Acta Astronomica Sinica
0001-5245
2023
2
21
10.15940/j.cnki.0001-5245.2023.02.009
article
一种计算垂线偏差的抗差最小二乘严密解法
A Robust Least Squares Rigorous Solution Method for Calculating Vertical Deflections
针对当前利用大地水准面模型求解垂线偏差精度不高、稳健性差的问题, 设计了一种严密的垂线偏差抗差最小二乘解法. 首先, 基于大地水准面与垂线偏差的关系, 采用EGM2008 (Earth Gravity Model 2008)重力场模型计算参数初始解; 然后, 引入中位数抗差法, 并选用Huber权函数计算等价权, 迭代计算出稳健的垂线偏差最小二乘解; 最后, 结合两个实测算例对设计方法进行验证. 试验结果表明, 该方法计算的垂线偏差分量与约定真值最大偏差在0.5^{"}左右, 相较于对比方法精度更高; 同时, 该方法能有效抵抗粗差值的影响, 具有较强的稳健性.
To address the current problems of low accuracy and poor robustness in solving the vertical deflections using the geodetic level model, a rigorous robust least squares solution for vertical deflections is designed. Firstly, based on the relationship between geoid and vertical deflections, the Earth Gravity Model 2008 is used to calculate the initial parameters. Secondly, this method introduces the median robust method and chooses the Huber weight function to calculate the equivalent weights, and the robust least squares solution of the vertical deviations is obtained by iterating. Finally, the design method is validated by two experimental examples. The results show that the maximum deviation of the vertical deflections components calculated by this method from the theoretical value is around 0.5^{"}, which is more accurate than the comparison method. Meanwhile, the proposed method can effectively resist the influence of gross error and has strong robustness.
垂线偏差, 最小二乘, 抗差估计, Huber权函数, EGM2008重力场模型
vertical deflections, least squares, robust estimation, Huber weight function, EGM2008 gravity field model
杨浩,李宗春,冉佳欢,刘忠贺,何华
YANG Hao, LI Zong-chun, RAN Jia-huan, LIU Zhong-he, HE Hua
战略支援部队信息工程大学地理空间信息学院 郑州 450001
Institute of Geospatial Information, Strategic Support Force Information Engineering University, Zhengzhou 450001
twxb/article/abstract/20230209