整体最小二乘的迭代解法

在引入整体最小二乘平差准则的基础上,推导了整体最小二乘的迭代解法;同时,引入多元函数隐函数求导的方法以确定未知参数对观测数据的线性信息,解决了整体最小二乘下的精度评定问题。给出了运用新的解法在拟合函数确定以及坐标转换参数确定等方面的应用实例,验证了新算法的可行性。

Iterative Method for Total Least-Squares

The conventional solution method for TLS is based on matrix singular value decomposition.This method is rigorous in theory,but is complex and not easy to be programed.The complexity of the method is an important reason restricting TLS application in the field of Geomatics.By introducing the total least-squares adjustment standard,we derive the total least-squares iterative method,which is simple and easy to be programed.Through the introduction of multi-function derivative knowledge of the implicit function to determine the linear information of the parameters to observational data,we solve the problem of assessing the accuracy based on TLS.Finally,we apply the new method to the fitting function determination and coordinate transformation parameters determination based on measured data,and verify the feasibilities of the new method.The new method has a great significance to the popularization and application of TLS.