Accurate Pointing Determination of Space Targets under the Stars Background

This study proposes a method for determining the direction of space targets using existing satellite constellations. Usually, when optical satellites point towards deep space for imaging, stars inevitably appear in the image. This study conducts all targets extraction, star identification, camera calibration. Ultimately obtaining high-precision space targets longitude and latitude information. One of the Jilin-1 GF06A series satellite was used to conduct observation experiments on space targets of this study. Each scene has an exposure time of 10 seconds, and a total of 90 seconds of observation data was obtained. This study analysed the results of star extraction and the identification result which indicate that GF06A can capture a maximum magnitude of 15.6. After using the extraction star coordinate information for calibration, the interior accuracy of camera was better than 0.48 arcseconds. Then, the precise longitude and latitude information of 5 space targets were obtained. Finally, cataloguing information of these stars is provided, which is beneficial for determining the orbit of the target in the future.


Introduction
With the increasing number of objects such as artificial satellites, rocket bodies and their debris orbit the Earth, space target monitoring has become an important task in the aerospace field.The risk of spacecraft damage caused by space debris impacts is the third largest risk, second only to risks related to launch and deployment phases (Lupo et al., 2018).At present, space targets are mainly achieved through ground-based observation, including target catalogue, pointing determination, and orbit determination.Traditionally, there are two methods for ground observation: optical and radar (Liu et al., 2022).Ground based radar observation is not affected by light and is not limited by instrument's weight and size.The larger the radar antenna and power, the higher the detection accuracy of the target and the farther the detection distance.However, the signal loss of the target is proportional to the fourth power of the distance, and ground radar monitoring is usually limited to low Earth orbit (LEO) targets.The detection method of ground-based optical, where the brightness attenuation of the space target is proportional to the square of the distance, can be used to detect targets in higher orbits.The European Space Agency (ESA) has established the Schmidt telescope to detect objects up to 15cm in size in geosynchronous orbit (GEO).The simulation results show that the estimation accuracy of satellite position is better than 5 arcseconds (Samadzadegan et al., 2013).However, due to factors such as atmospheric environment, sunlight, and weather, the size and accuracy of space targets monitored by ground-based optical monitoring are limited.In addition, due to the latitude limitation of a single foundation system, the sustained observation ability of certain targets is restricted for ground based observation (Gruntman et al., 2014).
In recent years, the gradually established LEO satellite constellations can be used to observe and measure space targets, effectively avoiding the above drawbacks.For instance, the U.S. DoD (Department of defence) is planned to establish a constellation for tracking space objects, which is called the SBSS (Space-Based Surveillance System).The Canada has been also designed for the monitoring of space debris from LEO as part of the Canadian space surveillance system (CSSS) (Lupo et al., 2018).As shown in Figure 1, this study mainly uses Jilin-1 optical satellite constellations in LEO to observe space targets in medium to high orbits, such as satellites in high elliptical orbits (HEO) and GEO satellites.
During the process of imaging with an optical camera aimed at deep space, stars inevitably appear in the image and are confused with the target information.The recognition and extraction of stars can not only eliminate the interference of stars, but also can be used as stars control points (SCPs) to improve the pointing accuracy and eliminate interior distortions of the camera (Guan et al., 2023).Thereby, the pointing determination accuracy of the space target could be further improving.
Figure 1.The LEO constellations observe HEO and GEO target.

Method
This study will achieve high precision pointing determination of space target through four steps as Figure 2 shown.First, the data is pre-processed to remove background noise from the image, and all the potential targets are extracted.Second, identify stars within the camera's field of view based on the geometric imaging model and existing star catalogue data.The third step has two optional options, one is to calibrate the camera based on the extracted stars.Another step is to remove the extracted stars and filter out the space targets in the image.Finally, based on the attitude of the satellite, camera parameters, and the coordinates of the target in the image, the precise pointing direction of the target can be calculated.

