Star sensors are currently the most accurate among attitude sensors, with an accuracy of up to sub angular seconds. They calculate the corresponding three-axis attitude information based on the reference coordinate position of the star in the celestial coordinate system and the actual observation coordinates of the detector plane where the star is located, providing accurate basis for spacecraft attitude measurement and control systems. In addition, star sensors can also be used in fields such as long-range bomber navigation, ballistic guidance, and ship attitude measurement, with broad application prospects.
When the star sensor points towards a certain sky area in a specific attitude, the starlight signal of the target star is imaged on the image sensor through an optical system. The imaging system captures the starry sky image pointed by the current star sensor’s line of sight, and then sends it to the signal processing circuit. By extracting the position coordinates and magnitude information of the star on the detector plane, the star map recognition algorithm finds the corresponding match of the observed star in the navigation database, Finally, based on the direction vectors between these matched star pairs, the three-axis attitude of the star sensor is calculated, and the attitude information of the spacecraft is obtained.
Astronomically, in order to conform to the subjective perception of human observation of the sky, the sky is assumed to be a sphere, which is called the celestial sphere. The celestial sphere is centered around the center of the Earth, with a radius extending to infinity. Due to the infinite radius of the celestial sphere, any finite distance in space can be ignored compared to it, so any point on the ground or near the ground can be considered to coincide with the center of the celestial sphere. Figure 2.3 shows the celestial sphere model, as follows:
(1) Celestial axis and celestial pole: The straight line passing through the center of the celestial sphere and parallel to the Earth’s rotation axis is the celestial axis, as shown in Figure 2.3, pp ‘. The intersection point of the celestial axis and celestial sphere is the celestial pole, divided into north and south celestial poles, corresponding to P and P’ in Figure 2.3.
(2) The celestial equator and celestial equatorial plane: The plane passing through the center of the celestial sphere and perpendicular to the celestial axis is called the celestial equatorial plane, and its intersection with the celestial sphere is called the celestial equator, as shown in QEQ’W in Figure 2.3.
(3) Time circle: The large circle passing through the north and south celestial poles and intersecting with the celestial sphere is called the time circle.
(4) The ecliptic and ecliptic: The average orbital plane around the sun at the center of the Earth is called the ecliptic plane, and the large circle formed by the intersection of the ecliptic plane and the celestial sphere is called the ecliptic. The intersection of a perpendicular line passing through the center of the celestial sphere and perpendicular to the ecliptic with the celestial sphere is called the yellow pole. The angle between the ecliptic and the equatorial plane is the ecliptic angle, which is 23 ° 27 ‘.
(5) Vernal Equinox: The intersection of the equator and the ecliptic at two points, where the intersection where the equator passes from the southern hemisphere to the northern hemisphere is the vernal equinox, corresponding to the point in Figure 2.3 γ。
The celestial coordinate system is based on the definition of the celestial sphere, with the second equatorial coordinate system being the most commonly used in astronomical navigation, as shown in Figure 2.4. It is based on the celestial equator (abscissa circle) and passes through the vernal equinox γ The main circle is the time circle, with the southern celestial pole P ‘pointing towards the northern celestial pole P and the celestial axis P’ P ‘as the Z-axis, passing through the center of the celestial sphere and pointing towards the vernal equinox γ The coordinate axis of is the X axis, which is determined by the right-hand coordinate system rules to point towards the Y axis. The second equatorial coordinate system, also known as the right ascension coordinate system in astronomy, is commonly referred to as the celestial coordinate system. The celestial coordinate system is based on the right ascension α And declination δ Numeric values are used to describe the position of celestial bodies. The declination is measured counterclockwise from the vernal equinox (i.e. opposite to the direction of Sunday motion), with a range of 0 ° to 360 °. The declination is measured north and south from the celestial equator, with a range of 0 ° to 90 ° in the north direction of the celestial equator and 0 ° to -90 ° in the south direction of the celestial equator. Note: Due to the precession and nutation of stars, the position of the vernal equinox will slowly move westward along the celestial equator, resulting in changes in the celestial coordinate system established based on the celestial model at different epochs. Therefore, in practical applications, it is necessary to indicate the corresponding epochs of the celestial coordinate system.
As the observation target of star sensors, stars are the reference basis for attitude measurement. Therefore, it is necessary to study the relevant characteristics of stars. The characteristics of stars can be summarized as follows:
(1) Distance: The distance between a star and Earth is very far, with the nearest star (excluding the Sun) being 4.2 light-years away in the constellation Centauri. Therefore, for star sensors, stars can be considered as celestial bodies at infinity.
