Error analysis of strapdown inertial navigation using dual quaternion algebra

2004 ◽  
Author(s):  
Yuanxin Wu ◽  
Xiaoping Hu ◽  
Meiping Wu ◽  
Dewen Hu
Keyword(s):  
Error Analysis ◽  
Quaternion Algebra ◽  
Inertial Navigation ◽  
Dual Quaternion ◽  
Strapdown Inertial Navigation

Simplified Design of Dual Quaternion Strapdown Inertial Navigation Integration Algorithms

2012 ◽  
Vol 239-240 ◽  
pp. 1421-1427
Author(s):  
Yu Rong Lin ◽  
Liang Chen ◽  
Zhen Xian Fu
Keyword(s):  
Inertial Navigation System ◽  
Inertial Navigation ◽  
Dual Quaternion ◽  
Velocity Increment ◽  
Time Performance ◽  
Navigation Algorithm ◽  
Integration Algorithms ◽  
Simplified Algorithm ◽  
The Cost ◽  
Strapdown Inertial Navigation

Dual quaternion navigation algorithm gain higher accuracy than traditional strapdown inertial navigation algorithm at the cost of real-time performance. In order to reduce tremendous computation amount of the former, a simplified design scheme for navigation integration algorithms is presented in this paper. First, based on update principle and computation rules of dual quaternion we separate rotational and translational increment information from dual quaternion increment, and deduce exact solutions defined by the spiral vector for thrust velocity increment, gravitational velocity increment and displacement increment. Then, considering characteristics of a strapdown inertial navigation system, implementation schemes of simplified integration algorithms for dual quaternion differential equations in three frames, including thrust velocity coordinates, gravitational velocity coordinates and position coordinates, are designed separately. Under the premise of ensuring the accuracy advantage of the original dual quaternion inertial navigation algorithm, the proposed simplified algorithm significantly improve the computational efficiency. This will lay favorable foundation for engineering realization of the dual quaternion strapdown inertial navigation algorithm.

Strapdown Inertial Navigation Algorithms Based on Lie Group

2016 ◽  
Vol 70 (1) ◽  
pp. 165-183 ◽  
Author(s):  
Jun Mao ◽  
Junxiang Lian ◽  
Xiaoping Hu
Keyword(s):  
Differential Equations ◽  
Lie Group ◽  
Algorithm Design ◽  
Inertial Navigation ◽  
Direction Cosine ◽  
Group Method ◽  
Dual Quaternion ◽  
Lie Group Method ◽  
Direction Cosine Matrix ◽  
Strapdown Inertial Navigation

This paper presents a framework for a strapdown Inertial Navigation System (INS) algorithm design by using Lie group and Lie algebra. The general way to solve Lie group differential equations is introduced. Investigations reveal that this general Lie group method provides a simpler unified way to solve differential equations involving direction cosine matrix, quaternion and dual quaternion, which are widely used in INS algorithm design. Furthermore, we also present a new INS algorithm based on the Special Euclidean group se(3) under the guidelines of Lie group method. Analyses show that se(3) algorithm has the same accuracy as a dual quaternion algorithm, this is also justified by numerical simulations. Though the se(3) algorithm has no improvements in accuracy, the general Lie group method used in the design process shows its brevity and uniformity.

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