Potential Targets Extraction
When the camera photo the deep space, the background is black.
But the camera has a certain background noise due to factors such as sensor current.It needs to be segmented by the threshold to separate the targets and the background in the image.Assuming that the digital number (DN) value of the image containing the space target is expressed as (, ), and  is the background threshold, the image binarization is: Since this experiment involves deep space photography at different orbital positions, the image will inevitably be affected by sunlight at some imaging angles.Therefore, the size and distribution of background noise vary, and thresholds can be set based on the mean and variance of the entire image.
The part of (, ) with a value of 1 is marked by the connected domain algorithm, and  groups of connected domains Ω  ,  = {1,2, … } are obtained.Each group of connected domains is composed of different numbers and adjacent pixels, which can be expressed as follows: Each connected domain combination is a potential target (star or space target).If the attitude remains unchanged in the inertial frame during satellite imaging, the stars are shown as a round shape.By calculating the area and circularity of the connected domain, some brighter stars can be preliminarily filtered out.The round rate calculation formula is as follows (Guan, et al., 2022): among them,  represents the round rate,  represents the area of the connected domain, and  represents the perimeter of the connected domain.From the relationship between the circular area and the perimeter, it can be seen that the closer  is to 1, the more circular the connected domain is.Usually, the round rate of the star is greater than 0.6.
When the stars are filtered out, the centroid coordinates (, ) of the star coordinates can be extracted by the grey square weighted centroid method.The calculation formula is:

Identify Stars
It is difficult to perform star identification directly based on the extracted stars.Because typical star identification requires a large number of bright stars in the field of view (usually brighter than 7th magnitude stars).However, the field of view of satellite cameras is small, and there may not be a bright star in image.But we can use satellite imaging models, combined with detailed star catalogues, to obtain the possible positions of stars in the image.Furthermore, distinguish between stars and non-star targets in the image.So, the geometric relationship between the image-side and the object-side is the key to this study.
According to the small hole imaging model, there should be a one-to-one correspondence between the star vector obtained by the camera and the star catalogue vector.The ascension and declination of the -th star in the J2000 coordinate system are (  ,   ), which can be expressed as the azimuth vector   : When the -th star is photographed, the attitude matrix of the camera in the J2000 coordinate system is  2000  , then the relationship between the vector   (the -th star in the camera coordinate system) and   is: After imaging by the camera, the coordinates of the -th star on the image are (  ,   ), then the relationship between   and the coordinates of the image point is: among them,  is the main distance of the optical lens of the camera, and ( 0 , 0 ) is the intersection of the optical axis of the camera and the image plane.According to the above formula, the calculation formula for the coordinates of the -th star can be obtained as: Bring all the stars from the star catalogue into formula ( 5), ( 6), ( 7) and ( 8), then the stars which will be projected on the image are selected.Comparing the distance between the projected stars and the extracted targets.Within a certain threshold range, the pairing is considered as stars.And the corresponding relationship between the star coordinates in image and the right ascension/declination of stars in the J2000 system is established.

Camera Calibration
The above calculation process did not consider the error of camera's exterior and interior parameters.The accurate camera exterior parameters can be easily calculated based on the formula (6) (Guan et al., 2019).The interior distortion of camera can be divided into two types: radial distortion and tangential distortion.
Usually, taking the first order of two kinds of distortion can well fit the lens distortion.Therefore, the distortion model is expressed as follows (Chen et al., 2022): where,  = √(  −  0 ) 2 + (  −  0 ) 2 ,  1 represents first-order radial distortion, and  1 and  2 represent two parameters of firstorder tangential distortion.The angular distance between any two stars, can be considered constant.So, for the star a and star b, the angle   between them is unchanged, and has the following relationship: =      = (  )    =        =      (10) According to the corresponding relation, the error model can be constructed for all the identified stars.The interior orientation parameters of camera to be estimated are: The error model is as follows: The least square iteration method can effectively estimate the above parameters, and after several iterations, the estimated value tends to be stable.

Space Target Pointing Determination
Based on all the targets extracted in the first step, excluding the stars extracted in the second step, potential space target coordinates are obtained.Suppose that the coordinates of the space target in the image plane coordinate system are (  ,   ).
The target pointing determination could be composed of the right ascension and declination (α, δ) as: On the right side of the formula ( 15) are all known quantities, including the attitude of the camera   2000 and the interior parameters (  0 ,  0 ,  ) after camera calibration.The right ascension and declination (α, δ) information of space targets in the J2000 coordinate can be accurately obtained.

Data
In just one launch mission on Jun. 15 th , 2023, more than 30 GF06A satellites were launched, making this series of satellites very suitable for tasks such as space target detection and monitoring.Figure 3 shows the satellite structure design diagram of Jilin-1 GF06A series.The GF06A series satellites can provide video and push-broom imaging, with a ground resolution of 0.75m and a satellite weight of only 22kg.Table 1 provides more detailed information on this series of satellites.The data for this experiment comes from a deep space imaging mission of the GF06A-20 satellite on January 22 nd , 2024.The imaging time for this task was 90 seconds.Each image was exposed for 10 seconds and a total of 9 images were captured.

