### Motivation & Objectives  
Several successful examples exist in the literature regarding the estimation of the upper limb movements using a wide variety of techniques along with IMU sensors. An inertial tracking system can be used in rehabilitation applications to derive the upper limb movement and its trajectory in real time. Furthermore, such a system can provide additional information, such as the movement amplitude, the range of motion, the angles between upper limb segments, or even the movement velocity. This information allows the medical stuff and the patient to evaluate the upper limb exercises, either at a medical center or at home. In the latter case, the patient can be monitored by the therapists without the need to visit a medical facility. In this work a sensor system for monitoring the upper limb rehabilitation procedure is presented. The core of this system is a 9 Degrees of Freedom (DoF) IMU. Thus, the sensor node is aimed to be attached on various human body segments for motion capturing purposes. Regarding the specific case of upper limb, such sensors can be mounted on upper arm, forearm and hand, gather measurements and transmit the data to a base station. Further processing and filtering of these raw data result to each segment individual orientation, while the estimation of the upper limb joints and segments position and orientation in the 3D space, is accomplished by a reconstruction procedure based on the upper limb model. The overall processing procedure includes a series of well defined mathematical expressions for the calculation of the upper limb's joint angles in closed form. This is performed by exploiting the extracted orientation of the individual segments. Then, these joint angles represent the DoFs angles of a biomechanical model of the upper limb structure based on the Denavit-Hartenberg configuration. The efficiency of this methodology is evaluated by experimental studies on some common rehabilitation exercises, which are applied on a human's upper limb. Furthermore, the comparison between the cost effective motion capture sensor node, that is proposed in this work, and an off-the-shelf sensor, emphasizes the effectiveness of the proposed system along with the total processing methodology. The present work is an extension of our previous paper [29], where a custom-made sensor node was used for motion acquisition and 3D reconstruction of the upper limb segments movement. Here, the sensor fusion algorithm has been improved, in order to account for the relationship between the Euler angles' time rates of change and the angular velocity resolved in the body fixed frame, as is presented in [30]. Moreover, we turn the previous device into a low-cost wearable device that did not exceed the cost of 20 dollars. Rehabilitation exercises were performed wearing the device to ensure that it is comfortable for the patient. Finally, motion capturing results using this sensor node and a much more expensive off-the-shelf device are compared to verify the validity of the custom-made device. The upper limb model representation based on the Denavit-Hartenberg configuration, is adopted to achieve the 3D motion reconstruction of the upper limb motion, and, is presented in Section 2. In Section 3, the followed methodology regarding the gathering, processing and filtering of sensor nodes' inertial measurements is described. This results to the calculation of the links/segments orientation, where the sensor nodes are attached to. The estimation of the joints' angles for the upper limb model using this orientations, is also presented for each segment of the upper limb. In Section 4, the experimental results of a human performing a set of typical rehabilitation exercises are shown. Based on the motion capture sensor node raw data, the proposed methodology is utilized to provide the upper limb segments trajectories. The estimated 3D trajectories are compared with the trajectories that are concurrently derived by Shimmer3 motion capture sensor nodes.