Fixed-time Bearing-based Distributed Network Localization

This paper studies the fixed-time distributed localization problem for directed network based on bearing measurements. The orientation of the global coordinate system is not available to nodes whose local coordinate systems do not to be aligned. First, the barycentric coordinate representation is obtained relying only on the bearing information. Then, a fixed-time distributed network localization algorithm is proposed. By applying the proposed algorithm, the localization problem is converted to the consensus tracking problem for localization errors. When nodes distribution and communication topology meet the requirements, one can prove that the position estimates can convert to the truth after a fixed time. Finally, the simulation verifies the validity of the algorithm.