1.2. ContributionsIn the present work, a quaternion-based attitude observer/estimator of a rigid body is presented. In the proposed approach, the attitude estimation problem is solved in two parts. Firstly, a quaternion attitude is estimated by means of vector observations. In this first step, the attitude estimation is performed using an SVD (singular value decomposition) approach. Then, the quaternion obtained in this step is considered an attitude measurement. Contrary to conventional techniques, the SVD maintains the quaternion’s unit constraint naturally. Furthermore, the numerical robustness and numerical stability are guaranteed [26]. The second part of the proposed method consists of the design of a nonlinear observer in order to produce an estimate of the time-varying gyro bias and the attitude quaternion.

This observer is driven by an attitude error obtained by means of the quaternion propagated by the observer, and this one obtained from the SVD technique. Asymptotic convergence of the estimation error is proven. Moreover, it is shown that the error dynamics can be decomposed in two passive subsystems connected in ��feedback��. This result is exploited to prove that the observer is input-to-state stable (ISS) [27,28] when the rate gyro noise is seen as the input and the error as the state. In this sense, using the small gain theorem, one claims that the observer is ��robustly stable��. To evaluate the proposed attitude observer behavior in real-time, a complete Attitude and Heading Reference System (AHRS) based on low-cost inertial and magnetic sensors and a 16-bit microcontroller is designed and implemented.

A comparison with a high precision motion system Cilengitide is carried out, in order to demonstrate the observer performance.The ISS paradigm in an attitude observer, the problem of estimating the attitude from vector observations using an SVD approach, as well as a real-time implementation have never been addressed in the literature. These facts show the originality of the present work.The document is organized as follows. In Section 2, a mathematical background of the attitude parametrization and sensors modeling is given. The main problem is formulated in Section 3. The formulation of the nonlinear attitude observer and stability analysis is presented in Sections 4-6. The AHRS implementation and experimental results are given in Section 7. Finally, conclusions and further research are mentioned in Section 8.2.?Mathematical Background2.1. Unit Quaternions and Attitude KinematicsConsider two orthogonal, right-handed coordinate frames: the body coordinate frame, Eb=[e��1b,e��2b,e��3b], located at the center of mass of the rigid body, and the inertial coordinate frame, Ef=[e��1f,e��2f,e��3f], located at some point in the space.