Cooperative Localisation of a GPS-Denied UAV in 3-Dimensional Space Using Direction of Arrival Measurements

TL;DR

This paper introduces a method for localising a GPS-denied UAV in 3D space using a GPS-enabled UAV's broadcasts and direction of arrival measurements, employing SDP and Procrustes algorithms for noisy data.

Contribution

It proposes a novel framework combining DOA measurements with SDP and Procrustes algorithms for accurate 3D UAV localisation without GPS.

Findings

Exact localisation in noiseless conditions

Robustness to measurement noise demonstrated

Factors like noise level and measurement count affect accuracy

Abstract

This paper presents a novel approach for localising a GPS (Global Positioning System)-denied Unmanned Aerial Vehicle (UAV) with the aid of a GPS-equipped UAV in three-dimensional space. The GPS-equipped UAV makes discrete-time broadcasts of its global coordinates. The GPS-denied UAV simultaneously receives the broadcast and takes direction of arrival (DOA) measurements towards the origin of the broadcast in its local coordinate frame (obtained via an inertial navigation system (INS)). The aim is to determine the difference between the local and global frames, described by a rotation and a translation. In the noiseless case, global coordinates were recovered exactly by solving a system of linear equations. When DOA measurements are contaminated with noise, rank relaxed semidefinite programming (SDP) and the Orthogonal Procrustes algorithm are employed. Simulations are provided and factors affecting accuracy, such as noise levels and number of measurements, are explored.