Aircraft attitude estimation requires fusing several sensors in order to recover both high and low frequency information in an observable manner. This thesis explores the fusion of gyroscope integration, gravity vector estimation, and magnetic field vector estimation using a complementary filter and an extended Kalman filter (EKF), both of which use a unit quaternion to represent the attitude portion of the state.

First, a set of models, which contain bias, scale factor errors, alignment errors, and Gaussian white noise, is introduced to govern the available sensors. The gyroscope bias is modeled as a random walk. A calibration routine is then established to minimize scale factor and bias errors. After some definitions and derivations for quaternion algebra are established, the attitude solution is then estimated using the complementary filter. Then the EKF is introduced and used to estimate both the quaternion state and gyroscope bias.

The thesis is concluded with a Monte Carlo run to compare the complementary filter with the EKF. Due in large part to the estimation of gyroscope bias in the EKF, this filter is shown to give a significantly more accurate state estimate. The robustness is also evaluated, with both filters initialized with the incorrect initial quaternion and gyroscope bias estimate. The EKF is shown to converge relatively quickly, while the complementary filter does not reliably converge due to the lack of gyroscope bias estimation.