A distributed continuous-time algorithm for network localization using angle-of-arrival information

This paper studies the angle-of-arrival (AOA) localization problem, namely, localizing networks based on the angle-of-arrival measurements between certain neighboring network nodes together with the absolute locations of some anchor nodes. We propose the concepts of stiffness matrix and fixability for the anchored formation graphs modeling the networks, and show that they provide a complete characterization of the AOA localizability as well as an explicit formula for the localization result. Moreover, a distributed continuous-time algorithm is proposed that converges globally to the correct localization result on fixable formation graphs. Performances of the proposed algorithm, e.g., convergence rate and robustness to communication delay, are characterized and optimized. Sensitivities of the localization results with respect to errors in AOA measurements and anchor node positions are also analyzed.