As the most accurate attitude sensor at present, star sensors are widely used in various high-precision positioning and navigation systems, with an accuracy of up to angular second level. Star sensors are independent of orbital motion and are not limited by spatial position. However, traditional star sensors generally have problems with high mass, volume, and power consumption, and their internal algorithms are complex, which cannot meet the customization requirements of small satellites.
How to accurately extract feature information from the star map captured by the CMOS image sensor in the star sensor involves extracting star point targets and obtaining the precise centroid coordinates of the stars on the star map. With the increasing demand for the accuracy of star sensor determination, the accuracy of star target extraction will directly affect the success rate of subsequent star map recognition and the accuracy of attitude determination. Therefore, star target extraction is a key processing part of star sensors.
Star point extraction is the process of locating star point targets on the star map captured by the star sensor and calculating their centroid coordinates in the image coordinate system. Due to the fact that most image detectors on star sensors currently use planar array (CCD, CMOS, etc.) sensors, defocusing and other techniques are used in the imaging process of stars to disperse and diffuse star targets onto multiple pixels. Based on the grayscale distribution of these star targets onto multiple pixels, interpolation and subdivision algorithms can be used to break through the pixel size limitations of image sensors for the centroid positioning accuracy of star targets, Achieve sub pixel positioning accuracy. Therefore, sub pixel interpolation positioning methods have been applied in many fields such as star sensor star point target positioning, biological particle position measurement and tracking, infrared target detection and tracking, and so on.
Jia Hui et al. systematically introduced and summarized the development of subpixel interpolation positioning methods in the literature. The use of subpixel interpolation positioning for centroid positioning of star targets was first applied in astronomical measurements in the 1960s to 1970s. Auer et al. analyzed positioning methods such as centroid method, median method, derivative search method, and Gaussian fitting, and the results showed that Gaussian fitting method has relatively higher star positioning accuracy. Stone and Saleh respectively improved the centroid method and proposed the maximum likelihood estimation method, which promoted the development of subpixel localization methods to a certain extent; The emergence of CCD star sensors in the 1970s played a greater role in the development of star point extraction algorithms. Salomon et al. used the centroid positioning method on the first CCD star sensor and sampled the 4 * 4 pixel window, resulting in a positioning accuracy of star point targets exceeding 1/16 of a pixel; Mcaloon et al. analyzed and studied the star point extraction algorithm on MADAN star sensors, using centroid method, median method, and curve fitting method. They pointed out that the error in star point positioning accuracy mainly comes from the nonlinearity of the algorithm and incomplete sampling. By reducing the sampling window, the sub pixel positioning accuracy reached 1/20 pixel.
In addition, Grossman et al. proposed a Gaussian pixel energy distribution model and energy function for positioning infrared target positions. Through a large number of numerical simulation experiments, it was found that various star point extraction algorithms have errors in the system, and it was verified through experiments that the 3-pixel centroid method has the highest positioning accuracy; According to Seitz’s proposed Gaussian function correlation method, the positioning accuracy of star point targets can reach 0.7% of pixels; Fillard conducted experimental verification on his proposed Fourier phase shift method, achieving a star point target positioning accuracy of 1% pixel; However, due to the influence of pixel energy distribution, these two methods may have significant system errors when the sampling frequency decreases; Rufino proposed a relatively complex neural network-based system error correction method, which can reduce the system error to 0.5% pixels.
In recent years, many scholars have conducted relevant research on star point extraction in terms of signal-to-noise ratio, error factor influence, error influence mechanism, and photoelectric sampling noise influence. For example, Thomas et al. used theoretical and numerical analysis to analyze threshold method, centroid method, weighted centroid method, four grid method, and correlation method, and studied the applicability of algorithms under different signal-to-noise ratio conditions; Hancock studied the relationship between the accuracy of star point target extraction using the centroid method and the imaging size of star point targets, Grossman et al. studied the relationship between the pixel size of imaging sensors and extraction accuracy, etc; Alexander et al. studied the relationship between system error and the actual centroid position of the image point through frequency domain analysis, and explained the phenomenon of system error decreasing as the image point blurs; Zhang Hui and Grossman from Chengguang Institute have analyzed and studied the impact of star sensor imaging noise on star point extraction accuracy, and provided the impact function of relevant noise on star point extraction accuracy.
