Cooperative localization of a cascading quadrilateral network

In this paper, we introduce a set of sensor networks, called the cascading quadrilateral network, and study how to compute the positions of its nodes in a cooperative way. We investigate the condition for determining whether all the sensor nodes are localizable. If not, we provide a method to detect the un-localizable nodes for the whole network. The necessary and sufficient conditions for the network localizability and node localizability are given from the view of algebraic property, respectively. Specifically, we provide algorithms to show how to detect un-localizable nodes from a partially localizable network. Numerical simulation is provided to show the effectiveness of the developed method of computing positions.