Research on the Necessity of Lie Group Strapdown Inertial Integrated Navigation Error Model Based on Euler Angle

Abstract

In response to the lack of specific demonstration and analysis of the research on the necessity of the Lie group strapdown inertial integrated navigation error model based on the Euler angle, two common integrated navigation systems, strapdown inertial navigation system/global navigation satellite system (SINS/GNSS) and strapdown inertial navigation system/doppler velocity log (SINS/DVL), are used as subjects, and the piecewise constant system (PWCS) matrix, based on the Lie group error model, is established. From three aspects of variance estimation, the observability and performance of the system with large misalignment angles for low, medium, and high accuracy levels, traditional error model, Lie group left error model, and right error model are compared. The necessity of research on Lie group error model is analyzed quantitatively and qualitatively. The experimental results show that Lie group error model has better stability of variance estimation, estimation accuracy, and observability than traditional error model, as well as higher practical value.

Online calibration method for SINS/LDV integrated navigation system based on left group error definition

“…To alleviate the inconsistency of the coordinate system of the velocity error vector caused by specific force in the traditional process model, Scherzinger proposed a new velocity error transformation, and Wang et al developed the state transformation extended Kalman filter based on this idea [22][23][24]. Recently, the Lie group theory has been introduced in some inertial navigation fields [25][26][27][28][29][30][31][32]. The group of double direct spatial isometries SE 3 (3) is introduced to formulate the attitude matrix, velocity vector, and position vector into a group.…”

The Kinematic Models of the SINS and Its Errors on the SE(3) Group in the Earth-Centered Inertial Coordinate System

“…Zhu et al derived the quaternion-based error model on the group and compared it to the Euler angle error model and its counterpart on the group [ 14 ]. Qian et al examined the necessity of the Lie group error model from three perspectives: the stability of variance, estimation accuracy, and observability, and proved its superiority to traditional error models [ 15 ].…”