  Mutual localization stands as a foundational component within various domains
of multi-robot systems.
  Nevertheless, in relative pose estimation, time synchronization is usually
underappreciated and rarely addressed, although it significantly influences
estimation accuracy.
  In this paper, we introduce time synchronization into mutual localization to
recover the time offset and relative poses between robots simultaneously.
  Under a constant velocity assumption in a short time, we fuse time offset
estimation with our previous bearing-based mutual localization by a novel error
representation.
  Based on the error model, we formulate a joint optimization problem and
utilize semi-definite relaxation (SDR) to furnish a lossless relaxation.
  By solving the relaxed problem, time synchronization and relative pose
estimation can be achieved when time drift between robots is limited.
  To enhance the application range of time offset estimation, we further
propose an iterative method to recover the time offset from coarse to fine.
  Comparisons between the proposed method and the existing ones through
extensive simulation tests present prominent benefits of time synchronization
on mutual localization.
  Moreover, real-world experiments are conducted to show the practicality and
robustness.
