Strapdown INS error model for multiposition alignment

The relationship between quaternion errors and tilt angles from true navigation frame to analytic platform frame is newly derived for strapdown inertial navigation system (SDINS). Using the relationship it is shown that the quaternion error model for attitude and velocity is equivalent to the conventional perturbation error model. Based upon the equivalency, the quaternion errors during a multiposition alignment are determined and analyzed. Furthermore, it is shown that the heading rotation of 180 deg achieves the minimal quaternion error for 2-position ground alignment.