We analyse the performance of Lie-algebraic joint tracking and sensor fusion algorithms in the application of human motion compensation for the non-contact monitoring of respiratory rate during exercise. Using depth cameras and pose detection algorithms we estimate the pose of the subject and extract a region of interest for the anterior chest surface. Measuring respiratory rate using the unprocessed depth of the subject's chest is shown to be ineffective. Instead, we present a framework for estimating the orientation of the subject's torso and use it to compensate for general dynamic pose adjustments. We select several algorithms to test and apply them to the problem of monitoring a cyclist in an interval training workout. Finally we examine the robustness of the algorithms in the face of degraded data and discuss the use of alternative and additional sensing modalities.