# Use of Total Least Squares Adjustment in Geodetic Applications
## 4 Discussion and Conclusions
In our opinion, the total least squares approach for determining the transformation parameters can represent a significant advancement in the phase of determining transformation parameters and consequently in the process of transforming all official spatial data to the new coordinate system on a national level. Another application of the TLS approach that we wanted to emphasize in this article is in the field of deformation analysis, when computing the displacements of points in a geodetic network measured at different time epochs. The appropriately defined geodetic datum is very important when aiming to compute the correct values of point displacements. Many methods have been developed in the past in the field of deformation analysis, with the common task of determining the set of points that maintain their positions (are stable). Based on these points, the adjustment solution for displacements in a free geodetic network is then transformed to the correctly defined geodetic datum of stable points using the S-transformation. In our research, we utilized the computational process of the TLS approach developed for coordinate transformations and implemented it into the process of the S-transformation. We compared this solution with the solutions for point displacements using the \"ordinary\" S-transformation, LS and SVD approaches. We found that the different approaches yield the same results in the new geodetic datum when the selected reference or datum points have not moved between two compared epochs. In other cases, when there is a combination of stationary ('good') and moved ('bad') points, differences occur, which can also indicate an inadequately defined geodetic datum. Additionally, an iterative procedure can be utilized to find an appropriate set of 'good' geodetic datum points that can serve as the reference points for computing the displacement in a geodetic network. We consider this finding as a solid basis for further investigations in the field of computing the correct values of point displacements and consequently determining the true deformation state of the considered object. In this article, we have focused only on the presence of normally distributed random errors in the model. The implications of outliers, which can cause distortions in estimates of unknown parameters, in the adjustment of observations could be also among the appropriate themes for further research. Investigating the response of the computational method to the presence of outliers could enhance the reliability and accuracy of adjustment results, thus contributing to the advancement of TLS data processing in geodetic applications. **Author Contributions:** Conceptualization, A.M. and T.A. ; methodology, A.M.; software, A.M.; validation, A.M., T.A. and S.S.; formal analysis, A.M., T.A. and S.S.; investigation, A.M., T.A. and S.S.; data curation, A.M.; writing--original draft preparation, A.M., T.A. and S.S.; writing--review and editing, A.M., T.A. and S.S.; visualization, A.M.; supervision, T.A. and S.S. All authors have read and agreed to the published version of the manuscript. The authors acknowledge the financial support from the Slovenian Research and Innovation Agency-ARIS (research core funding No. P2-0227 Geoinformation infrastructure and sustainable spatial development of Slovenia). Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.