Msplit Estimation – Theoretical Foundations, Properties, Extensions, and Potential Practical Applications & A Recent Advance in Geodetic Deformation Analysis

Topic1 : M_split Estimation – Theoretical Foundations, Properties, Extensions, and Potential Practical Applications

By Dr. hab. Eng. Marek Hubert Zienkiewicz

The method of estimating competing parameters in a split functional model, also known as Msplit estimation, is an innovative approach to geodetic data processing developed by the Polish geodesist Prof. Zbigniew Wiśniewski. The method was formally derived within the framework of maximum likelihood theory and can be considered as a specific generalization of the family of M-estimation methods. Particular variants of Msplit estimation, obtained for example by assuming a normal distribution as the probabilistic model of measurement errors, may also be interpreted as a special extension of the least squares method. In simplified terms, the method of Msplit estimation enables the identification and estimation of competing solutions within a given observational system. This concept creates both theoretical challenges and practical opportunities in such areas as estimation theory, robust statistics, deformation analysis of geodetic networks, and the processing of data obtained using laser scanning technologies. The seminar will introduce the theoretical foundations of Msplit estimation and its most widely used versions and extensions, including Msplit(q) estimation, Shift-Msplit estimation, and squared Msplit(q) estimation. Particular attention will be given to the relationships between Msplit estimation and M-estimation, maximum likelihood estimation, and the least squares method. The theoretical considerations will be complemented by numerical examples, ranging from elementary linear regression problems to selected geodetic applications, illustrating the practical behaviour of Msplit estimators. The seminar will also address the robustness properties of the method, approaches to accuracy assessment of competing estimators, and selected potential applications of Msplit estimation in geodetic practice.

Topic 2 : A Recent Advance in Geodetic Deformation Analysis

By Dr. Krzysztof Nowel

One of the important tasks of geodesy is the monitoring of deformations of the Earth’s surface and engineering structures. For this purpose, geodetic control networks are established on and around the object under investigation. Geodetic measurements within these networks are then carried out in two or more epochs, and the obtained observations are processed using mathematical methods. This processing is referred to as Geodetic Deformation Analysis. In practice, such an analysis is most often limited to the analysis of single-point displacements of control network points. The presentation addresses this processing. First, a brief review of the conventional computational procedure used in the analysis of single-point displacements will be given, including the corresponding quality control procedure. Next, some problems related to this processing will be highlighted, followed by a presentation of recent advances developed to address them. The first advance concerns deformation model identification, which is the most critical computational step. Two new and currently the most effective approaches to this task will be presented. The second advance concerns the quality control procedure. It will be demonstrated that the conventional procedure provides only approximate description of the quality of single-point displacement analysis. Subsequently, a rigorous procedure that should be used in practice will be presented.

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