3-D Network Localization Using Angle Measurements and Reduced Communication

Other than the relative position-based and bearing-based localization with aligned coordinate frames on all sensor nodes, the existing 3D network localization algorithms using distance/bearing/angle measurements without aligned coordinate frames usually require each node to have at least four neighbors, which poses large communication burden for the network system. To reduce the communication burden in each iteration, this paper studies the 3D network localization problem where each node is allowed to have angle measurements with respect to only
three
neighbors. Firstly, we use a tetrahedral angularity to describe the network consisting of a set of nodes and tetrahedra among the nodes. Given that at least one node in each tetrahedron has the knowledge of the direction of the global
$Z$
-axis, the geometric constraint of each tetrahedron is described by an angle-induced linear constraint whose coefficient matrices are only related to the interior angles among the four nodes in the tetrahedron and the angles between the global Z-axis and the inter-node edges. Secondly, both algebraic and topological localizability conditions are derived based on the coefficient matrices of the tetrahedra’s angle-induced linear constraints. Moreover, a distributed method is also presented to check the network localizability. Lastly, distributed localization laws are designed under the cases of continuous communication, aperiodic communication, and aperiodic communication on jointly localizable angularities, respectively. Simulation examples are provided to validate the effectiveness and advantages of the proposed localization laws.