Institute of Geodesy, University of Warmia and Mazury in Olsztyn, 1 Oczapowskiego St., 10-957 Olsztyn, Poland.
Sensors (Basel). 2019 Nov 19;19(22):5047. doi: 10.3390/s19225047.
Sets of geodetic observations often contain groups of observations that differ from each other in the functional model (or at least in the values of its parameters). Sets of observations obtained at various measurement epochs is a practical example in such a context. From the conventional point of view, for example, in the least squares estimation, subsets in question should be separated before the parameter estimation. Another option would be application of M estimation, which is based on a fundamental assumption that each observation is related to several competitive functional models. The optimal assignment of every observation to the respective functional model is automatic during the estimation process. Considering deformation analysis, each observation is assigned to several functional models, each of which is related to one measurement epoch. This paper focuses on the efficacy of the method in detecting point displacements. The research is based on example observation sets and the application of Monte Carlo simulations. The results were compared with the classical deformation analysis, which shows that the M estimation seems to be an interesting alternative for conventional methods. The most promising are results obtained for disordered observation sets where the M estimation reveals its natural advantage over the conventional approach.
测地观测数据集通常包含在功能模型上彼此不同（或者至少在其参数值上不同）的观测组。在这种情况下，在不同测量时期获得的观测数据集是一个实际的例子。例如，从传统的角度来看，在最小二乘估计中，在参数估计之前应该将有问题的子集分开。另一种选择是应用基于基本假设的 M 估计，即每个观测值都与几个竞争的功能模型相关。在估计过程中，每个观测值会自动分配给相应的功能模型。在考虑变形分析时，每个观测值被分配到几个功能模型，每个模型都与一个测量时期相关。本文重点研究了该方法在检测点位移方面的效果。该研究基于示例观测数据集和蒙特卡罗模拟的应用。结果与传统变形分析进行了比较，表明 M 估计似乎是传统方法的一个有趣替代方案。在观测集无序的情况下，M 估计显示出其优于传统方法的自然优势，结果最有前途。
