Several biomedical contexts such as diagnosis, rehabilitation, and ergonomics require an accurate estimate of human upper limbs kinematics. Wearable inertial measurement units (IMU s) represent a suitable solution because of their unobtrusiveness, portability, and low-cost. However, the time-integration of the gyroscope angular velocity leads to an unbounded orientation drift affecting both angular and linear displacements over long observation interval. In this work, a Denavit-Hartenberg model of the upper limb was defined in accordance with the guidelines of the International Society of Biomechanics and exploited to design an optimization kinematics process. This procedure estimated the joint angles by minimizing the difference between the modelled and IMU-driven orientation of upper arm and forearm. In addition, reasonable constraints were added to limit the drift influence on the final joint kinematics accuracy. The validity of the procedure was tested on synthetic and experimental data acquired with a robotic arm over 20 minutes. Average rms errors amounted to 2.8 deg and 1.1 for synthetic and robot data, respectively. Clinical Relevance - The proposed method has the potential to improve robustness and accuracy of multi-joint kinematics estimation in the general contexts of home-based tele-rehabilitation interventions. In this respect adoption of multi-segmental kinematic model along with physiological joint constraints could contribute to address current limitations associated to unsupervised analysis in terms of monitoring and outcome assessment.