## 3 Results
### CLS, OLS, and RLS Adjustment  
The result of the post-processing stage was obtaining 24 time-tagged lists of GNSS receiver coordinates. UTC enabled synchronization of the records for each epoch of four static sessions. The procedure was not provided in the post-processing software and required the creation of custom software. The initial aim of the field survey campaign was to collect 100,000 epochs of synchronous positions of six receivers. Dataset was to provide a sufficient sample representing various satellite configurations and receiver-dependent errors during the railway dynamic measurement campaign. Due to the break in the recording in session Stat2, the final cardinality of the set was 96,729 observations (21,855 in Stat1, 16,694 in Stat2, in Stat3, and 29,742 in Stat4). Figures 5 and 6 present the results of the post-processing of four static sessions. Figure 5: Front-line receivers’ post-processed coordinates from four sessions. The colors representing six GNSS receivers correspond to the time series presented in Figure 2. Fixed linear dimensions used in the railway platform were added to the figures to highlight the outliers recorded during the field campaign. Three compared LS-adjustment methods were applied on the sets of synchronous coordinates of six receivers from each GNSS-measurement epoch. Standard OLS adjustment includes equations describing relations between \(z\)- and \(y\)-coordinate parameters. Robust RLS estimation introduces the iterative procedure, including weight-dependent observational corrections. The algorithm of the CLS adjustment yields estimators that satisfy the geometrical assumptions of the railway platform frame recreated in the case of this study by receivers staked out on tripods in the field. An example of the result of adjustment with parameter-binding conditions is presented in Figure 7.  
The initial positions from the post-processing of six receivers are marked with circles. The CLS estimators of the receiver positions are marked with crosses. The figure presents an atypical case of epoch with the outlier position of the left-front (LF) receiver. The red arrow indicates the correction applied by conditions-based CLS adjustment. The right panel of the figure contains control quantities computed based on the adjusted coordinates. The presented distances and angles indicate that estimators comply with the design fixed dimensions of the platform frame shape. Three algorithms of OLS, RLS, and CLS adjustments were applied to 96,729 sets of synchronous observations. In order to illustrate the result, the initial (unadjusted) and CLS-adjusted observations are presented in Figures 8 and 9. The observations before and after the adjustment are marked with lighter and darker color shades, respectively. Horizontal panels with different colors refer to six GNSS receivers. The results obtained for four individual static sessions are presented in the columns. Each panel contains the reference position of the receivers in the PL-2000 coordinate system determined by the tachymetric method. Figure 6: Back-line receivers’ post-processed coordinates from four sessions. Figure 7: Example of the CLS adjustment result. The most precise initial (post-processed) coordinates were obtained in static session Stat1. The least precise results occurred in session Stat3, especially in the case of the LB receiver (top panel of Figure 9). The CLS estimation resulted in a decrease in the subsets' standard deviation values. Part of the estimates of the coordinates of the frame back-line receivers was significantly affected by the anomalous LB receiver coordinates. Figure 8: Results of the CLS adjustment of the front-line LF, CF, and RF receivers’ observations. Figure 9: Results of the CLS adjustment of the back-line LB, CB, and RB receivers’ observations. The next stage of the study was the comparison of initial receivers' coordinates from post-processing and coordinates calculated using ordinary (OLS), robust (RLS), and conditions-binded (CLS) least-squares estimation.