This thesis develops an approach for rigid body pose estimation using dual quaternion mathematics. Dual quaternions combine quaternion mathematics with concepts from dual numbers, offering a compact framework for describing the six-degrees-of-freedom of rigid body motion. Using quadrotor dynamics as a test case, this work formulates a dual quaternion model of dynamics and implements an Unscented Kalman Filter (UKF) for state estimation. Using concepts from Lie theory, the traditional UKF is extended to the unit dual quaternion manifold, while appropriately handling state covariance.

In addition to simulations of the dual quaternion Lie Algebraic UKF (LAUKF), results are presented of the LAUKF running on a purpose built flight computer. The flight computer software is developed using embedded Rust within the RTIC2 framework, and discussion is included on the benefits and challenges encounter when developing the flight computer.