摘要
非线性模型广泛存在于大地测量数据处理的各个方面。误差传播定律是精度评定理论的基础。非线性函数的误差传播计算通常采用近似函数法,然而,在处理多维复杂的非线性函数时,近似函数法存在导数运算困难且繁琐的缺陷。自适应蒙特卡洛法虽然可以避免导数运算,但其受不完善的计算终止条件影响,在实际计算中存在一定几率提前满足数值容差,进而输出不准确的计算结果。针对上述问题,本文改进现有自适应蒙特卡洛法,并设计了一套用于非线性函数误差传播的修正自适应蒙特卡洛方法。算例结果表明,本文方法可以避免自适应蒙特卡洛法过早结束模拟计算的缺陷,从而获得更为准确合理的非线性函数误差传播结果。
Nonlinear models are widely applied in various as⁃pects of data processing in geodesy.The error propagation law is the foundation of accuracy assessment theory.The er⁃ror propagation calculation of nonlinear functions is usually carried out by the approximate function method.However,when dealing with multi-dimensional and complex nonlinear function error propagation calculations,the approximate func⁃tion method has the defect of difficult and tedious derivative operations.Although the adaptive Monte Carlo(AMC)method can avoid derivative operations,it is affected by im⁃perfect computational termination conditions,and there is a certain probability of meeting the numerical tolerance prema⁃turely,resulting in inaccurate calculation results.To address these issues,this paper improves the existing AMC methods and designs an algorithm flow for the modified adaptive Monte Carlo method for error propagation of nonlinear functions.The results show that the method in this paper can avoid the defects of the AMC method that ends the simulation computa⁃tion too early,so as to obtain more accurate and reasonable re⁃sults of the error propagation of nonlinear functions.
作者
罗鑫磊
姜卫平
LUO Xinlei;JIANG Weiping(GNSS Research Center,Wuhan University,Wuhan 430079,China)
出处
《测绘地理信息》
CSCD
2024年第1期36-41,I0001,共7页
Journal of Geomatics
基金
中央高校基本科研业务费专项资金项目(2042022kf1196,2042023kf1008)。
关键词
非线性函数
误差传播
修正的自适应蒙特卡洛法
nonlinear function
error propagation
modified adaptive Monte Carlo method
