The development of star sensors is based on the development of spacecraft and satellites. At present, various models of star sensors have been successfully developed by the United States, Russia, Japan, ESA countries, India, and others, and are widely used in satellites, spacecraft, space shuttles, space stations, and missiles. Most foreign star sensors have characteristics such as high reliability, small integration, full autonomy, large field of view, high data update rate, and high accuracy, which can be applied to orbital spacecraft such as LEO, MEO, GEO, and fully autonomous star sensors can also be applied to deep space exploration. Some foreign star sensors have the ability to calibrate in orbit, and some small field of view star sensors have an accuracy of one angular second or better.
At present, China’s Ministry of Space, Chengdu Institute of Optoelectronics, Beijing Observatory and other units are actively developing star sensors. Compared to the world’s advanced level, China’s overall development level of star sensors is still relatively backward. Mainly reflected in:
① Low accuracy: The wide field of view attitude measurement accuracy in foreign countries can reach up to 1 arcsecond, while currently in China it can only reach around 10 arcseconds;
② The data update rate is low, reaching up to 10Hz in foreign countries and only around 1Hz in China;
③ The lifespan is relatively short, reaching over 10 years abroad, while only a few years can be achieved domestically.
The technology of using American star sensors on stationary meteorological satellites has been developed for many years and has accumulated rich experience. GOES-N improves image accuracy by four times by using a star sensor attitude determination and control system. There are a total of three star sensors installed on the star, including two main machines and one backup machine. The installation angle between the three star sensors is approximately 120 °, and each of them continuously observes the starry sky and selects the first five bright stars in the field of view as observation stars. The star sensor inputs the top 5 bright stars in its current field of view to the onboard computer every 0.1 seconds. The onboard computer determines the precise attitude of GOES-N through star recognition with 5000 known stars in the navigation star database. The onboard computer guides the four flywheels to change gears and redirect the spacecraft to a precise attitude by calculating the difference between the reported and predicted star positions, as well as the angular rate information from the inertial reference unit. Its stable and accurate fixed point observation benchmark enables onboard instruments to achieve maximum directional accuracy. The geostationary meteorological satellite GOES-NEXT in the United States can perform autonomous all star attitude determination, but currently requires a large amount of ground support. GOES13, launched in May 2006, is the first satellite in the GOES N-P series. The GOES N-P image positioning and registration (INR) system design meets the requirements of compact positioning and inter frame registration in the N-P series. Its major innovations include: stellar inertial attitude determination (SIAD) used for precise attitude determination, optical axis reference for imagers and detectors, improved image motion compensation (IMC), and continuous operation of INR during star eclipse. GOES13 has successfully completed post launch testing (PLT) and INR performance certification, and the test results show that the INR performance is better than 100% compared to the previous generation of GOES satellites, and is very close to the performance of the next generation (GOES R) satellites. The reason why GOES-13 has such excellent INR performance is that it replaces the Earth sensitive attitude determination system used by GOES I-M with the SIAD system, and the accuracy of the SIAD star sensor is better than that of the Earth sensor. The SIAD system provides three axis pointing relative to the inertial reference system. The SIAD system is composed of three CCD star sensors (2 main and 1 backup) and two internal redundant inertial reference units (1 main and 1 backup). It is a high-precision, fully autonomous, and fast recovery three-axis attitude determination system.
Many domestic units are competing to develop and tackle star sensors. Compared to the international level, China is still relatively backward in the development and application of star sensor technology, and the use of star sensors on China’s geostationary meteorological satellites is still the first time. The development of the FY-4 meteorological satellite attitude determination algorithm based on star map recognition in ground systems can serve as a ground support and mutual verification method for the attitude determination system on board based on star map recognition.
