In this paper, a real-time tracking-based approach to human action recognition is proposed. The method receives as input depth map data streams from a single kinect sensor. Initially, a skeleton-tracking algorithm is applied. Then, a new action representation is introduced, which is based on the calculation of spherical angles between selected joints and the respective angular velocities. For invariance incorporation, a pose estimation step is applied and all features are extracted according to a continuously updated torso-centered coordinate system; this is different from the usual practice of using common normalization operators. Additionally, the approach includes a motion energy-based methodology for applying horizontal symmetry. Finally, action recognition is realized using Hidden Markov Models (HMMs). Experimental results using the Huawei=3DLife 3D human reconstruction and action recognition Grand Challenge dataset demonstrate the efficiency of the proposed approach.