###### Abstract  
The study aims to assess the applicability of the ordinary least squares method, robust estimation, and conditions-binded adjustment in processing the six synchronous coordinate pairs of global navigation satellite system (GNSS) receivers. The research is part of the research project InnoSatTrack, focused on the enhancement of the determination of geometrical parameters of railway tracks using GNSS, inertial, and other sensors. A fixed frame of installation of six receivers is used in the data processing. Due to the limited availability of railway routes for measurements, the stationary campaign was conducted to gather data for the adjustment procedures tests. Six GNSS receivers in the frame-restricted configuration were set up using the tachymetric method for recording 96,729 synchronous static observations. Post-processed coordinates of the receivers were adjusted according to the geometrical conditions of the survey frame. Analysis showed higher applicability of the conditions-binded method than other estimation methods by obtaining superior results in both the precision and the maintenance of the design conditions factors than in the OLS and robust estimators. parameter-binding conditions; ordinary least squares; robust estimation; global navigation satellite system; railway track geometry Article Assessment of Adjustment of GNSS Railway with Parameter-Binding Conditions in a  
circulate on the medium Earth orbits (MEO). Additionally, the BeiDou system uses the geostationary (GEO) and inclined geosynchronous (IGSO) satellites [24] that enhance the positioning services in the Far East region. The increasing availability of navigation satellite signals was a motivation for studies that used several GNSS receivers in measurements of railway and tramway routes [25; 26; 27]. An important milestone was the InnoSatTrack project, which addressed the issues of efficiency, accuracy, and applicability of satellite positioning techniques in Polish national railways. In the InnoSatTrack project, a low-sideboard railway carriage designed for transporting coal and iron ore was adopted as a mobile railway platform for advanced railway surveys [28]. A multi-modal system of frames and custom supports was constructed to enable the installation of various devices, e.g., GNSS receivers, accelerometers, vision systems, mobile laser scanners, and inclinometers [29]. The introduction of active geodetic networks [30] services was also used to assess the accuracy parameters of several mobile devices used in sports and recreational applications [31]. The project aimed to increase the accuracy and efficiency of determining the geometric parameters of railway tracks compared to previously used measurement methods. A uniform structural frame for sensor support was used in several measurement campaigns during the project. The core devices were GNSS receivers that followed the railway track axis due to the installation above two platform kingpins. The remaining four receivers were installed on the sides of the platform above the railway tracks. The tachymetric method was used to ensure the millimeter accuracy of the installation of devices with fixed linear and angular conditions. In the tachymetric measurement, the three-dimensional coordinates of a point are calculated based on slope distance and horizontal and vertical angles. This solution enables the application of various adjustment methods, e.g., conditions-binded adjustment [32], the standard ordinary least squares (OLS) method, robust estimation with dumping functions [33; 34; 35; 36], or the M-estimation [37; 38]. Estimates of coordinates that maintain the design geometry between six GNSS receivers are used in joint processing resulting in the determination of the railway axis and other track parameters. However, the synchronous six-receiver dynamic registration along the railway route is frequently limited by the lack of redundant observations.