Distributed estimation of both position and orientation for networked systems on the sphere

In this paper, we propose a distributed localization algorithm for the networked multi-agent system on the sphere domain. Each agent only measures the relative position of neighbors with respect to its own local reference frame. The proposed algorithm exploits kinematic relationships between relative position and relative orientation; relative orientation of neighboring agents is calculated by the relative positions. We show that the relative orientation is sufficient to estimate both orientation and position for the networked system on the sphere. The result implies that localization problem of networked system can be solved by using only relative position measurement in the case of misaligned local frames.