###### Abstract  
This paper presents the challenges encountered in the dimensional control of ships, platforms, and offshore units. This novel approach utilizes machine learning (MLP--Multilayer Perceptron Neural Network) for three-dimensional (3D) spatial coordinate transformations when only three common points are known. The proposed method was verified based on laboratory and field data. The main issue was to provide a sufficient number of valid training points. The oversampling method was used to meet this criterion. The achieved results indicate equal or better accuracy when the points were located inside the adjustment points array. In the case where the points lay outside this array, no improvement in the accuracy of the transformation was observed. The neural approach restores the transformation symmetry, and in some cases, such as the study of deformation of engineering objects, breaks the symmetry rather than restoring it. three-dimensional coordinates transformations; off-shore surveying; dimensional control; marine geodesy; artificial neural networks; applied engineering +
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about each axis of the coordinate system. The external orientation elements of a measuring instrument (sensor) can be measured with measuring devices such as a GNSS receiver, an Inertial Measurements Unit (IMU), and a Motion Reference Unit (MRU) mounted on the measuring instruments or calculated based on external reference points with a known position. In all the cases mentioned above, to calculate the position of the sensor and the points measured by it, it is necessary to use a seven-parameter conformal transformation, which consists of: translations (3D vector coordinates), rotations (three Euler angles), and the scale factor [10; 11; 12; 13; 14]. Through conformal transformations, it is possible, inter alia, to generate a cloud of measurement points obtained from several freely oriented measurement stations. as well as to compare the stability of the location of the same points at certain time intervals, e.g., when testing the deformation of engineering structures or tectonic plate movement [15; 16; 17; 18; 19]. Conformal transformation is also commonly used in computer vision, photogrammetry, and remote sensing [20; 21; 22; 23]. Conformal transformation is also called similarity transformation or Helmert transformation and is often written as Equation (1) [24; 25; 26] or is solved using novel gradient methods [27; 28]. At the same time, the works [23; 29] show that traditional and gradient methods of solutions of the similarity transformation give very similar results in terms of accuracy of the adjustment points. An alternative approach to the above-described methods is the use of machine learning, especially ANNs, for coordinate transformation. The use of artificial neural networks has proved their versatility in various fields. In the case of positioning and geodetic measurements, the ANNs are of increasing interest due to their enormous potential for application in many different areas of science and technology. Previous studies on the transformation of coordinates with the use of ANNs have been conducted many times, but generally, they were based on sets from several dozen points to even several hundred thousand points (in cartographic applications). However, ANNs can determine the relationship between two coordinate systems without a mathematical model, which is beneficial in its use of complex data models of coordinates [23; 27; 28]. In geodetic measurements, the number of common points between measurement stations is usually lower (from a few to a dozen). In offshore surveys, combining the measurement stations into one point cloud is even more difficult. Due to the space limitations determined by the structure of the measured object (ship, platform, etc. ), it is difficult to locate the areas where the measurement network points can be installed to ensure their good geometry from the point of view of accuracy.