An advanced nonlinear observer for rigid bodies evolving in 3D-space relying on measurement data provided by an IMU and linear velocity measured in the body-fixed frame has been recently proposed, but without specifying its domain of convergence and stability. With respect to conventional attitude observers, which do not involve linear velocity measurements, this observer is better adapted for vehicles subjected to sustained accelerations. This paper presents further modifications yielding two velocity-aided attitude observers, with rigorous almost global convergence and stability analysis. Moreover, the estimation of the gravity direction is globally decoupled from magnetometer measurements. (C) 2015 Elsevier Ltd. All rights reserved.