The navigation star is an important basis for star sensor to achieve star map recognition. How to select a navigation star from the basic star catalog will have an impact on the establishment of the navigation star database, star map recognition algorithm, and satellite attitude determination. Therefore, different star map recognition algorithms choose and establish different navigation star databases. At present, the method for selecting navigation stars is generally based on conditions such as magnitude, excluding binary and variable stars, and setting the minimum diagonal distance of stars from a single catalog. Among them, Kan Daohong et al. analyzed the basic conditions that navigation stars should have and the field density of view of navigation stars; Zheng Sheng et al. used a support vector machine based automatic selection algorithm for navigation stars based on dynamic magnitude threshold to establish a navigation star catalog with a small number and uniform distribution of navigation stars; Liu Chaoshan and others designed a navigation catalog based on trajectory, greatly simplifying the missile borne catalog. S. P. Airey et al. have more stringent conditions for selecting navigation stars in the HYPER high-precision star sensor, only selecting stars with visible magnitudes between [+2.81+3.99] and B-V color indices between [+0.15+1.67], and are not variable or binary stars. Their self motion accuracy is better than 8 × 10-3 arcseconds/year, with declination, declination, and parallax better than 3 × A total of 48 stars in the sky of 10 to 3 arcseconds; Based on the advantages of abundant computing and storage resources in ground application systems, Wang Sujuan et al., starting from improving attitude determination accuracy, combined multiple catalogs with the Hipparcos catalog as the center, and for the first time used precision epoch conversion position accuracy as the basic condition for extracting navigation stars, introduced auxiliary navigation stars, and established navigation star catalogs for different purposes of star map recognition and attitude determination. After selecting a navigation star, additional elements that describe the navigation star are usually stored conditionally based on their respective application purposes. For example, Liu Chaoshan et al. reduced the number of matched star diagonal distances based on the star light guided convex polygon algorithm they used; Chen Yuanzhi et al. used the storage of mid year flat positions to shorten the time for visual position conversion; Tian Jinwen et al. extracted navigation star triangles from the triangles generated by the navigation star catalog based on support vector machines; Xu Shiwen, Li Baohua, and others used 1 to represent a star in each region of the celestial sphere, and 0 to represent a non star in that region. They stored the original string composed of 0 and 1 to support their proposed star map recognition using character matching.
The currently recognized basic catalog with the highest accuracy is the Hipparcos catalog, which is obtained by placing a telescope on a satellite, cross measuring the diagonal distance of stars with large angular distances, and then conducting global adjustment. After about a hundred observations of each star over a period of three and a half years, the positions, parallax, and self motion of nearly 120000 stars were obtained after processing. It has not been found that there is a systematic error in their positions and self motion systems that varies with the sky region, and they are basically a rigid celestial reference frame. Due to the fact that this observation is conducted under the condition of weightlessness outside the atmosphere, it completely avoids the influence of the Earth’s atmosphere and instrument gravity deformation, and the observation accuracy is improved by more than one order of magnitude compared to ground measurements. Hipparcos space observations have made unprecedented progress in optical observation, with the mean square error of positions, parallax, and annual motion obtained for stars brighter than 9 degrees within the range of 0.7 mas to 0.9 mas. The uncertainty of aligning the reference frame of the Hipparcos catalog published in 1997 with the reference frame of the river source at epoch J1991.25 is ± 0.6mas (1 σ)， The remaining rotation rate is ± 0.25 mas/yr, becoming the main implementation of the International Celestial Reference System (ICRS) in the optical band; The Tycho-2 catalog is derived from ESA’s Hipparcos satellite observations and incorporates the results of astronomical catalogs and 143 other ground observation catalogs. The Tycho-2 catalog data has high accuracy, ignoring the systematic error of Hipparcos astronomical data, at a temperature greater than or equal to 6 ° × At a scale of 6 °, the position system error of Tycho-2 is less than 1mas (milliarcseconds), and the self system error is less than 0.5mas/yr.
