曾文宪, 刘泽邦, 方兴, 李玉兵. 通用EIV平差模型的线性化估计算法[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20200243
引用本文: 曾文宪, 刘泽邦, 方兴, 李玉兵. 通用EIV平差模型的线性化估计算法[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20200243
ZENG Wenxian, LIU Zebang, FANG Xing, LI Yubing. Linearization Estimation Algorithm for Universal EIV Adjustment Model[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20200243
Citation: ZENG Wenxian, LIU Zebang, FANG Xing, LI Yubing. Linearization Estimation Algorithm for Universal EIV Adjustment Model[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20200243

通用EIV平差模型的线性化估计算法

Linearization Estimation Algorithm for Universal EIV Adjustment Model

  • 摘要: 通用EIV模型将EIV模型扩展到了最一般化的形式,其加权整体最小二乘算法同时顾及了观测向量、观测向量的系数矩阵和参数的系数矩阵中的随机误差。本文将非线性的通用EIV函数模型展开,并将二阶项纳入模型的常数项,从而将通用EIV模型表示为线性形式的高斯-赫尔默特模型,推导出了通用EIV模型的线性化整体最小二乘算法和近似精度估计公式。通过模拟数据和实例进行了评估和分析,该算法与通用EIV模型的WTLS算法估计结果一致,验证了该算法的正确性和可行性。当模型含大量估计量时,通用EIV模型的线性化估计算法显著提升了计算效率,收敛速度更快。

     

    Abstract: The universal EIV model extends the EIV model to the most general form, and the weighted total least squares (WTLS) algorithm is proposed to take into account the random errors in observation vector, observation vector coefficient matrix and parameter coefficient matrix. In this paper, the nonlinear universal EIV function model is expanded, and the second-order term is included into the constant term of the model, so the universal EIV model is represented as Gauss-Helmert model in linear form, and the Linearized total least squares algorithm and approximate precision estimation formula of the universal EIV model are derived. Through the simulation data and examples, this algorithm is consistent with the estimation results of the WTLS algorithm of the universal EIV model, which verifies the correctness and feasibility of this algorithm. When the model contains a large number of estimators, the linearized estimation algorithm of the universal EIV model significantly improves the computational efficiency and converges faster.

     

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