同伦函数与填充函数相结合的非线性最小二乘平差模型

Nonlinear Least Squares Adjustment Based on Homotopy Functions and Filled Functions

提出了同伦函数与填充函数相结合进行非线性最小二乘平差的方法。先采用同伦函数求解非线性恰定方程组,得到一个局部最优解,然后以该局部最优解为基础构造填充函数,通过对填充函数求解,得到比当前局部最优解更小的局部极小点,再以该局部极小点为基础重新构造同伦函数和填充函数进行求解,通过有限步的循环迭代,最终找到非线性最小二乘平差的全局最优解。实例验证,该方法能有效地寻找出非线性最小二乘平差的全局最优解。

The method combining homotopy functions with filled functions to solve nonlinear least squares adjustment is presented. We first solve the well-posed nonlinear equations with homotopy method to obtain local optimal solutions, and reasonable filled functions are generated according to the local optimal solutions. It obtains better local optimal solutions than current solutions by the filled functions. Then, the homotopy functions and filled functions will be restructured. Finally, we can find the optimal solutions by limited loop-iteration method. The results show that the method can find optimal solutions effectively.