一维和多维误差分离技术的统一理论

在回顾和评述误差分离技术的多种方法的基础上，将这些对象迥异、操作各不相同的诸多方法，用多维误差分离技术理论统一起来，给出了基于两个左阵的一维和多维误差分离技术的统一方程。据经论述了误差分离的通则，以及误差分离技术的反滤波实质。

Unified Theory of One-dimension and Multi-dimension Error Separation Techniques

Fermented in 1950's and originated in 1960's, EST(Error Separation Techniques) have been made great advances along with the rapid development of computing techniques,microcomputer and sensing transmitting techniques. Up to now,dozens of EST have been developed domestically and overseas which are aimed at different objects and have their distinct skills. The pity is that they are not unified, and this condition presents an obstacle to fasten the tenor of developing new EST methods. This paper reviews these EST methods and unifies different EST methods with an unified theory of multi-dimension error separation technique, and presents the uniform equation of 1-D and multi-dimension EST which are based on two mapping matrices,i.e.mapping matrix representing form error of workpiece and mapping matrix representing error motion of operating parts of machine or measuring apparatus. Several criteria are put forward according to the unified theory. And the essence of inverse filteration of EST is discussed according to the unified error separation theory.