Application of Least Squares with Conditional Equations Method for Railway Track Inventory Using GNSS Observations  
[PERSON]  
1 Department of Geodesy and Oceanography, Faculty of Navigation, Gdynia Maritime University, 81-374 Gdynia, Poland; [EMAIL_ADDRESS]  
2 Department of Geodesy, Faculty of Geoeningening, University of Warmia and Mazury, 10-719 Olsztyn, Poland; [EMAIL_ADDRESS]  
3 Department of Electrical Transportation, Faculty of Electrical and Control Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland; [EMAIL_ADDRESS]  
4 Department of Teleinformation Networks, Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, 80-233 Gdansk, Poland; [EMAIL_ADDRESS]  
5 Department of Transport and Logistics, Faculty of Navigation, Gdynia Maritime University, 81-225 Gdynia, Poland; [EMAIL_ADDRESS]  
6 Department of Rail Transportation and Bridges, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, 80-233 Gdansk, Poland; [EMAIL_ADDRESS]  
(P.C. ); [EMAIL_ADDRESS]  
(P.C. ); [EMAIL_ADDRESS]  
(P.C. ); [EMAIL_ADDRESS]  
(P.C. ); [EMAIL_ADDRESS]  
(P.C. ); k.czaplewski@wn. to monitor trackages, both at the construction stage and during operation [3]. The assessment of railway track is important not only for assurance of a high level of rail transport, but it is also necessary for providing high-quality transport services, as described in [4]. For the assessment of railway track geometry, track gauges and measuring trolleys are used, whose application examples can be found in the literature on the subject, e.g., in [5] or in [6]. However, in the last twenty years, Global Navigation Satellite Systems (GNSS) have become the very basic precise instrument used worldwide. GNSS and the relative instrumentation are under systematic development and constantly increase the application possibilities, which has resulted in their widespread use despite the emerging hazards in operation [7,8]. The main application of GNSS is in geodesy but they are more often used to determine the position of objects in motion [9,10] in the process of directly ensuring a high level of safety of maritime navigation, e.g., [11], or they support the process of modelling the surrounding reality in the computer environment, e.g., [12]. It has become clear that there are possibilities for the application of GNSS in railway transport, e.g., for monitoring railway infrastructure. The proposal for the performance of mobile surveys involving the geodetic inventory of railway tracks using Global Navigation Satellite Systems (GNSS) in railway engineering appeared for the first time in Poland [13]. The proposals for the new use of positioning techniques were verified during the initial experimental tests while taking an inventory of the railway route between Kosicerzyna and Kartuzy in Poland [14], when four GNSS receivers were used as well as the ASG-EUPOS Polish active satellite GNSS surveying network [15]. The study results confirmed the extensive application possibilities for the method and drew attention to its limitations due to signal availability in a built-up area. Launching new GNSS systems (Galileo, Beidou) and creating multiconstellation GNSS surveying networks [16] while increasing the accuracy of the existing ones (Navstar GPS/Glonass) allowed the authors to develop this method [17]. In the period 2009-2017, while developing the method of mobile satellite surveys, research was carried out in two main directions, i.e., the land surveying method associated with increasing accuracy and availability of measurements ([18, 19, 20]) and the construction method aimed at developing new design and operational methods [21, 22, 23, 24, 25]. At other research centres, analogous studies were also undertaken to integrate tacheometric and GNSS surveys [26], with measurement support through the application of inertial navigation systems (INS) [27, 28] or the application of mobile laser scanners [29, 30]. In addition, studies were conducted to apply multisensor methods [31, 32, 33, 34, 35, 36].