Star map recognition is based on the feature information of the star image captured by the star sensor and the feature information of the entire sky star map stored inside the star sensor, and through certain algorithms to recognize and match each other’s features to determine the direction of the star sensor’s field of view. The star maps captured by star sensors are mostly constant-star point targets without any other shape features. Therefore, star map recognition is mainly assisted by constant-star and other features, and the relative position between star points is the main feature of star map recognition, which is matched with the navigation star library for recognition. The earliest star map recognition algorithm that emerged was the triangle star map recognition algorithm proposed by Junkins, Strikwerda, Turner, etc. in 1970. The triangle star map recognition algorithm constructs a triangle from three adjacent star points on the star map, and uses the edge length (angular distance) of the triangle as the recognition feature to search in the navigation star database and complete matching. The triangle algorithm is relatively simple in principle and easy to implement, but due to its only three feature dimensions, errors and redundant matching often occur in practical applications, and its anti-interference ability to noise is also weak. In 1993, Liebe reported on the application of the triangle algorithm for autonomous star map recognition on star sensors, and discussed the impact of uncertainty in magnitude and star point positions. Subsequently, various methods for improving and optimizing triangle algorithms, such as introducing magnitude information, using multiple points as features, and improving star libraries, have achieved certain results. However, the issues of redundancy and incorrect matching in triangle algorithms have not yet been resolved.
In 1989, Van Bezooijen also proposed a star map recognition method using star point angular distance and magnitude information as recognition features, called the main star recognition algorithm. It selects one star point as the main star and other star points as companion stars on the observation star map, and searches for the angular distance and magnitude information between the main and companion stars in the navigation star library within a certain threshold range for feature matching. If the matching is successful, the matching group is retained. Then, another star point is selected as the main star, and the matching group is searched to remove excess matching groups, completing the autonomous recognition and matching of the star map. This star map recognition algorithm does not require repeated matching of star points, and has fast recognition speed and success rate, making it suitable for autonomous recognition of star maps in the entire sky area. However, when multiple stars appear on the star map that are close to each other and have similar brightness, redundancy leads to incorrect recognition and reduces the recognition success rate.
Currently, the demand for dynamic performance and anti noise interference ability of star sensors is increasing, which requires star sensors to be able to stably achieve autonomous star map recognition even with large star position and magnitude noise. However, star map recognition algorithms that use star point angular distance and magnitude information as recognition features still exist due to the low dimensionality of the features, Easy to generate redundancy and incorrect matching, making it difficult to meet current application requirements. The algorithm that uses star pattern as star recognition feature effectively solves the problem of redundancy and incorrect matching in star recognition. The grid method is a typical star pattern recognition algorithm proposed by Padgett et al. in 1997. This method uses the grid image generated by binary projection of each star point target on the star map as the recognition feature for star map recognition, greatly increasing the dimensionality of the recognition feature. Moreover, searching in the navigation star database is relatively simple and the recognition speed is fast. However, this method requires the star image to be rotated at a certain angle to achieve correct matching, and the star closest to the identified star should be used as the identification. Therefore, if the identified star is subject to significant noise and other interference, it will have a significant impact on the recognition results, and even result in incorrect recognition. Other methods such as Close used Bayesian decision theory for verification, which showed significant improvement in recognition rate. Silani et al. introduced subgraph isomorphism and Meng Na et al. added star magnitude information during the recognition process. These methods improved the grid and effectively increased the success rate of recognition. However, the problem of rotating recognition is still unresolved.
In addition to the star map recognition algorithms mentioned above, many image recognition algorithms such as Hausdorff [36] distance determination method, K-vector method, singular value decomposition method, neural network method, and genetic algorithm have been introduced into star map recognition in recent years, greatly expanding the variety of star map recognition algorithms.
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