In this chapter, we'll focus on the attitude estimation problem of a body moving in 3D space. This study is devoted to the reconstruction of the posture (orientation), linear accelerations, positions and their cost in free ranging animal where the access to GPS locations is limited or impossible (application in Bio-logging). In this context, the chosen attitude representation is the quaternion, and the available data are issued from a triad of sensors including a 3-axis accelerometer, a 3-axis magnetometer and a 3-axis gyroscope (Inertial Measurement Unit). Three different approaches for the estimation of the quaternion from the data set are then proposed. The first one is based on an additive nonlinear observer design and uses the quaternion addition technique for updating attitude estimates. The second and the third approaches propose the design of a sliding mode observer and a complementary filter, respectively. In this case, the update of the estimates is based on a quaternion multiplication. This technique shows that it is a good alternative to address this problem and seems more appropriate for the quaternion algebra. The obtained results from both simulation and experimental studies show the efficiency of the proposed methodologies to reconstruct the attitude with a good accuracy for the Bio-logging application. Moreover, they allow estimating the linear acceleration and the energetic index of the animal. Finally the end of the chapter will be devoted to a dead reckoning approach to estimate the 3D position of pedestrian locomotion animal by exploiting only data from an inertial measurement unit. We'll show that obtained experimental results in the case of human locomotion, with an adjusted velocity, are satisfactory and remain promising for the application of this approach in the context of the Bio-logging.