# Distributed Localization of Non-Cooperative Targets in Non-Coplanar Rendezvous Processes
## 1 Introduction
[PERSON] et al. [11] conducted a study on the angle-only relative navigation algorithm based on dual line of sight in coplanar rendezvous. They derived its error propagation rule, and proposed that when the two LOS are collinear, the system degrades to single LOS measurement, leading to a significant decrease in positioning performance. [PERSON] [1] enhanced the observability of a dual-LOS navigation system by introducing the baseline distance between two space robots, and they designed a distributed filtering algorithm, which effectively reduces the system dimensions. In this type of research, the trackers and the target are in the same orbital plane, the state model and the configuration optimization model are established based on the relative dynamics of the satellite, and the error propagation law is deduced by analyzing the change in the geometric configuration and the influencing factors. The other type is concerned with the problem of space situational awareness, where the observer does not need to rendezvous with the target. In order to meet the tracking and positioning requirements of high-orbit space targets, [PERSON] [12] studied the orbit determination method for high-orbit targets based on optical bearing-only measurements and improved it by using angle and direction vectors. [PERSON] [13] proposed an initial orbit determination method applicable to space-based target monitoring, which can effectively solve the problem of converging to trivial solutions and reduce the sensitivity of initial distance values in the orbit determination process. [PERSON] [14] designed a multi-LOS scheme for near-field situation awareness (NSA), proposing that when the angle between LOS approaches 90\({}^{\circ}\), the convergence speed and accuracy of target relative estimation errors can be improved. Considering the space environmental factors and the formation relative motion constraints, the NSA formation optimization issue is transformed into a non-linear programming problem for solution. The above studies confirmed that it is feasible to improve the observability of LOS localization by multi-satellite collaboration; however, there are still many issues to be resolved regarding the situation of non-coplanar encounter. For the non-coplanar targets with long distance, traditional relative dynamics models such as the C-W/T-H equations become inapplicable. Therefore, a new multi-LOS positioning scheme needs to be proposed. Similarly, the traditional method based on relative dynamics is no longer suitable for satellites configuration optimization, either. Since the rendezvous problem is constrained by the terminal position constraints of rendezvous, it is difficult to transform it into a non-linear programming problem for solutions. Therefore, new configuration optimization methods need to be explored. In addition, most of the current multi-LOS cooperative positioning schemes use a centralized Kalman filtering method, which will increase the dimensions of the observation matrix and the computational cost, which is not conducive to the implementation of the algorithm [15]. Furthermore, the robustness of the centralized system is poor when the observation data of one tracker are contaminated or lost, as this causes the collapse of the whole positioning system. To resolve the above issues, this paper proposes a distributed three-LOS collaborative bearing-only positioning scheme for non-cooperative target localization in the process of non-coplanar encounter. The orbit dynamics equation considering J2 perturbation is utilized as the state equation, while the Line-of-Sight (LOS) angles of three satellites with respect to the target are employed in the measurement equation. Based on consensus on estimation (CE), a distributed extended Kalman filter (DEKF) was designed as the positioning algorithm, which reduces the system dimensions and improves the robustness of the collaborative positioning system when a single-tracker signal is lost.