doi:10.16186/j.cnki.1673-9787.2020.5.5

Received:2019/11/25

Revised:2020/02/26

Published:2020/09/15

Differential Rodrigues matrix algorithm for three-dimensional coordinatetransformation of arbitrary rotation angle

LUO Xiang1,2, LIU Zhiping1,2

1.Key Laboratory for Resources and Environment Information Engineering of Jiangsu Province， China University of Mining and Technology ，Xuzhou  221116 ， Jiangsu， China;2.School of Environment Science and Spatial Informatics， China University of Mining and Technology， Xuzhou 221116 ， Jiangsu， China

Abstract:In order to analyze the existing problems of three-dimensional coordinate transformation with small and arbitrary rotation angle， the matrix differential form was transformed into parameter vector differential form， and then the differential Rodrigues matrix algorithm was proposed based on the theory of Rodrigues matrix， anti-symmetric matrix and vector product operation. The algorithm avoided the matrix derivation problem which was common in the existing algorithms， and realized synchronous iterative updating of function model and random model to improve the precision and efficiency of iteration. The comparison between the proposed algorithm and the three existing algorithms was carried out through literature examples and simulation examples. The statistical results such as the number of iterations and the true error of parameters showed that the improved algorithm was effective.

Key words:arbitrary rotation angle;three-dimensional coordinate transformation;differential Rodrigues matrix;anti-symmetric matrix

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