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Unbiased least-squares modification of Stokes' formula

机译：斯托克斯公式的无偏见最小二乘修改

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As the KTH method for geoid determination by combining Stokes integration of gravity data in a spherical cap around the computation point and a series of spherical harmonics suffers from a bias due to truncation of the data sets, this method is based on minimizing the global mean square error (MSE) of the estimator. However, if the harmonic series is increased to a sufficiently high degree, the truncation error can be considered as negligible, and the optimization based on the local variance of the geoid estimator makes fair sense. Such unbiased types of estimators, derived in this article, have the advantage to the MSE solutions not to rely on the imperfectly known gravity signal degree variances, but only the local error covariance matrices of the observables come to play. Obviously, the geoid solution defined by the local least variance is generally superior to the solution based on the global MSE. It is also shown, at least theoretically, that the unbiased geoid solutions based on the KTH method and remove-compute-restore technique with modification of Stokes formula are the same.
机译：由于通过将Stokes在计算点周围的球形帽中集成重力数据的重心数据的kth方法，并且一系列球形谐波由于截断数据集而受到偏差，则该方法基于最小化全局均方估算器的错误（MSE）。然而，如果谐波序列增加到足够高的程度，则截断误差可以被认为是可忽略的，并且基于大地区估计器的局部方差的优化使得公平意义。这种非偏见类型的估计器，导出在本文中，具有不依赖于不完全已知的重力信号度方差的MSE解决方案的优点，但只有观察到的本地错误协方差矩阵来播放。显然，由局部最少方差定义的大地区解决方案通常优于基于全局MSE的解决方案。至少在理论上，还示出了基于KTH方法和Remove-Compute-Restore技术的非偏见的大线溶液，其改变Stokes公式是相同的。

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