3-D Relative Localization of Mobile Systems Using Distance-Only Measurements via Semidefinite Optimization

In a network of cooperating unmanned aerial vehicles (UAVs), individual UAVs usually need to localize themselves in a shared and generally global frame. This paper studies the localization problem for a group of UAVs navigating in three-dimensional space with limited shared information, viz., noisy distance measurements are the only type of interagent sensing that is available, and only one UAV knows its global coordinates, the others being GPS denied. Initially, for a two-agent problem, but easily generalized to some multiagent problems, this paper first establishes constraints on the minimum number of distance measurements required to achieve the localization. This paper then proposes a composite algorithm based on semidefinite programming (SDP) in a first step, followed by maximum likelihood estimation using gradient descent on a manifold initialized by the SDP calculation. The efficacy of the algorithm is verified with experimental noisy flight data.