In this paper we consider a collection of relative pose problems which arise naturally in applications for visual indoor navigation using unmanned aerial vehicles (UAVs). We focus on cases where additional information from an onboard IMU is available and thus provides a partial extrinsic calibration through the gravitational vector. The solvers are designed for a partially calibrated camera, for a variety of realistic indoor scenarios, which makes it possible to navigate using images of the ground floor. Current state-of-the-art solvers use more general assumptions, such as using arbitrary planar structures; however, these solvers do not yield adequate reconstructions for real scenes, nor do they perform fast enough to be incorporated in real-time systems. We show that the proposed solvers enjoy better numerical stability, are faster, and require fewer point correspondences, compared to state-of-the-art approaches. These properties are vital components for robust navigation in real-time systems, and we demonstrate on both synthetic and real data that our method outperforms other solvers, and yields superior motion estimation.