Method for solving three-dimensional coordinate conversion parameters based on random rotation angles

Abstract

The invention discloses a method for solving three-dimensional coordinate conversion parameters with random rotation angles. The method comprises the following steps: firstly, obtaining three-dimensional coordinates of common points under two coordinate systems; secondly, establishing a Bursa conversion model; thirdly, establishing a constraint equation; fourthly, establishing an error equation; fifthly, solving the error equation; sixthly, calculating errors in unit weight; seventhly, estimating validity of a rotation matrix, scale factors and three-dimensional translation components according to a variance-covariance matrix; eighthly, displaying results of the rotation matrix. According to the method, nine parameters in the rotation matrix are taken as unknown parameters, and the constraint equation is established as a constraint condition to be introduced into the error equation for solving parameters of the three-dimensional coordinate conversion with the random rotation angles;; the method is rigorous, the mathematical model is simple and easy to realize, the unknown parameters do not need to be linearized, and initial values of the rotation angles in the two three-dimensionalcoordinate systems can be randomly given.

Description

technical field [0001] The invention belongs to the technical field of three-dimensional coordinate transformation, and in particular relates to a method for solving three-dimensional coordinate transformation parameters of an arbitrary rotation angle. Background technique [0002] In space geodetic surveying, the conversion between coordinates of different three-dimensional coordinate systems is often involved. The essence is to use the coordinates of common points in two three-dimensional coordinate systems and the non-common points in the first three-dimensional coordinate system to estimate the non-common points in the second three-dimensional coordinate system. 2D and 3D coordinate system coordinates. The 3D datum transformation usually adopts the similarity transformation with 7 parameters (3 translation parameters, 3 rotation parameters and 1 scale parameter), that is, first calculate the transformation parameters with the common point coordinates, and then use the tr...

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Problems solved by technology

At present, the commonly used 3D datum transformation models include Bursa-Wolf model, Molodensky model, Veis model, etc., but the derivation of this formula is based on the situation of three second-level small rotation angles. The model solved by space Cartesian coordinates with a large rotation angle at the level is a nonlinear model, and the difficulty lies in the inability to give accurate initial values. The existing calculation method obtains accurate initial values ​​of 7 transformation parameters through an iterative method, based on scale parameters. The singular value decomposition estimation of SVD solves the problem of large rotation angle. By constructing auxiliary common points among 3 or more common points, establishing the linear equations of common points, translation and rotation matrix elements, nonlinearization in the rotation matrix cannot be avoided. caused by the error

Therefore, it appears that the 9 elements of the rotation matrix are set as unknown parameters, and the constraints between these 9 unknown parameters and the other 4 transformation parameters (3 translation parameters and 1 scale parameter) are established as constraints between 13 unknown parameters. Virtual observations, but there are two problems in this model: First, when the constraints between 13 unknown parameters are introduced as virtual observations, there is a problem that the weight cannot be determined accurately. Different weights lead to different conversion parameters in the final solution. ; Second, the normal equation of the constraints in the indirect adjustment formed when the constraints between 13 unknown parameters are introduced is irreversible, so it cannot be solved according to the indirect adjustment with constraints

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