  In this paper, we consider a randomized gossip algorithm for the
bearing-based network localization problem. Let each sensor node be able to
obtain the bearing vectors and communicate its position estimates with several
neighboring agents. Each update involves two agents, and the update sequence
follows a stochastic process. Under the assumption that the network is
infinitesimally bearing rigid and contains at least two beacon nodes, we show
that when the updating step-size is properly selected, the proposed algorithm
can successfully estimate the actual sensor nodes' positions with probability
one. The randomized update provides a simple, distributed, and cost-effective
method for localizing the network. The theoretical result is supported with a
simulation of a 1089-node sensor network.
