Singularity-free extraction of a quaternion from a direction-cosine matrix

1976 ◽  
Vol 13 (12) ◽  
pp. 754-755 ◽  
Author(s):  
Allan R. Klumpp
Keyword(s):  
Direction Cosine ◽  
Direction Cosine Matrix

Attitude reconstruction from strap-down rate gyros using power series

2021 ◽  
pp. 1-19
Author(s):  
Habib Ghanbarpourasl
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Direction Cosine ◽  
Analytical Description ◽  
Double Precision ◽  
Angular Velocity Vector ◽  
Higher Order Terms ◽  
Direction Cosine Matrix ◽  
The Stability ◽  
Better Than

Abstract This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

Coordinate Transform Methods Used in Dynamic Simulation of Satellite Separation

2012 ◽  
Vol 569 ◽  
pp. 712-717 ◽  
Author(s):  
Xing Zhi Hu ◽  
Xiao Qian Chen ◽  
Yong Zhao
Keyword(s):  
Dynamic Simulation ◽  
Direction Cosine ◽  
Transformation Method ◽  
Euler Angles ◽  
Adams Software ◽  
Software Platforms ◽  
Direction Cosine Matrix ◽  
The Common ◽  
Compression Springs ◽  
Coordinate Transformation Method

Direction cosine matrix, Euler angles and quaternions are the common methods for translating vector equations into scalar equations. These methods used in separation simulation lack systematic discussion and comparison. This article is trying to present a proper coordinate transformation method for dynamic analysis of satellite separation. 321 and 123 rotations of Euler angles are proposed to construct the dynamic equations, which is different from simulation of missiles by the rotation of 321 and 231. Both Euler angles and quaternions are adopted to model the separation process of a small satellite that uses the helical compression springs mechanism. Feasibility and practicability of the approach are proved by comparing the simulation results, which are solved in MATLAB and ADAMS software platforms. It is concluded that the method of quaternions is more accurate and efficient in dynamic simulation of satellite separation.

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