The application of quaternions and other spatial representations to the reconstruction of re-entry vehicle motion.

The analysis of spacecraft kinematics and dynamics requires an efficient scheme for spatial representation. While the representation of displacement in three dimensional Euclidean space is straightforward, orientation in three dimensions poses particular challenges. The unit quaternion provides an approach that mitigates many of the problems intrinsic in other representation approaches, including the ill-conditioning that arises from computing many successive rotations. This report focuses on the computational utility of unit quaternions and their application to the reconstruction of re-entry vehicle (RV) motion history from sensor data. To this end they will be used in conjunction with other kinematic and data processing techniques. We will present a numerical implementation for the reconstruction of RV motion solely from gyroscope and accelerometer data. This will make use of unit quaternions due to their numerical efficacy in dealing with the composition of many incremental rotations over a time series. In addition to signal processing and data conditioning procedures, algorithms for numerical quaternion-based integration of gyroscope data will be addressed, as well as accelerometer triangulation and integration to yield RV trajectory. Actual processed flight data will be presented to demonstrate the implementation of these methods.