Deformation measurements have a repeatable nature. This means that deformation measurements are performed often with the same equipment, methods, geometric conditions and in a similar environment in epochs 1 and 2 (e.g., a fully automated, continuous control measurements). It is, therefore, reasonable to assume that the results of deformation measurements can be distorted by both random errors and by some non-random errors, which are constant in both epochs. In other words, there is a high probability that the difference in the accuracy and precision of measurement of the same geometric element of the network in both epochs has a constant value and sign. The constant errors are understood, but the manifestation of these errors is difficult to determine in practice. For free control networks (the group of potential reference points in absolute control networks or the group of potential stable points in relative networks), the results of deformation measurements are most often processed using robust methods. Classical robust methods do not completely eliminate the effect of constant errors. This paper proposes a new robust alternative method called REDOD. The performed tests showed that if the results of deformation measurements were additionally distorted by constant errors, the REDOD method completely eliminated their effect from deformation analysis results. If the results of deformation measurements are only distorted by random errors, the REDOD method yields very similar deformation analysis results as the classical IWST method. The numerical tests were preceded by a theoretical part. The theoretical part K. Nowel (B) · W. Kamiński Institute of Geodesy, University of Warmia and Mazury in Olsztyn, 1 Oczapowskiego Str., 10-719 Olsztyn, Poland e-mail: krzysztof.nowel@uwm.edu.pl W. Kamiński e-mail: waldemar.kaminski@uwm.edu.pl describes the algorithm of classical robust methods. Particular attention was paid to the IWST method. In relation to classical robust methods, the optimization problem of the new REDOD method was formulated and the algorithm for its solution was derived.

ALS point cloud filtering involves the separation of observations representing the physical terrain surface from those representing terrain details. A digital terrain model (DTM) is created from a subset of points representing the ground surface. The accuracy of the generated DTM is influenced by several factors, including the survey method used, the accuracy of the source data, the applied DTM generation algorithm, and the survey conditions. This article proposes the use of a new estimation method in the filtering of point clouds obtained from airborne laser scanning (ALS), provisionally called M splitestimation. The application of M split -estimation in ALS data filtering requires the determination of the appropriate functional model for the surface, which will be used in the filtering of the set of points. A polynomial terrain surface model was selected for this purpose. Two methods of filtering using the M split method are presented. The first is based on the estimated parameters of the polynomial describing the surface (called the 'quality' approach in the article). The second method (provisionally called the 'quantity' method) is carried out in two stages. The first stage is point cloud filtering, which results in two subsets being created. One of these is the subset of points intended for DTM creation, while the other contains the remaining points. The second stage of the approach is the creation of a DTM from the first subset.Since the M split method has an analytical character, the ATIN method was selected to verify the correct operation of the method. The ATIN method is based on computational geometry and uses repeated Delaunay triangulation and statistical evaluation of the geometric parameters. Comparison of M split with a method based on different principles mitigates errors arising from similarly functioning methods belonging to the same group of filters. The choice of the ATIN method was also dictated by its established position among filtering algorithms. The method is well-known, documented, and verified and this ensures that filtering by this method provides a reliable result that can serve as a reference for comparison with the proposed new filtering method.The theoretical discussion presented in this article was verified with two practical examples. The results obtained from computation by the M split method with appropriate terrain models encourage more detailed theoretical and empirical tests of this method for the filtering and segmentation of ALS data-sets.

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Electronic tacheometers are currently a standard instrument used in geodetic work, including also geodetic engineering measurements. One of the many applications of tacheometers in engineering geodesy are 3D control measurements of crane rail axes. This paper proposes a new method of computing adjustment corrections for crane rail axes based on 3D polar measurements performed with an electronic tacheometer. The intermediary method with conditions on parameters was used in the solution of the problem. The theoretical discussion was complemented with an example application on simulated results of observations. The obtained results confirmed the theoretical assumptions and encourage the verification of the presented proposal on practical examples.