Adaptive collocation with application in height system transformation
Adaptive collocation with application in height system transformation
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DOI：
10.1007/s00190-008-0226-9
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发表时间：
2009-05
影响因子：
4.4
通讯作者：
Y. Yang;A. Zeng;J. Zhang
中科院分区：
文献类型：
--
作者：
Y. Yang;A. Zeng;J. Zhang
在配置应用中，信号与观测值之间的先验协方差矩阵或权重矩阵应与其不确定性相一致；否则，搭配解将会失真。为了平衡信号和观测值的协方差矩阵，推导了一种新的自适应搭配估计器，该估计器通过信号和观测值的方差分量之比构造相应的自适应因子。基于搭配函数模型和随机模型，导出了方差分量的极大似然估计量。引入了一种简化的Helmert型估计，并与导出的极大似然型估计进行了比较。通过调整自适应因子，得到信号与观测值合理一致的协方差矩阵。将由方差分量构造的自适应因子与新的自适应搭配应用于GPS测地高度与正交高度之间的变换。结果表明，自适应配置不仅计算简单，而且能有效地平衡配置模型中观测值和信号的贡献。
In collocation applications, the prior covariance matrices or weight matrices between the signals and the observations should be consistent to their uncertainties; otherwise, the solution of collocation will be distorted. To balance the covariance matrices of the signals and the observations, a new adaptive collocation estimator is thus derived in which the corresponding adaptive factor is constructed by the ratio of the variance components of the signals and the observations. A maximum likelihood estimator of the variance components is thus derived based on the collocation functional model and stochastic model. A simplified Helmert type estimator of the variance components for the collocation is also introduced and compared to the derived maximum likelihood type estimator. Reasonable and consistent covariance matrices of the signals and the observations are arrived through the adjustment of the adaptive factor. The new adaptive collocation with related adaptive factor constructed by the derived variance components is applied in a transformation between the geodetic height derived by GPS and orthometric height. It is shown that the adaptive collocation is not only simple in calculation but also effective in balancing the contribution of observations and the signals in the collocation model.