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TLS algorithm for GPS height fitting based on robust estimation

机译：基于鲁棒估计的TLS高程拟合算法

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摘要

Application mathematical model for GPS height fitting problem, rational fitting model and accurate parameters of fitting model have impact on the final fitting accuracy. It is known that researchers are used to applying least squares (LS) to establish Gauss-Markov model (G-M model) for computation parameters of mathematical models to realise GPS height fitting. The premise of establishing G-M model based on LS is under the assumptions that coefficient matrix of fitting model is error-free, and random error exists only in observation data. However, two kinds of factors mean that this hypothesis does not exist exactly: first, both coefficient matrix and observation data of control points have random error unavoidably; second, gross error may exist in observation data. In this paper, a solution is presented to solve the problems due to these factors. To take into account random error both in coefficient matrix and observation data while computing the parameters, method of establishing G-M model based on total least squares (TLS) is discussed, and to take into account that the accuracy of observation data is unequal because of gross error, method of applying TLS algorithm to compute parameters based on robust estimation is proposed. We cite instances to prove that the solution is feasible, in the instance, weight of control point which contains gross error is computed by iteration. And the numerical results from our experiment clearly demonstrate that compared with LS and TLS, mean square error of parameters which is computed by the robust TLS is more accurate, and conclusions can be drawn that application robust TLS for GPS height fitting is more scientific.
机译：GPS高度拟合问题的应用数学模型，合理的拟合模型和拟合模型的准确参数对最终拟合精度有影响。众所周知，研究人员习惯于应用最小二乘法（LS）建立高斯-马尔可夫模型（G-M模型），用于数学模型的计算参数，以实现GPS高度拟合。基于LS建立G-M模型的前提是拟合模型的系数矩阵没有误差，且随机误差仅存在于观测数据中。但是，有两种因素导致该假设不完全存在：首先，系数矩阵和控制点的观测数据不可避免地具有随机误差；其次，观测数据中可能存在严重误差。本文提出了一种解决这些问题的解决方案。为了在计算参数的同时考虑到系数矩阵和观测数据的随机误差，讨论了基于总最小二乘（TLS）建立GM模型的方法，并考虑到观测数据的精度由于总误差而不相等。提出了一种基于鲁棒估计的TLS算法来计算参数的方法。我们列举实例证明该解决方案是可行的，在该实例中，通过迭代计算包含粗差的控制点的权重。实验结果表明，与LS和TLS相比，鲁棒TLS计算出的参数均方误差更为准确，可以得出结论：鲁棒TLS在GPS高度拟合中的应用更为科学。

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  • 来源
    《Survey Review》 |2014年第336期|184-188|共5页
  • 作者

    Y.-Q. Tao; J.-X. Gao; Y.-F. Yao;

  • 作者单位

    Key Laboratory for Land Environment and Disaster Monitoring of SBSM, China University of Mining and Technology, Xuzhou 221116, China,School of Earth Science and Engineering, SuZhou University, Suzhou 234000, China;

    Key Laboratory for Land Environment and Disaster Monitoring of SBSM, China University of Mining and Technology, Xuzhou 221116, China;

    Key Laboratory for Land Environment and Disaster Monitoring of SBSM, China University of Mining and Technology, Xuzhou 221116, China;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    GPS height fitting; Robust estimation; Total least squares (TLS); Least squares (LS);

    机译：GPS高度拟合;可靠的估计;总最小二乘（TLS）;最小二乘（LS）;

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