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<p>The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with those angles. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates into quaternion rates, which are in turn integrated to obtain quaternions. The outputs of the model are values of three-dimensional angular rates, three-dimensional linear accelerations, and three-dimensional magnetic field vector. Gauss-Newton iteration is utilized to find the best quaternion that relates the measured linear accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The quaternion obtained from the optimization algorithm is used as part of the observations for the Kalman filter. As a result, the measurement equations become linear. A new approach to attitude estimation is introduced in this thesis. The computational requirements related to the extended Kalman filter developed using this approach are significantly reduced, making it possible to estimate attitude in real-time. Extensive static and dynamic simulation of the filter using Matlab proved it to be robust. Test cases included the presence of large initial errors as well as high noise levels. In all cases the filter was able to converge and accurately track attitude.
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Marins, Joao L.</div>
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