The star sensor optical system completes optical imaging of the starry sky and captures images of stars within the field of view of the star sensor; Digitizing and processing the image to calculate the specific coordinates of the observation star on the imaging plane or line array is the process of determining the center of mass. Due to the influence of protons on the detector, as well as the influence of space debris, other satellites, the moon, Earth, stray light, solar panels, etc., distinguishing between real stars and pseudostars in the field of view has become the most challenging task. In order to improve the positioning accuracy of the observed star in the star map and achieve sub pixel positioning accuracy of the star centroid, it is necessary to spread the image of the star on the image plane to several pixels, which is called optical system defocusing technology. At the same time, how to extract useful information (star position coordinates) for star map recognition from the original star map image output by the image sensor is an important foundational work in star sensor design. At present, the main algorithms for finding the centroid of star images are the centroid method and fitting method. Tian Jinwen et al. combined high pass filtering and dynamic threshold to extract the position coordinates of stars from star maps; Li Chunyan et al. utilized the principle of cross correlation matching to achieve image positioning, positioning the centroid of the star image to sub pixels to improve centroid accuracy. Wang Guangjun et al. used high-precision interpolation algorithms to treat starlight imaging as a Gaussian point spread function model, and fitted sub pixel level star position and magnitude information using linear interpolation and least squares methods; Liu Jian et al. used the least squares vector machine to perform the best fitting of the grayscale surface on the local area of the original star map, solved the pixel points with the maximum grayscale value on the fitting surface, obtained the preliminary position of the center point of the observed star, and then used the star map pixel clustering method to obtain the accurate center position of the observed star in the star map. Wei Xinguo et al. applied the traditional centroid method, centroid method with threshold, square weighted centroid method, and Gaussian surface fitting method to star subdivision positioning of star image in star sensors. Simulation experiments found that centroid method with threshold is a relatively ideal method for star subdivision positioning. The positioning accuracy of star position coordinates not only affects the accuracy of attitude calculation, but also affects the efficiency of star map recognition algorithms.
So far, there are various star map recognition algorithms proposed for star sensors, with simple and intuitive recognition modes including triangle algorithm, polygon algorithm, matching group algorithm, grid algorithm, and pyramid algorithm; The relatively complex algorithms for identifying patterns include singular value decomposition, genetic algorithm based methods, neural network based algorithms, and string pattern matching. The above algorithms have achieved good recognition results under their respective specific conditions, among which the triangle algorithm is a star pattern recognition method that has been widely used so far. Its basic principle is to use the angular distance between three stars as the feature vector, and store the navigation triangles that can be formed by the navigation stars for search and matching. If a certain observation triangle and a navigation triangle form a one-to-one match, it is considered successful recognition. In cases where the number of navigation stars is relatively large, triangles are prone to redundant (ambiguous) matching, and more stars need to be added for further assistance in recognition. Therefore, when there are relatively many observed stars in the field of view, algorithms such as quadrilateral algorithm, pyramid algorithm, and polygonal algorithm have emerged to further improve recognition efficiency; The main star recognition method proposed by Bezooijen is to use one bright star in the observed star as the main star and the other stars as companion stars. The angular distance between the main star and the companion star is within a given threshold to find the corresponding navigation star pair, and then perform brightness level matching to retain the matching group. Then, the next star is selected as the main star and excess matching star groups are deleted. This algorithm is suitable for all sky star map recognition, with fast recognition speed and high recognition rate, but there are some shortcomings. In the field of view with many similar bright stars, the recognition rate is severely reduced. The above algorithms all rely on the magnitude of stars, and due to various factors such as sunlight or moonlight pollution, measurement errors, and technical limitations, the magnitude of stars cannot be accurately measured. The 4-star matching algorithm proposed by Dong Ying, which does not rely on brightness, constructs a K-vector star diagonal distance for angular distance matching. The accuracy is greatly improved compared to the ordinary triangle method, ensuring the reliability of recognition. However, this algorithm is based on a large field of view (24.5 °) × Based on the small navigation star library (1631 stars), the application range is targeted. Michael Kolomenkin proposed a geometric voting algorithm similar to the matching group algorithm, which states that if the observed star pair and the star pair in the navigation catalog have similar star diagonal distances, they vote for each other. Due to the symmetry of the star diagonal distance, the two observation stars and two navigation stars that make up the star diagonal distance each receive one vote. Generally speaking, the correctly identified observation star pair is the observation star pair with the most votes, This algorithm overcomes the problem of pseudo stars in star maps and achieves good recognition results under large field of view conditions.
