非线性二维转换模型的稳健总体最小二乘算法

A solution for two dimension coordinates transformation of nonlinear model based on robust TLS algorithm

针对应用线性最小二乘估计准则求解非线性平面转换模型参数时,通过定义间接参数将模型线性化的方法不能直接求解转换模型参数的问题,该文在非线性平面转换模型的基础上,建立线性模型,实现平面坐标的转换。为解决控制点已知坐标与观测坐标中均含有误差对转换参数求解的影响,对应用稳健总体最小二乘求解线性模型参数的算法进行讨论。最后,通过算例比较稳健总体最小二乘算法与最小二乘算法在抗差性方面的优势。结果表明,稳健总体最小二乘算法更适用于应用线性模型求解未知控制点的转换坐标。

In order to apply linear least squares estimation to compute the parameters of nonlinear transformation model, researchers define other parameters to linearize the transformation model. However, this method is not convenient for the actual use because model parameters cannot be computed directly. This paper presented a linear model based on the nonlinear plane transformation model to realize the coordinate＇s transformation. The robust total least squares（robust TLS）was applied to compute the parameters of linear model on the condition that error which exists in both known coordinates and observation coordinates of control points has impact on computing parameters. Then, the problem that control points have gross error makes the result out of tolerance was focused, and the difference of robust estimation based on robust TLS and LS was analysed through instance. Experimental results demonstrated that the computation value of parameters based on robust TLS algorithm is more close to the simulation value, and robust TLS for plane coordinates transformation is more accurate.