Matrix Lie Group-Based Extended Kalman Filtering for Inertial-Integrated Navigation in the Navigation Frame
Yarong Luo, Fei Lu, Chi Guo, Jingnan Liu
Abstract
This article proposes a variant of extended Kalman filtering (EKF) based on the group of double direct isometries ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {SE}_{2}(3)$ </tex-math></inline-formula> ) for the inertial-integrated navigation with low-cost inertial measurement unit (IMU) in the navigation frame (n-frame). The navigation state is first decomposed on the matrix Lie group <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {SE}_{2}(3)$ </tex-math></inline-formula> and then the associated kinematic system is discretized as an iterative update calculation. Next, the group-affine property in discrete time is leveraged to recovery the linear state transition matrix. Finally, the linear inertial error dynamics in discrete time of the error states and biases are obtained for inertial-integrated navigation with low-cost IMU. The superior performance of the left <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {SE}_{2}(3)$ </tex-math></inline-formula> -based EKF is evaluated under large misalignment angles by the field experiments on global navigation satellite system (GNSS)/inertial navigation system (INS) loosely integrated navigation.