A Computational Geometry Framework for Efficient Network Localization

Network localization is an emerging paradigm for providing high-accuracy positional information in GPS-challenged environments. To enable efficient network localization, we propose node prioritization strategies for allocating transmission resources among network nodes. This paper develops a computational geometry framework for determining the optimal node prioritization strategy. The framework consists of transforming each node prioritization strategy into a point in a Euclidian space and exploiting geometric properties of these points. Under this framework, we prove the sparsity property of the optimal node prioritization vector (NPV) and reduce the search space of the optimal NPV. Our approach yields exact optimal solutions rather than ε-approximate solutions for efficient network localization. Numerical results show that the proposed approach can significantly reduce the computational complexity of prioritization strategies and improve the accuracy of network localization.