The observation of space objects under the sky survey mode requires a wide field of view, which benefits the acquisition of the objects of interest and also provides us with long observable arcs for their precise orbit determination. Meanwhile, with the continuously improving scientific complementary metal oxide semiconductor (sCOMS) processing and integration, data processing of massive high-resolution images including astronomical positioning of space objects has become notably challenging for the timely objects’ detection and following observation deployment. Star map matching, especially for a large amount of stars in wide-field-of-view images, is the most time-consuming procedure in astronomical positioning. Obvious edge effects in wide-field-of-view image processing can lower the calculation accuracy. Thus, we adopt the method of gradually increasing the center localization of the images for programming acceleration and then employ three-order plate constants fitting to reduce the positioning error of the objects observed in the edge localization in wide-field-of-view observations.

After selection and reduction of the star catalog, the stars in the sky area are compiled into the navigation stars’ list. By employing the standard coordinate system, the navigation stars are projected to the focal plate to be recognized (Fig. 1). Meanwhile, we adopt a dimension reduction method to compare every two star pairs with the same partner rather than triangle matching conducted within three stars. In the actual algorithm implementation, a dynamic data structure based on red and black tree (RB-Tree) is utilized to adapt to the increasing center. RB-Tree balances the computational complexity of the data insertion (Fig. 2) and then the angle distances between either observation or navigation stars can be efficiently organized in every-cycle center increase. Additionally, we extend the original in-order traversal for all data in the range visited (Fig. 3). Finally, the suitable initialization and enlargements in the center increase can be fixed (0.5° and 0.1° respectively in our study), but not set based on the center quality judged by the operators. To more precisely position the objects outside the center, we afterward employ the GeoHash encoding technology to match the stars in the catalog with the stars observed (Fig. 4). We encode the celestial coordinates of navigation stars with five-digit precision (for detailed precision of GeoHash encoding in Table 1) and then the observation stars by the previously calculated plate constants of the center localization. Therefore, the matching can be made by comparing the GeoHash of the navigation stars (and eight neighbors of each) with their counterparts (Fig. 5). In the massive data application, GeoHash encoding and relevant operations instead of the two-dimension data matching by traversal in the whole sky area can provide matching acceleration and potential of parallel computing in data searching.

All employed data are from recent real observations (using the instrument shown in Fig. 6, from which an observation image and its initial center localization are shown in Fig. 7) to test our method. Firstly, by testing the increasing ordered fitting constants and their coverage of the matched area in the whole frame, the model of 20 plate constants is determined in the matching (Figs. 8 and 9). Then the experiments for its performance are carried out. By comparing the results of eight objects’ positioning with those of the system built-in software, the errors are both in 5″, which sufficiently shows the correction when the image taking with about 6″ per pixel is considered (Fig. 10). Additionally, we organize multi-sky-area observations to test its speed, in which the calculation time of triangle matching can be reduced by 70.68% compared to the previously proposed algorithm which is referred to as searching sorted array method (Fig. 11 and Table 2). According to the experiments of the orbit correlation of 12 satellites tracked by laser ranging (SLR), the differences (O-C) are all in 20″. Furthermore, multi-pass positioning indicates sound wide-field-of-view uniformity by the similar value of the center and the edge fields (Fig. 12). The long-period experiment of the proposed method in one month indicates that the data post-processing can be completed within two hours after the observation. The method successfully matches about 650,000 frames of images total with a recognition accuracy of over 90%, and 580 objects on average can be recognized per observation night. The root mean square (RMS) value of the SLR positioned among the objects is comparable to that obtained by the system built-in software (Fig. 13).

The sub-image isomorphism characteristics can be expressed in different scales, but too small area may lose identifiability and too large area reduces the recognition efficiency. As a result, a gradually increasing center matching could be an ideal method to process wide-field-of-view star maps, in which the dynamic data structure of RB-Tree is employed to save the frequent re-sorting time in the performance. Meanwhile, to precisely position the objects at the edges of observation images, we adopt high-order plate constants as a feasible practice to explain some edge effects, such as optical distortion and atmospheric refraction discrepancy. To this end, whole image matching is necessary, in which the GeoHash encoding method is adopted to deal with the large data load. The experiments of the real observations show that the accuracy of our method can be proved both in multi-object positioning and SLR orbit determination. By utilizing the proposed method, the time consumed per frame can be controlled in about 1 s to save some hours for one-night data processing.