# A Staring Tracking Measurement Method of Resident Space Objects Based on the Star Tacker
## 1 Introduction  
With an increasing number of resident space objects (RSOs), the space beyond Earth is becoming more and more crowded. This greatly threatens the safety of on-orbit spacecraft operations [1; 2; 3]. For protecting spacecraft from potential collisions, it is critical to accurately determine the RSO position in a timely manner [4; 5; 6]. Compared with conventional ground-based observations, space-based optical observations have unique advantages in measuring the RSO position for eliminating the restrictions on weather and terrain [7; 8; 9; 10]. Among space-based optical devices, dedicated measurement payloads such as telescopes are expensive and difficult to manufacture [11]. Therefore, this paper adopted star trackers as the payloads for observing RSOs, because of their advantages in terms of compact structure, low cost, and high precision [12]. The precondition of star tracker imaging is collecting sufficient energy from RSOs [13]. When the star tracker receives enough sunlight radiation reflected from the RSO, the image would have a high signal-to-noise ratio (SNR) and the RSO can be detected [14]. However, this kind of optical observation belongs to the bearings-only passive positioning, which can only directly obtain the angle information of RSOs [15]. Additionally, the measurement arcs are usually less than 20 s through one observation because of the limitations of the star tracker, namely the relative dynamics and the small field of view (FOV). In general, a measurement arc is defined as an excessively short arc (TSA) whose measurement arc is less than 60 s [16]. Under TSA conditions, there are some works which consider the orbit determination (OD) of RSO as an optimization problem. [PERSON] et al. proposeda genetic algorithm (GA) to yield a good estimation of the orbital parameters through genetic operators [17]. [PERSON] et al. proposed a solution group optimization method to consider the error of the estimated orbits on the projection plane for a well-optimized solution [18]. [PERSON] et al. proposed a differential evolution algorithm (EA) with multimodal properties to solve the OD problem from the perspective of multimodal optimization [19]. However, it is still challenging to obtain the accurate orbit determination of RSOs directly from original TSA, because the limited solution constraints can lead to unrealistic and multiple optimal results. Therefore, the researchers prefer to use long measurement arcs to solve the TSA problem and obtain accurate RSOs positions. The main idea of getting sufficiently long measurement arcs is the correlation of short measurement arcs [20; 21]. There have been many studies about the correlation of the arcs obtained from multiple star trackers. [PERSON] et al. proposed a TSA correlation method based on the principle of epiploic geometry, which has a correlation accuracy of more than 90% [22]. [PERSON] et al. calculated the initial orbit parameters by improving the Laplacian method and the fuzzy correlation principle to realize the correlation between the orbits [23]. [PERSON] et al. proposed a space target correlation method based on sine fitting, which distinguishes the space targets from different orbits [24]. These long-arc-based OD methods combine short arcs from the multiple measurements of the same object into one long arc. However, the orbital elements' solutions using multiple short-arc observations will be affected by the specific contingency of the correlation algorithms and the orbital perturbation [25]. Therefore, we need find a way to directly obtain the long measurement arc of the RSO in one observation, which not only increases the arc data, but also reduces the error generated by the correlation algorithms. Satellites are commonly used as a platform in space-based observation missions. Recently, a new dynamic imaging mode based on the high agility of satellites [26; 27], called staring imaging, was proposed for Earth observation in remote sensing [28].