顾及系数矩阵误差的平面拟合新方法

针对整体最小二乘SVD解法在平面拟合中存在的复杂矩阵运算、无法考虑观测值的权值信息以及默认系数矩阵中所有元素均含有误差等问题,该文在原有误差方程的基础上,增加以系数矩阵中误差元素为观测向量的误差方程,并将误差元素作为参数进行求解。该方法利用最小二乘框架,解决平面拟合中系数矩阵含有随机误差的问题,简化了解算过程;不仅考虑了观测值的权值信息,而且只对系数矩阵中的误差元素进行改正。最后的算例证明了该方法在平面拟合中的可行性。

A new trial for considering random error of coefficient matrix in plane fitting

There are some problems which mainly include involving complex matrix operations,neglecting weight information of observations and regarding all elements in coefficient matrix as error elements existed in SVD method of total least square for plane fitting.In this paper,a new method was presented,which took the error elements as new observations,and added error equation of new observations based on original error equation.Meanwhile the error elements were regarded as parameters which would be calculated.The problem of coefficient matrix containing random error using least squares frame was solved by this method,so calculating procedure was simplified.In addition,weight information could be concerned and only error elements were corrected;numerical tests were conducted to prove the feasibility of the proposed method.