Distributed network localization using angle-of-arrival information Part I: Continuous-time protocol

In this paper, we propose a distributed continuous-time linear dynamics for solving the localization problem based on signal angle-of-arrival information. We first formulate the AOA localization problem within the framework of formation graph theory, which is an extension of the classical graph theory by incorporating the positional information of the vertices. Solving the AOA localization problem is equivalent to finding the solution to a system of linear equations. To avoid matrix inversion, we propose a continuous-time dynamics whose global asymptotic equilibrium is the desired localization. This dynamics turns out to have a very similar expression to that of the continuous-time consensus dynamics. The convergence and delay performance of the protocol is also studied. We finally argue that through optimizing the condition number of the stiffness matrix, the convergence and delay performance of the protocol can be simultaneously improved.