The Improved Iteration Method by Correcting Characteristic Value for Transformation of Three-Dimensional Coordinates Based on Large Rotation Angle and Quaternions
Abstract：We propose a new method for ill-posed problems in the large rotation angle three-dimensional coordinate transformation based on the unit quaternion. This method constructs a rotation matrix by unit quaternion, which avoids complex trigonometric function derivations, is easy to linearize, and has a more concise coefficient matrix. Considering the ill-posedness of the normal equation matrix, the ridge parameter and the functional matrix are introduced, which reduces the adverse effects caused by the ill-posedness of the equation, and generates a stable equation solution. At the same time, the estimated value of the solution when the equation is iteratively solved is closer to the true value than the traditional iteration method by correcting characteristic value. The algorithm is verified by simulation and measured data, showing that the algorithm has the characteristics of fast convergence, no initial value of conversion parameters, global convergence, unbiased solution and easy program implementation. It provides a new way for general coordinate transformation.
JIANG Pan,YOU Wei. The Improved Iteration Method by Correcting Characteristic Value for Transformation of Three-Dimensional Coordinates Based on Large Rotation Angle and Quaternions[J]. jgg, 2019, 39(11): 1182-1187.
