Application Of Dual Quaternion Theory In Surveying Data Processing

In the process of surveying data processing,the expression of rotation matrix and translation parameters is often involved.The traditional representation method deals with rotation and translation separately and ignores the relation between rotation and translation.Therefore,this way fails to take into account the coupling errors between rotation and translation and also increases the complexity of data processing.And the traditional euler angle method describing the rotation matrix makes the adjustment model have a high dependence on the initial values and a strong correlation among the calculated parameters,which is not conducive to obtaining stable and reliable results of surveying data processing.Dual quaternion is an important mathematical tool in geometric algebra.It has the advantage of representing rotation matrix and translation parameters as a whole;it can avoid the tedious trigonometric function calculation;it can reduce the dependence on the initial values and the correlation among the parameters.Based on its above characteristics,dual quaternion theory is applied to the surveying data processing in this paper,and the research work is mainly conducted as follows:(1)Dual quaternion is applied to the single image space intersection.Based on the collinear condition equation,a dual quaternion single image space intersection model using matrix differentiation is derived and then the indirect adjustment method with constraint conditions is used to solve the exterior orientation elements iteratively.This method avoids direct linearization of collinear equations and makes the error equations more uniform.Simulation data and real data experiments have verified its correctness and applicability to large inclination angles and high altitude data.(2)Dual quaternion is applied to absolute orientation.Firstly,scale factor is solved according to the least square principle,and then a dual quaternion absolute orientation iterative method is constructed to solve the absolute orientation elements based on the absolute orientation equation and taking into account the errors of model points.The feasibility and convergence of the method are verified by experiments,and it can be applied to the absolute orientation problem of large scale factors.(3)Dual quaternion is applied to 3D coordinate transformation and a 3D coordinate transformation model of Plücker line described by dual quaternion is derived.Firstly,the scale parameter is determined in this model;then the rotational motion and translational motion are treated as the spatial spiral motion,and the spiral motion is described by the action of dual quaternion on the Plücker line coordinates to make its geometric meaning clearer.The correctness of the model is verified by experiments,and the model can guarantee the accuracy and improve the computational efficiency compared with other methods.(4)Dual quaternion is applied to point cloud registration using line primitives.Based on the geometric conditions of plane normal vector equality,a multi-scale line-based point cloud registration model represented by dual quaternion is established.Then the model is linearized and the point cloud registration parameters are solved iteratively.The effectiveness and practicability of the registration model are verified by experiments,and the problem of point cloud registration with different scale can be solved.The line feature is used as the registration primitive in this model,so this registration model can to a certain extent solve the point cloud registration problem caused by occlusion.It is found that the dual quaternion method can achieve the equivalent or better accuracy as the traditional method.In addition,it also shows a good adaptability to large angles data.Therefore,the application of dual quaternion to the above research can increase the stability of model solution and improve the reliability of surveying data processing results.