A Geometry-Based Node Activation Method for Relative Localization

In multi-agent systems, the hybrid active-silent relative localization framework is widely employed, where only active nodes transmit signals. The selection of active nodes, known as node activation, significantly impacts the positioning accuracy. This paper investigates the node activation in anchor-free localization systems. First, the constrained Cramér-Rao lower bound (CRLB) is derived to evaluate the localization error. Then the combinatorial optimization problem on node activation is presented and approximately solved using the difference of convex programming (DCP) method. Moreover, to reduce computational complexity, we propose a geometry-based greedy iterative (GBGI) algorithm which leverages a geometry metric to evaluate and iteratively refine the selection of active nodes. Finally, simulation results demonstrate the performance of proposed algorithms. Especially the GBGI algorithm closely approaches the optimal solution.