基于辅助测量装置中栅格板的不同位姿,构建了有关工作台误差和栅格板误差的数学模型。根据最小二乘原理将误差方程转化为正规方程。通过研究位姿方案对关系矩阵的秩的影响,归纳总结了位姿与自校准模型之间的规律。依据方程具备最小二乘解的条件,自校准过程中栅格板必须在初始位姿的基础上经过旋转90°及平移的位姿变换,并进行了仿真。研究结果表明,只有包含三种基本位姿的位姿方案才能使仿真计算值接近真实值,此基本三位姿是实现最小二乘法自校准的充分必要条件。

A mathematical model related to stage errors and grid plate errors is constructed according to the different positions of grid plate in the auxiliary measuring device. Based on the least square principle, the error equation is converted into a regular equation. The influence of position scheme on the rank of a relation matrix is investigated to summarize the law between the position and the self-calibration model. With the the conditions that the equation need for the least square solution, in the self-calibration process, the grid plate must be rotated by 90° and simultaneously translated from its initial position, and this position transformation is also simulated. The research results show that it is only the position scheme containing three basic positions that makes the simulation result closer to the true value. These three basic positions are the necessary and sufficient conditions for the achievement of self-calibration by the least-squares method.