(2) Displacement: Stars are not stationary celestial bodies. In fact, stars maintain a high-speed motion state in space, and the speed of star motion can be decomposed into apparent velocity and tangential velocity. Visual velocity refers to the component along the observer’s line of sight (positive when away from the observer, negative when close to the observer), which does not cause a change in the position of the star in the celestial coordinate system. Therefore, there is no need to consider the influence of visual velocity in astronomical navigation; The tangential velocity is perpendicular to the direction of the apparent velocity, and is represented by the displacement of a star on the celestial sphere, which is called its own motion in astronomy. According to observational data, the self motion velocity of stars is mostly less than 0.1 “per year, and the self motion effect should be considered when using star catalogs.
(3) Brightness: In astronomy, the brightness of a star refers to the apparent brightness observed from Earth, which is not only related to the star’s own luminous ability (such as temperature, size, etc.), but also depends on the star’s distance. Astronomers use magnitude (Mv) to characterize the brightness of stars, with lower magnitudes indicating higher brightness. The magnitude difference is 1 degree, corresponding to a brightness difference of 2.512 times, and Vega is designated as a zero degree star standard to define other constellations. In practical applications, the measurement accuracy of magnitude data is generally relatively low.
(4) Size: The actual volume of stars varies greatly, but due to their distance from Earth, all star angles observed from Earth are much smaller than 1 “. In the star sensor model, stars can be approximately equivalent to a point light source.
(5) Spectra: The radiation spectrum of stars is mainly related to the temperature of their surface. Based on the relative temperature of stellar spectral lines, more than 24000 stars are divided into 7 main types such as O, B, A, F, G, K, M, as well as sub types such as R, N, and S. Each type can be further divided into 10 subcategories. In the star sensor model, the star is equivalent to an infinitely distant, approximately stationary point light source with certain spectral characteristics.
Basic Catalog
Astronomy refers to a catalog of stars in the sky that is compiled and compiled according to different needs. At present, some of the catalog data is directly measured by precision instruments, while others are compiled through multiple catalogs. The catalog usually records information such as the position (right ascension, right ascension), brightness (magnitude), spectral type, and self worth of stars. Typical star catalogs include: Hipparcos, Tycho, Smithsonian Astrophysical Observatory (SAO), Guide Star Catalog (GSC), Global Astrometric Interferometer for Astrophysics (GAIA) The United States Naval Observatory (USNO) and CCD Photographic Catalog (UCAC), among others, are listed in Table 2.1 for information related to each catalog.
In star navigation, the SAO catalog is often used as the basic catalog, which has high measurement accuracy and a star position error of 1 “. Therefore, this article uses the SAO catalog as the data source for the corresponding navigation star. In 1966, the Smithsonian Observatory of the United States developed the SAO catalog to meet the technical requirements of determining the position of space vehicles through photography. The current version of the SAO catalog comes from the HEASAC database version provided by NASA (National Aeronautics and Space Administration). Compared with the previous version (1984 version), some duplicate and incorrect data have been deleted and modified accordingly, And provided the position and self motion data of the standard epoch J2000, which includes a total of 258997 stars with brightness higher than 11Mv. There is a significant correlation between the number of stars in the catalog and their magnitudes. As the magnitudes increase, the corresponding number of stars increases rapidly. Table 2.2 shows the statistical results of the number of stars in the SAO catalog with magnitudes below 8.0Mv changing with their magnitudes.
For star sensors, the effective information in the catalog is mainly the position and brightness data of stars. The projection point of a star on the celestial sphere is called the position of the star, which corresponds to the declination and declination data in the star table. The positions of stars recorded in the SAO catalog are their flat positions during the standard epoch (J2000). To meet the high-precision attitude calculation requirements of star sensors, astronomical corrections need to be made to the self motion, precession, nutation, and other effects of stars in the standard catalog to obtain their corresponding apparent positions, i.e. the coordinates of stars in the celestial coordinate system at the observation time. For simplicity, this article directly uses the declination and declination in the standard catalog as star position data. In addition, the magnitude value of a star is closely related to the spectral responsivity of the receiver. In practical applications, it is necessary to fully consider the spectral type of the star itself and the spectral responsivity function of the star sensor detector pixels, in order to convert the apparent magnitude into the instrument magnitude. The star sensor model studied in this article mainly detects in the visible light band, and the apparent magnitude in the SAO catalog is directly used here. Star sensors use the basic star catalog as the data source for constructing a navigation star database, where stars with brightness higher than the star sensor’s maximum magnitude can be detected by the star sensor, known as observation stars. According to certain selection rules, select a portion of stars from the observation star set for star map matching, and then determine the three-axis attitude of the star sensor. Due to their navigation function for space vehicles, they are called navigation stars.
The Catalog properties list:
Statistical results of the number of stars with magnitude in the SAO catalogue:
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