摘要
针对线性最小二乘法处理非线性模型产生模型误差的问题,文章将高斯牛顿迭代法引入测角网坐标平差模型中,给出测角网坐标平差模型的高斯牛顿迭代法计算过程。考虑到非线性平差模型的参数估计值是有偏估计,结合Bootstrap重采样方法对参数估值进行改善,提出测角网坐标平差模型的Bootstrap参数估计方法,并给出详细的迭代流程图。针对等精度与不等精度角度观测数据,设计两个测角网案例。实验结果表明,测角网坐标平差模型的高斯牛顿迭代解法能够削弱线性近似带来的模型误差影响,其参数估值优于传统的线性近似方法;而测角网坐标平差模型的Bootstrap参数估计方法比高斯牛顿迭代解法在提高测角网坐标平差参数估值质量方面更加有效。实验证明将高斯牛顿迭代解法应用于测角网坐标平差模型的必要性与实用性,也证明将Bootstrap重采样参数估计方法与高斯牛顿迭代解法结合并用于测角网坐标平差的可行性与有效性。
Focusing on the linear least squares(LS)method generates model error for the nonlinear model,the Gauss-Newton Iteration(GNI)method is introduced into the adjustment model of triangulation network in this paper,and the detailed calculation steps are given.Considered that the parameter valuations of nonlinear model are biased,the bootstrap resampling parameter estimation method for adjustment of triangulation network is identified to optimize the parameter estimates,and the whole procedure and flow chart for parameter estimation using the new method are given.This contribution focuses on the following two aspects:equal precision data and unequal precision data.From the experimental estimation results,the GNI solution for adjustment of triangulation network can weaken the influence of model error caused by linearization of the model,and its parameter estimates are superior to the traditional LS method.Furthermore,the bootstrap resampling parameter estimation method is more effective than the GNI method in improving the quality of the parameter estimates in triangulation network adjustment.The numerical case studies verify the necessity and practicality of using GNI method to estimate the parameter in triangulation network,and also verify the feasibility and effectiveness of combining bootstrap resampling theory with the GNI method for parameter estimation in adjustment model of triangulation network.
作者
王乐洋
李志强
WANG Leyang;LI Zhiqiang(School of Geomatics, East China University of Technology, Nanchang 330013, China;College of Surveying and Geo-Informatics, Shandong Jianzhu University, Jinan 250101, China)
出处
《测绘工程》
CSCD
2021年第1期6-13,19,共9页
Engineering of Surveying and Mapping
基金
国家自然科学基金资助项目(41874001,41664001)。
