Application of vectorized attitude determination using global positioning system signals

In this paper, an analysis of two techniques for finding a point-by-point (deterministic) attitude solution of a vehicle using Global Positioning System phase difference measurements is preformed. These techniques transform a general loss function into a more numerically efficient form. One technique determines three-dimensional vectors in the body coordinate system, and the other in the reference coordinate system. Covariance relationships for both vectorized approaches show that they produce suboptimal estimates of the attitude unless the baseline or sightlines are proportional to an orthonormal set, in which case they produce optimal estimates. Both vectorized techniques are tested on a hardware dynamic simulator. Results from this study are useful to determine the circumstances for which vector transformation yields the more accurate results.