Node bipartition for rigidity and localization of networks with heterogeneous sensing

Graph rigidity theory is an important tool for examining the solvability of sensor network localization (SNL) problems, and ensuring global convergence of localization algorithms. Along this direction, diverse measurements such as signed angle (SA) and ratio of distance (RoD) have been considered. However, little is known about how the bipartition of nodes based on perceptual abilities affects the rigidity property of the network. In this paper, we study the rigidity and localization of networks with heterogeneous nodes, namely, two types of sensors measuring SA and RoD, respectively. Interestingly, the rigidity property is shown to be strongly dependent on the bipartition of nodes, and exhibits a duality. Moreover, an SA-RoD constrained network can be uniquely determined up to uniform rotations, translations, and scalings (global SA-RoD rigidity) even if it is neither SA rigid nor RoD rigid. A scalable approach to construction of globally SA-RoD rigid frameworks is proposed. Localizability analysis and localization algorithm synthesis are both conducted based on weaker network topology conditions, compared with SA- or RoD-based SNL approaches. Numerical simulations are worked out to validate the theoretical results.