ERROR ANALYSIS OF QUATERNION TRANSFORMATIONS

Abstract

Three transformation formulas are derived that related the quaternions to the direction cosine matrix used in strapdown inertial systems. Transformation errors associated with these formulas are fully analyzed. The drift errors evaluated under constant angular velocity have been shown to vary slightly among three different transformations. It is shown that the skew errors in three transformation schemes are not all intrinsically zero. Yet the scale errors may differ largely by two orders of magnitude among transformation schemes. This may become a selection criteria for selection of attitude transformation schemes.