This paper proposes a method for determining the vertical deformations treated as random fields. It is assumed that the monitored surfaces are subject not only to deterministic deformations, but also to random fluctuations. Furthermore, the existence of random noise coming from surface’s vibrations is also assumed. Such noise disturbs the deformation’s functional models. Surface monitoring with the use of the geodetic levelling network of a free control network class is carried out. Assuming that, in some cases, the control networks are insufficient in surface’s deformation analysis, additional and non–measurable reference points have been provided. The prediction of these points’ displacements and estimation of the free control network points’ displacement are carried out using the collocation method applying the total least squares adjustment. The proposed theoretical solutions were verified by the simulation methods and on the example of a real control network.

中文翻译：

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应用总最小二乘配置法估计和预测随机表面的垂直变形。

本文提出了一种确定垂直变形为随机场的方法。假定所监视的表面不仅经受确定性变形，而且还经受随机波动。此外，还假设存在来自表面振动的随机噪声。这种噪声干扰了变形的功能模型。使用自由控制网络类别的大地测量水准网络进行表面监控。假设在某些情况下，控制网络在曲面变形分析中不够充分，则提供了额外且不可测量的参考点。这些点的位移的预测和自由控制网络点的位移的估计是使用应用总最小二乘平差的搭配方法进行的。