We present a new framework for learning-free 3D human pose estimation from Inertial Measurement Unit (IMU) data. The proposed method does not rely on a full motion sequence to calculate a pose for any particular time point and thus can operate in real-time. A cost function based only on joint rotations is used, removing the need for frequent transformations between rotations and 3D Cartesian coordinates. A Jacobian that preserves skeleton structure is derived using Adjoint methods from Variational Data Assimilation. To facilitate further research in IMU-based Motion Capture, we provide a dataset that combines RGB and depth images from an Intel RealSense camera, marker-based motion capture from an Optitrack system and Xsens IMU data. We have evaluated our method on both our dataset and the Total Capture dataset, showing an average error across 24 joints of 0.45 and 0.48 radians respectively.