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The localizability analysis for wireless sensor network is of great significance to network localization, and topology control. In this paper, the localizability problem for the bearing-based localization is investigated. An identification method for bearing rigid component is presented, and the localizability is studied for the determined bearing rigid component. In the identification process for bearing rigid component, the center node is introduced, and an approach for identifying the bearing rigid component is proposed based on the characteristic of the bearing rigid graph by using the center nodes. Then, taking the redundancy, and complexity of calculation into account, the node management strategies, and the selection principle for the center nodes are put forward subsequently to provide the guidance for determining all bearing rigid components. The localizability analysis for an determined bearing rigid component reveals its complete localizability with two arbitrary anchor nodes. Finally, some simulation results are provided to demonstrate the effectiveness, and simplicity of the proposed identification approach for bearing rigid components, and to illustrate the superiority of the bearing rigidity-based localization compared with the distance rigidity-based localization from the perspective of localizability.
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