Experimental Result and Analysis
In the following part of this study, we will provide a detailed result to the key parts used for accuracy pointing determination of space targets, namely star extraction, star identification and camera calibration.There are many stars in the images captured in deep space.As shown in Figure 4, there are three typical sets of original deep space images and denoised images.These images are all captured from a small portion within the complementary metal oxide semiconductor (CMOS) field of view.The first set of original images contains a brighter star.The second set of target motion trajectories and stars appear simultaneously.The third set of original images can extract numerous stars after denoising.Statistics were conducted on all stars within the field of view, and Figure 5 provides images of typical stars and their coordinate information in the image and object sides.From the brightest magnitude of 6.08 to the darkest magnitude of 15.62.As the magnitude increases, the area of stars in the image becomes smaller and harder to identify.
Figure 5.Typical stars and their coordinate information.
In this deep space photography experiment, the attitude of the satellite in the inertial frame remains unchanged.So, within a 90 second imaging time, the stars within the field of view are basically the same for each CMOS.Each image is exposed for 10 seconds, so we can stack 9 images together.Figures 6 and 7 show the results taken by CMOS 1 and CMOS 2, respectively.The black origin is the position of the stars calculated through the star catalogue, and the larger it is, the brighter the stars (the smaller their magnitude).The red circle represents the stars identified in this study, with a maximum identified magnitude of 15.6.After the detection of this study, one space target was found in CMOS1, and four space targets were found in CMOS2.The red box in Figure 6 represents the position of the target in the 7 scenes.The number of times each space target appears in Figure 8 is different because they do not appear simultaneously.But the changes in these positions can reflect the motion of space targets in inertial coordinate.In a relatively short period of time (within a few years), the relative positions between the majority of stars in the sky are fixed.Therefore, the angular distance between two stars should be a fixed value and consistent with the calculated values in the star catalogue.Due to the orientation element error within the camera, there may be errors in the angular distance.Through these obtained stars, we can correct the camera's pointing.Due to the abundance of stars, we can even construct distortion models to obtain more accurate camera interior parameters.Before proceeding with the next step of space target extraction, it is necessary to perform the above two steps to achieve precise camera orientation.As shown in the Figure 8, the error of star diagonal distance before and after camera calibration.Before calibration, the root mean square error (RMSE) of the camera's star diagonal distance was 6.33 arcseconds, and after calibration, the RMSE was 0.48 arcseconds.Therefore, correcting the camera is a crucial step in determining the direction of space targets.
In this mission, due to long time exposure, a continuously moving target appeared in the field of view and formed a trajectory on the image.As shown in Figure 9.The left image is from the scene 4 of CMOS 2. S1 is the position of the space target at the beginning of the image exposure, and S2 is the position at the end of the image exposure.The white lines represent the motion trajectory of the space target during a 10 second exposure time.The image on the right is from the scene 5 of CMOS 2. After the previous scene ends exposure, the next scene starts exposure again.So, the starting exposure position S2 is exactly the same as the previous scene, and the ending exposure position is S3.The corresponding relationship between stars in the two graphs also reveals the trajectory of continuous motion of space targets.Due to the long duration of the entire trajectory, within the 10 second exposure time range, we are unable to determine the corresponding time for the middle part of the trajectory.But we can know the time when the trajectory starts or end to appear in the image.Therefore, we can measure the image coordinates of the starting position of the space target trajectory in each scene.Then, using the camera geometry model, accurate space target pointing determination results are obtained.By comparing the target grayscale value with the star grayscale value, it can be found that the grayscale value of the target is close to that of a 15-magnitude star.This is a very low brightness value, indicating that this series of satellites has great potential in space target detection.In the subsequent detection tasks, the exposure time of each scene will be reduced to obtain more target pointing information at different time.In this way, the movement pattern of the target can be calculated based on the position of the satellite, the direction of the target, and orbital dynamics.

Conclusion
This study proposes a method for pointing determination of space targets through satellite observation on deep space.The focus of this method is to extract the stars and use them to calibrate the camera.Finally, the high precision pointing of the space target can be calculated and cataloguing.

Figure 4 .
Figure 4. Original deep space images and background noise removal results.

Figure 6 .
Figure 6.Star identification and space target extraction results of CMOS1 after stacking multiple images.

Figure 7 .
Figure 7. Star identification and space target extraction results of CMOS2 after stacking multiple images.

Figure 8 .Figure 9 .
Figure 8. Star diagonal distance before and after calibration