The Quaternion-Based Attitude Error for the Nonlinear Error Model of the INS
Tiangao Zhu, Yong Liu, Wenkui Li, Kailong Li
Abstract
In this paper, the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame based nonlinear error model is proposed for the INS. According to the definition of the attitude error, the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame based nonlinear error model has been derived by additive and multiplicative relationship. Then, a discussion and analysis is made to compare the proposed model in additive and multiplicative relationship with the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model. In addition, an analysis and comparsion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model is made to have a theoretical justification to describe why <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame is superior to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model. Finally, field tests are carried out to access the performance of the quaternion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> -frame and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -frame based nonlinear error model in the additive and multiplicative relationship for the INS.