. In addition, some aspects disclosed in the present invention can be used alone or in any appropriate combination with other aspects disclosed in the present invention.
虽然本发明已以较佳实施例揭露如上，然其并非用以限定本发明。本发明所属技术领域中具有通常知识者，在不脱离本发明的精神和范围内，当可作各种的更动与润饰。因此，本发明的保护范围当视权利要求书所界定者为准。Although the present invention has been disclosed as above in preferred embodiments, it is not intended to limit the present invention. Those with ordinary knowledge in the technical field to which the present invention belongs can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be subject to what is defined in the claims.

Claims (10)

  1. 一种基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，所述实时天文定位和测光方法包括以下步骤：A real-time astronomical positioning and photometric method for space debris based on automatic pointing determination, characterized in that the real-time astronomical positioning and photometric method includes the following steps:
    S1：生成天文定位恒星星库、和用于表述天文定位恒星星库所包含的所有恒星自身信息的第一索引数据；基于天文定位恒星星库，生成全天区理论星图、和用于表述全天区理论星图所包含的恒星之间角距信息的第二索引数据；S1: Generate the astronomical positioning star library and the first index data used to express the information of all the stars contained in the astronomical positioning star library; based on the astronomical positioning star library, generate a theoretical star map of the whole sky and use it for presentation The second index data of the angular distance information between the stars contained in the theoretical star map of the whole sky;
    S2：接收至少一帧包括空间碎片和背景恒星的图像，获得图像上在预设检测门限内的恒星和空间碎片的星象信息；基于获取的恒星星象信息，计算得到任意两颗恒星之间的角距，生成恒星实测星图；S2: Receive at least one frame of image including space debris and background stars, and obtain star information of stars and space debris within the preset detection threshold on the image; based on the obtained star information, calculate the angle between any two stars Distance, generate the star map of the star;
    S3：根据全天区理论星图和第二索引数据，确定恒星实测星图的上下界限，获取最大角距
    Figure PCTCN2020102323-appb-100001
    最小角距
    Figure PCTCN2020102323-appb-100002
    中间角距
    Figure PCTCN2020102323-appb-100003
    结合最大角距
    Figure PCTCN2020102323-appb-100004
    最小角距
    Figure PCTCN2020102323-appb-100005
    中间角距
    Figure PCTCN2020102323-appb-100006
    按照预设的匹配规则，计算得到恒星实测星图中所包含的与全天区理论星图相匹配的若干个恒星星象；     S3: Determine the upper and lower bounds of the measured star map of stars according to the theoretical star map and the second index data of the whole sky area, and obtain the maximum angular distance
    Figure PCTCN2020102323-appb-100001
    Minimum angular distance
    Figure PCTCN2020102323-appb-100002
    Intermediate angular distance
    Figure PCTCN2020102323-appb-100003
    Combined maximum angular distance
    Figure PCTCN2020102323-appb-100004
    Minimum angular distance
    Figure PCTCN2020102323-appb-100005
    Intermediate angular distance
    Figure PCTCN2020102323-appb-100006
    According to the preset matching rules, several stellar images included in the actual star map that match the theoretical star map of the entire sky are calculated;
    S4：以匹配成功的若干个恒星星象信息为基础，计算得到中心指向偏差、像面旋转角、底片常数模型、相对测光模型；S4: Based on the information of several stellar images that have been successfully matched, the center pointing deviation, the image surface rotation angle, the film constant model, and the relative metering model are calculated;
    其中，测光模型为：Among them, the metering model is:
    Figure PCTCN2020102323-appb-100007
    Figure PCTCN2020102323-appb-100007
    其中，Gi是第i颗匹配成功的恒星星象扣除背景后的灰度值，
    Figure PCTCN2020102323-appb-100008
    是第i颗匹配成功的恒星星象对应的理论星等，i＝1，2，...，N 3，N 3是匹配成功的恒星星象的总数，A和B是采用最小二乘法计算得到的相对测光模型系数。     Among them, Gi is the gray value of the i-th matched star after subtracting the background,
    Figure PCTCN2020102323-appb-100008
    Is the theoretical magnitude corresponding to the i-th successfully matched star image, i=1, 2,..., N 3 , N 3 is the total number of matched star images, A and B are calculated by the least square method Relative metering model coefficients.
