Abstract
Most satellites are equipped with a gyroscope, allowing it to be used in dynamics replacement mode for attitude estimation. However, gyroscopes have been known to fail and not all satellites, such as STRaND-1, have a gyroscope. With gyroless attitude estimation requiring computationally expensive numerical integration for state prediction, efficient and accurate integration techniques need to be employed. Of the numerical methods available for integrating the differential equations of rigid body motion, the state of the art in geometric rigid body integration provides the most computationally efficient methods—such as the preprocessed Discrete Moser-Veselov algorithm—while preserving much, if not all, of the geometric structure of the underlying system. The research presented in this thesis analyses and improves upon previously proposed geometric attitude estimation algorithms, methods incorporating geometric integration such as the Geometric Multiplicative Extended Kalman Filter. Because the Geometric Multiplicative Extended Kalman Filter does not handle covariance prediction in a geometric fashion and is not robust against the realistic initial conditions that could be expected with a gyroless satellite, the Geometric Unscented Quaternion Estimator is proposed to overcome these limitations. Additionally, to meet a specific need of the STRaND-1 satellite mission, these geometric estimators are extended to include simultaneous estimation of the satellite moments of inertia; this includes the development of a methodology for creating proxy moment of inertia measurements that can be incorporated into the estimation algorithm. Extensive simulation testing based on the STRaND-1 mission parameters is performed for all of these estimators, alongside traditional gyroscope-based methods. This thesis also presents the Scaled Harmonic Form, a novel approach for deriving temporally stable analytical solutions to systems exhibiting perturbed harmonic motion. This is applied to the motion of the orbital plane of a satellite in a near-circular orbit about an oblate planet.