The Quaternion Based Error Model Based on SE(3) of the INS
Tiangao Zhu, An Li, Kailong Li, Fangjun Qin
Abstract
In this paper, an error model based on Special Euclidean group <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE</i> (3) of inertial navigation system (INS) is proposed using the quaternion. The attitude and velocity are formulated together as element of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE</i> (3). The quaternion based error model has a better performance than the Euler Angles based error model, especially for the large initial attitude error. The conclusion can be also applied to the error model based on Lie group due to the superiority of the quaternion. Further, two field tests for the INS are carried out to investigate the benefits and drawbacks of the quaternion and Euler Angles based error model based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE</i> (3) or Special orthogonal group <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SO</i> (3) for the INS.