测距定位方程非线性平差的封闭牛顿迭代公式

摘要

距离观测在测量中具有极其重要的地位，其观测方程为非线性函数模型。本文导出计算距离函数线性化二阶残余项的简洁公式，讨论测距定位观测方程的线性化近似条件；在此基础上，导出附加多余参数测距定位方程非线性平差的封闭牛顿迭代公式，给出牛顿迭代法退化为高斯-牛顿迭代法的条件。最后以 GPS 长距离伪距定位方程和短距离病态测距定位方程非线性平差为例，验证了本文的主要结论。%Distance observations play a key role in surveying,of which the related observation model is nonl inear.A brief formula is deduced for estimating the second order reminder of distance equations and its geometrical meanings are shown.Moreover,the precondition of traditional adjustment based on the l inear-ized model is discussed when solving the over-determined distance equations with nuisance parameters.A closed-form of Newton iterative formula is proposed and this novel formula immediately shows internal connection between the Newton method and the Gauss-Newton method as wel l as the difference.At last,as numerical examples very long pseudo-distance equations in GPS positioning and short distance-equations in mobi le positioning are solved by different nonl inear adjustment methods to verify the main results.