In this paper, we propose two methods based on quaternions to compute the angles of inclination and the angular velocity with 6 degrees of freedom using the measurements of a 3-axis accelerometer and a 3-axis magnetometer. Each method has singularities which occur during the computation of the orientation of the device in the 3-dimensional space. We propose solutions to avoid these singularities. Experimental results are given to compare our model with a real gyroscope. Copyright © 2012 IFSA.