This paper addresses the problem of mutual localization in multi-robot systems in presence of anonymous (i.e., without the identity information) bearing-only measurements. The solution of this problem is relevant for the design and implementation of any decentralized multi-robot algorithm/control. A novel algorithm for probabilistic multiple registration of these measurements is presented, where no global localization, distances, or identity are used. With respect to more conventional solutions that could be conceived on the basis of the current literature, our method is theoretically suitable for tasks requiring frequent, many-to-many encounters among agents (e.g., formation control, cooperative exploration, multiple-view environment sensing). An extensive experimental study validates our method and compares it with the full-informative case of bearing-plus-distance measurements. The results show that the proposed localization system exhibits an accuracy commensurate to our previous method [1] which uses bearing-plus-distance information.