Short-arc association algorithm for joint observation of multiple star sensors

star sensors is a high-precision attitude sensor with the ability to shoot space targets intermittently.It can be used as a new type of space target monitoring platform.Accurately associating the track segments of the star sensor with intermittent observations is the prerequisite for precise orbit determination of space targets.In order to solve the problem of trajectory association where the initial orbit cannot be determined because the target observation time is too short,a short arc association algorithm for space targets based on hypothetical boundary values is proposed.By using the multi-satellite sensor joint positioning method,only the angle measurement data of the star sensor are converted into the spatial coordinates of the target,and each point from the track segment to be associated is taken as a boundary.Based on the boundary association hypothesis,the theoretical values of the space target orbit under all assumed boundary conditions are calculated.The Mahalanobis distance and chi-square test are used to make related judgments.The algorithm in this paper can better adapt to many-to-many track association,and can reject uncorrelated tracks more accurately.After simulation,the algorithm in this paper is superior to the short arc correlation method based on the admissible region to determine the initial orbit and sine fitting in terms of association accuracy and execution time.

Based on the synchronized association results of spatial targets observed by multiple star sensors, the least squares method is used to fuse the angle measurement data observed by multiple star sensors at the same time, and calculate the coordinates of each spatial target in the J2000 coordinate system. When the standard deviation of star sensor position error is 100m and the standard deviation of angle measurement data error is 2 ″, the standard deviation of spatial target positioning error is 1.977 1km, which is sufficient to meet the accuracy requirements of subsequent correlation steps. The application premise based on assumed boundary values and sine fitting correlation algorithm is that at least two star sensors are required to observe spatial targets. According to the relevant research in the literature “Research on Universal Sensing Technology of Spatial Targets Based on Star Sensors”, 90% of synchronous orbit band targets can be synchronously observed by two or more star sensors.
Take a point from each new and old trajectory as the boundary, establish a set of all assumed boundaries, calculate the theoretical values of the space target orbit under all assumed boundary conditions, and use Markov distance and chi square test as the trajectory correlation criteria. After simulation verification, when the noise is Gaussian white noise (2 ″, 100m), the accuracy of the correlation between two sets of tracks with an interval of 10 hours can reach 95%. Compared with other short arc association algorithms, the trajectory association algorithm based on assumed boundary values has significant advantages in association accuracy while maintaining a faster operating speed.
The shortest observation used in the simulation is only 50 seconds, and the initial orbit cannot be determined using conventional orbit determination methods, which conforms to the definition of short arcs. The trajectory association algorithm based on assumed boundary values achieves the problem of trajectory association where the initial orbit cannot be determined due to the observation arc being too short. Moreover, the algorithm is not only limited to short arc association, but is also applicable to general trajectory association problems. If future inter satellite links can achieve data sharing between satellites, the process of spatial target association can be achieved on satellites without the need to transmit a large amount of data back to the ground. Due to the limited computing resources of satellites, algorithms should not be overly complex. Among the three short arc correlation algorithms, the trajectory correlation algorithm based on assumed boundary values is more conducive to achieving onboard data processing.
Considering that the actual measurement errors of each platform may vary, corresponding weights will be assigned to the observation errors of different platforms in the future to further improve the positioning accuracy of spatial targets. At present, star sensors are only used as attitude sensors in engineering, and the combination of measured data and simulation software can provide reference for subsequent engineering applications. With the development of new small field of view and high limit magnitude star sensors, further research on spatial object extraction will be conducted in real star maps in the future.