  2. 根据权利要求1所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，步骤S2中，所述生成恒星实测星图的过程包括以下步骤：The real-time astronomical positioning and photometric method for space debris based on automatic orientation determination according to claim 1, wherein in step S2, the process of generating actual star maps of stars comprises the following steps:
    按照给定门限，从图像中选择N 1颗恒星星象，定义成第一候选恒星，结合第一候选恒星在图像上的二维平面坐标和望远镜的焦距，计算得到任意两颗第一候选恒星之间的角距，选择三颗第一候选恒星组成三角形星图，生成恒星实测星图； According to a given threshold, select N 1 star images from the image and define it as the first candidate star. Combine the two-dimensional plane coordinates of the first candidate star on the image and the focal length of the telescope to calculate one of any two first candidate stars. Select the three first candidate stars to form a triangle star map, and generate a star map of the actual star;
    其中，采用下述公式计算任意两颗第一候选恒星之间的角距：Among them, the following formula is used to calculate the angular distance between any two first candidate stars:
    Figure PCTCN2020102323-appb-100009
    Figure PCTCN2020102323-appb-100009
    其中，f是望远镜的焦距，(x j，y j)是第j颗第一候选恒星的二维平面坐标，(x k，y k)是第k颗第一候选恒星的二维平面坐标。 Among them, f is the focal length of the telescope, (x j , y j ) are the two-dimensional plane coordinates of the j-th first candidate star, and (x k , y k ) are the two-dimensional plane coordinates of the k-th first candidate star.
  3. 根据权利要求1所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，步骤S1中，所述生成天文定位恒星星库、和用于表述天文定位恒星星库所包含的所有恒星自身信息的第一索引数据是指，The real-time astronomical positioning and photometric method for space debris based on automatic orientation determination according to claim 1, wherein, in step S1, said generating an astronomical positioning stellar library and expressing what the astronomical positioning stellar library includes The first index data of all stars' own information refers to,
    将给定星等的全天区恒星按照赤经增加及赤纬增加的顺序分区存放，并形成索引，生成天文定位恒星星库及索引数据。Store the stars in the whole sky area of a given magnitude in the order of increasing right ascension and increasing declination, and form an index to generate astronomical positioning star database and index data.
  4. 根据权利要求1所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，步骤S1中，所述基于天文定位恒星星库，生成全天区理论星图、和用于表述全天区 理论星图所包含的恒星之间角距信息的第二索引数据是指，The real-time astronomical positioning and photometric method for space debris based on automatic pointing determination according to claim 1, characterized in that, in step S1, the astronomical positioning-based stellar library generates a theoretical star map of the whole sky, and is used for The second index data that expresses the angular distance information between the stars contained in the theoretical star map of the whole sky area refers to,
    按照给定星等门限，选择全天区N 2颗恒星星象，定义成第二候选恒星，结合第二候选恒星的赤经和赤纬，计算得到任意两颗第二候选恒星之间的角距，按照给定角距门限，任选三颗第二候选恒星组成三角形星图，生成全天区理论星图，并按照每个三角形的角距大小进行排序，生成相应的索引数据。 According to the given magnitude threshold, select N 2 stars in the whole sky area and define them as the second candidate star. Combine the ascension and declination of the second candidate star to calculate the angular distance between any two second candidate stars , According to the given angular distance threshold, select three second candidate stars to form a triangular star map, generate a theoretical star map of the whole sky area, and sort according to the angular distance of each triangle, and generate the corresponding index data.
  5. 根据权利要求4所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，步骤S1中，采用下式计算任意两颗第二候选恒星之间的角距：The real-time astronomical positioning and photometric method of space debris based on automatic pointing determination according to claim 4, characterized in that, in step S1, the following formula is used to calculate the angular distance between any two second candidate stars:
    Figure PCTCN2020102323-appb-100010
    Figure PCTCN2020102323-appb-100010
    其中，(α u，δ u)是第u颗第二候选恒星的赤经和赤纬，(α v，δ v)是第v颗第二候选恒星的赤经和赤纬，
    Figure PCTCN2020102323-appb-100011
    是第u颗和第v颗第二候选恒星之间的角距。     Among them, (α u , δ u ) are the right ascension and declination of the u-th second candidate star, (α v , δ v ) are the right ascension and declination of the v-th second candidate star,
    Figure PCTCN2020102323-appb-100011
    Is the angular distance between the u-th and v-th second candidate stars.