The task of determining the attitude of a three-axis stabilized satellite based on star sensors is to use the observation vector information measured by the star sensors, and the navigation star vector information of the corresponding celestial coordinate system identified after the star map recognition process. Through the corresponding attitude determination algorithm, the attitude of the star sensor’s line of sight relative to the celestial reference coordinate system is obtained. Due to the known installation position of the star sensor on the satellite, the transformation matrix between the star sensor coordinate system and the satellite body coordinate system is also known. After obtaining the orientation of the star sensor’s line of sight, the three-axis attitude of the satellite relative to the celestial reference coordinate system can be obtained.
There are various forms of attitude parameters, the most general of which is the directional cosine between the ontology coordinate system and the reference coordinate system. This method is not intuitive and lacks clear geometric image concepts. The Euler angle of rigid body rotation is commonly used to represent the satellite attitude, but Euler rotation has singularities, so attitude quaternion equations are generally used. Quaternion is a vector representation of attitude, with only one redundant parameter. Describing rotation problems using quaternion is more intuitive than Euler’s method. The quaternion equation is linear, avoiding the inherent trigonometric operation of Euler’s angle method. Usually, the accuracy and speed of quaternion method are better than Euler’s angle method, and it avoids the singular phenomena that may occur in Euler’s angle method at large attitude angles. But Euler angles indicate that attitude angles are more vivid than quaternions,
More easily understood, Zhang Fan et al. proposed a conversion algorithm for full angle quaternions and Euler angles, making it easier to convert quaternions and Euler angles. To obtain the attitude of the star sensor’s axis of view from star observation, it is necessary to use the vector of the identified star in the star sensor’s coordinate system and the vector of the navigation star corresponding to the observed star in the inertial coordinate system. After identifying and querying the navigation star library through star maps to obtain measurement vectors and their corresponding reference vectors, there are many algorithms used to determine the attitude of the star sensor’s line of sight. Common algorithms include TRIAD (dual vector pose determination), q method (q method), and QUEST (quaternion estimation algorithm).
Almost all pose determination algorithms based on single frame star maps are based on the constrained least squares estimation method proposed by Wahba in 1965 for pose determination through vector observation – the Wahba problem. Its core is to find the optimal direction cosine matrix A, which minimizes the cost function.
TRIAD (Tri Axial Attitude Determination) is an algebraic pose determination algorithm proposed by Harold Black in 1964, which uses two absolute vectors in two different coordinate systems to obtain the attitude transformation matrix. The literature proposes an optimization algorithm to address the issue that the attitude conversion matrix obtained by the TRIAD algorithm is sensitive to the order of processing vectors and is affected by the first vector. This algorithm calculates the optimal estimation of the attitude conversion matrix by weighting the standard deviations of two different order obtained attitude conversion matrices.
In 1968, Davenport designed a q method for calculating the optimal single frame quaternion, known as the “q method”. By constructing a cost function, he transformed the problem of optimal estimation of quaternion into the problem of finding the eigenvector of the maximum positive eigenvalues of the K-matrix.
The QUEST (Quaternion ESTimator) algorithm proposed by M.D. Shuster in 1981 is a deterministic method that utilizes a point by point solution. It calculates the Davenport feature roots through a Newton Raphson iteration of an optimal initial value. This method solves the rotation problem in the attitude calculation process and introduces the attitude error covariance matrix of the ontology coordinate system and the reference coordinate system, This weakens the attitude error covariance matrix of the inertial reference frame in terms of Euler angles. Afterwards, many scholars improved the QUEST algorithm based on their own applications, F ESOQ proposed by Landis Markeley, Daniele Morary, et al
The EStimator of the Optimal Quaternion algorithm achieves attitude determination suitable for star sensors by correcting the maximum feature roots of the feature polynomial. Many scholars have also developed extended Kalman filtering algorithms for attitude observation equations based on star sensors, as well as kinematic and dynamic equations of space vehicles, according to their respective application needs. Liu Yiwu et al. reduced observation errors by improving the attitude filter observation equation, thereby improving the accuracy of satellite attitude determination. Tian Hong analyzed the factors that affect the accuracy of star sensor attitude calculation, providing a theoretical reference for obtaining high-precision attitude measurement.
Send us a message,we will answer your email shortly!
TY-Space Technology (Beijing) Ltd. is professional focusing on advanced attitude optical sensors, especially Star Trackers for space industry.
