## 4 Summary  
The aim of the study was the applicability assessment of three estimation methods in the adjustment of coordinates of six GNSS receivers distributed within a defined geometric configuration. Three least-squares methods were tested to mitigate random errors: ordinary least-squares (OLS), robust estimation (RLS), and adjustment with conditions binding parameters (CLS). The configuration used on the railway survey platform was re-created in the field on tripods using the precise tachymetric method. The site was chosen in the vicinity of the POLREF control network point. Six Trimble R10 GNSS receivers in four static sessions recorded 96,729 synchronous observations with a frequency of 20 Hz. The results were analyzed in terms of enhancement of precision, compliance with coordinates of the PL-2000 system, and meeting the geometrical criteria of the fixed frame used both in the railway platform and in the field test site. Gaussian standard deviation with 1\(\sigma\) degree of freedom was used for the assessment of changes in precision in the initial (unadjusted) dataset and three least-squares processed sets. Standard deviations in four static sessions showed a similar mean value of 5.5 mm in initial post-processed and OLS datasets. Values of 5.0 mm and 4.7 mm were obtained in RLS and CLS adjustments indicating improvement in precision using those methods. Analysis of coordinates determined using tachymetry showed the presence of systematic linear error in all LS-adjusted results. A significant reduction of precision was noted in OLS and CLS methods compared to the initial data. Analysis shows the impact of local control network quality and the necessity of assessing that factor during dynamic railway measurements. The final analysis was focused on maintaining the fixed geometry between estimators obtained in three LS methods. The initial dataset gave a mean linear error of 5.1 mm in 11 analyzed frame distances. Standard OLS adjustment did not improve the result and obtained a mean error of 5.4 mm. Values of 2.3 mm and 0.0 mm were obtained in RLS and CLS methods, respectively. Distance analysis showed that conditions-binded CLS estimation maintains the linear dimensions of estimates. Analysis of angles in the estimate sets covered 6 angles of 90\({}^{\circ}\) and 180\({}^{\circ}\) in vertices of the platform frame. Comparison of reference angles with angles calculated from adjusted coordinates yielded obtaining the greatest error in an unadjusted dataset with a mean value of 0.21\({}^{\circ}\). Slight improvement of the angular conditions occurred in OLS and RLS adjustments where errors of 0.12\({}^{\circ}\) and 0.14\({}^{\circ}\) occurred, respectively. Similarly to the distance errors analysis, the CLS method obtained the smallest mean error of 4.4\({}^{\prime\prime}\) that shows meeting the geometrical conditions of the railway platform frame. Performed field tests and analysis showed that the conditions-binded CLS is a more applicable solution than OLS and RLS adjustment methods. CLS estimates maintain the geometrical topology of the frame used for GNSS receivers' installation in railway measurements. The RLS method obtained linear errors of several millimeters and angular errors of several arc minutes relative to the theoretical platform frame, which places it in second place in the list of methods of alignment of satellite data. Hence, the CLS is recommended for application with the post-processed satellite data from receivers in the InnoSatTrack project. Conceptualization: C.S., P.S.D., M.S. and P.B. ; methodology: C.S. and P.S.D. ; software: P.S.D. ; validation: C.S., P.S.D., M.S. and P.B. ; formal analysis: C.S. and P.S.D. ; investigation: C.S., P.S.D., M.S. and O.L. ; resources: C.S., P.S.D., M.S. and O.L. ; data curation: P.S.D. ; writing--original draft preparation: P.S.D. ; writing--review and editing: C.S., P.S.D., M.S. and P.B. ; visualization: P.S.D. ; supervision: C.S. and P.B. ; project administration: C.S. ; funding acquisition: C.S. and M.S.