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Network localizability with link or node losses

The ability to localize a sensor network is important for its deployment. A theoretical result exists defining necessary and sufficient conditions for network unique localizability (for inter-sensor range-based localization); it has its roots in Graph Rigidity Theory where sensors and links/measurements are modelled as vertices and edges of a graph, respectively. However, critical missions do require a level of robustness for localizability, ensuring that localizability is retained in the event of link (edge) losses and/or sensor (vertex) losses. This work characterizes this robustness through a novel notion of redundant localizability, which is backed by redundant rigidity. Analogously to two well-known types of result for rigidity characterization, similar results are developed for edge redundant rigidity; they are supplemented by rather fewer results dealing with vertex redundant rigidity. These preliminary results may shed a light for any further study of redundant localizability.