  6. 根据权利要求1所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，步骤S3中，所述按照预设的匹配规则，计算得到恒星实测星图中所包含的与全天区理论星图相匹配的若干个恒星星象信息包括以下步骤：The method for real-time astronomical positioning and photometric measurement of space debris based on automatic orientation determination according to claim 1, wherein, in step S3, according to a preset matching rule, the calculated and included in the actual star map of the star are calculated. The astrological information of several stars matching the theoretical star chart of the whole sky area includes the following steps:
    S31：根据全天区理论星图和第二索引数据，确定候选星图的上下界限，获取最大角距
    Figure PCTCN2020102323-appb-100012
    最小角距
    Figure PCTCN2020102323-appb-100013
    中间角距
    Figure PCTCN2020102323-appb-100014
    S31: Determine the upper and lower bounds of the candidate star map according to the theoretical star map of the whole sky area and the second index data, and obtain the maximum angular distance
    Figure PCTCN2020102323-appb-100012
    Minimum angular distance
    Figure PCTCN2020102323-appb-100013
    Intermediate angular distance
    Figure PCTCN2020102323-appb-100014
    S32：依次计算上下界限中任意三颗定标星i，j，k组成的三角形的角距，设计算得到的角距由大到小顺序为
    Figure PCTCN2020102323-appb-100015
    根据下述匹配条件，将计算得到的角距
    Figure PCTCN2020102323-appb-100016
    对应
    Figure PCTCN2020102323-appb-100017
    Figure PCTCN2020102323-appb-100018
    进行匹配判断，直至匹配成功N 3颗恒星：     S32: Calculate the angular distances of triangles composed of any three calibration stars i, j, and k in the upper and lower bounds in sequence, and the calculated angular distances from large to small are in the order of
    Figure PCTCN2020102323-appb-100015
    According to the following matching conditions, the calculated angular distance
    Figure PCTCN2020102323-appb-100016
    correspond
    Figure PCTCN2020102323-appb-100017
    Figure PCTCN2020102323-appb-100018
    Perform matching judgment until N 3 stars are successfully matched:
    第j颗定标星和第k颗定标星之间满足下式：The following formula is satisfied between the j-th calibration star and the k-th calibration star:
    Figure PCTCN2020102323-appb-100019
    Figure PCTCN2020102323-appb-100019
    任意三颗i，j，k定标星之间满足下式：Any three i, j, k calibration stars satisfy the following formula:
    Figure PCTCN2020102323-appb-100020
    Figure PCTCN2020102323-appb-100020
    其中，ε 1和ε 2均为预设的角距门限。 Among them, ε 1 and ε 2 are both preset angular distance thresholds.
  7. 根据权利要求1所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，步骤S4中，所述以匹配成功的若干个恒星星象信息为基础，计算得到中心指向偏差、像面旋转角的过程包括以下步骤：The real-time astronomical positioning and photometric method of space debris based on automatic pointing determination according to claim 1, wherein in step S4, the center pointing deviation, the center pointing deviation, The image rotation angle process includes the following steps:
    设匹配成功的N 3颗恒星在图像上的二维平面坐标为(x i，y i)，i＝1，2，...N 3，对应的理论二维平面坐标坐标为(X i，Y i)，i＝1，2，...N 3； Suppose the two-dimensional plane coordinates of the successfully matched N 3 stars on the image are (x i , y i ), i=1, 2,...N 3 , and the corresponding theoretical two-dimensional plane coordinates are (X i , Y i ), i=1, 2,...N 3 ;
    利用下式，采用最小二乘方法，计算出系数a，b，c，d，e，f，从而得到中心指向偏差及像面旋转角：Using the following formula, the least squares method is used to calculate the coefficients a, b, c, d, e, f, so as to obtain the center pointing deviation and the image rotation angle:
    Figure PCTCN2020102323-appb-100021
    Figure PCTCN2020102323-appb-100021
  8. 根据权利要求1所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，步骤S4中，所述底片常数模型的获取过程包括以下步骤：The method for real-time astronomical positioning and photometry of space debris based on automatic orientation determination according to claim 1, characterized in that, in step S4, the process of obtaining the film constant model comprises the following steps:
    结合天文定位恒星星库和第一索引数据，根据图像对应的拍摄信息和全天区星图指向测定结果(α p，δ p)，检索出视场中满足给定星等门限的所有恒星的相关信息，所述满足给定星等门限的恒星的相关信息包括其所对应的二维平面坐标理论值(X，Y)、赤经和赤纬理论值(α s，δ s)、理想坐标理论值(ξ s，ζ s)、理论星等M，按照理论星等由小到大的顺序对检索出的恒星进行排序；其中，所述理想坐标(ξ s，ζ s)满足以下公式： Combining the astronomical positioning star database and the first index data, according to the corresponding shooting information of the image and the whole sky star map pointing measurement results (α p , δ p ), retrieve all the stars in the field of view that meet the given magnitude threshold Related information, the related information of the star meeting the given magnitude threshold includes its corresponding two-dimensional plane coordinate theoretical values (X, Y), ascension and declination theoretical values (α s , δ s ), ideal coordinates The theoretical value (ξ s , ζ s ), theoretical magnitude M, sort the retrieved stars according to the theoretical magnitude from small to large; wherein, the ideal coordinates (ξ s , ζ s ) satisfy the following formula:
    Figure PCTCN2020102323-appb-100022
    Figure PCTCN2020102323-appb-100022
    其中，所述图像对应的拍摄信息包括图像的拍摄时间、指向信息、测站经纬度、测站海拔高度、测站温度、测站湿度、大气压强、给定视场大小；Wherein, the shooting information corresponding to the image includes the shooting time of the image, pointing information, station latitude and longitude, station altitude, station temperature, station humidity, atmospheric pressure, and given field of view size;
    根据图像对应视场大小，结合匹配成功的N 3颗恒星在图像上的二维平面坐标(x i，y i)，及理想坐标
    Figure PCTCN2020102323-appb-100023
    i＝1，2，...N 3，进行常数模型计算，根据恒星的定位精度，自动优选底片常数模型，并且自动存储优选出的底片常数模型。     According to the size of the corresponding field of view of the image, combine the two-dimensional plane coordinates (x i , y i ) of the successfully matched N 3 stars on the image and the ideal coordinates
    Figure PCTCN2020102323-appb-100023
    i=1, 2,...N 3 , the constant model calculation is performed, and the film constant model is automatically selected according to the positioning accuracy of the star, and the selected film constant model is automatically stored.
  9. 根据权利要求8所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，所述进行常数模型计算包括，The real-time astronomical positioning and photometric method of space debris based on automatic pointing determination according to claim 8, wherein said performing constant model calculation comprises:
    结合匹配成功的定标星数量，分别选用六常数模型、十二常数模型、十四常数模型进行常数模型计算，其中：Combined with the number of successfully matched calibration stars, the six-constant model, the twelve-constant model, and the fourteen-constant model are respectively selected for constant model calculations, among which:
    所述六常数模型对应至少3个以上的定标星：The six-constant model corresponds to at least 3 calibration stars:
    Figure PCTCN2020102323-appb-100024
    Figure PCTCN2020102323-appb-100024
    所述十二常数模型对应至少6个以上的定标星：The twelve-constant model corresponds to at least 6 calibration stars:
    Figure PCTCN2020102323-appb-100025
    Figure PCTCN2020102323-appb-100025
    所述十四常数模型对应至少7个以上的定标星：The fourteen constant model corresponds to at least 7 calibration stars:
    Figure PCTCN2020102323-appb-100026
    Figure PCTCN2020102323-appb-100026
  10. 根据权利要求8所述的基于指向自动测定的空间碎片实时天文定位和测光方法，其特征在于，所述实时天文定位方法还包括：The real-time astronomical positioning and photometry method of space debris based on automatic pointing determination according to claim 8, wherein the real-time astronomical positioning method further comprises:
    S5：根据空间碎片的二维平面坐标实测值(x T，y T)，采用以下公式获得空间碎片的赤经和 赤纬(α T，δ T)： S5: According to the measured values of the two-dimensional plane coordinates of the space debris (x T , y T ), use the following formula to obtain the right ascension and declination (α T , δ T ) of the space debris:
    Figure PCTCN2020102323-appb-100027
    Figure PCTCN2020102323-appb-100027
    其中，(ξ T，ζ T)为空间碎片的理想坐标，由(x T，y T)代入六常数、十二常数或者十四常数模型获得。 Among them, (ξ T , ζ T ) are the ideal coordinates of the space debris, which are obtained by substituting (x T , y T ) into the six-constant, twelve-constant or fourteen-constant model.
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