Thanks to the support of Inertial Navigation Systems (INS), Global Navigation Satellite Systems (GNSS) provide a navigation positioning solution that, in the absence of satellite signals (in tunnels, forest and urban areas), allows the continuous positioning of a moving object (air, land and sea). Passenger and freight trains must, for safety reasons, comply with several formal navigation requirements, particularly those that concern the minimum acceptable accuracy for determining their position. Depending on the type of task performed by the train (positioning a vehicle on a route, stopping at a turnout, stopping at a platform, monitoring the movement of rolling stock, etc.), the train must have positioning systems that can determine its position with sufficient accuracy (1–10 m, p = 0.95) to perform the tasks in question. A wide range of INS/GNSS equipment is currently available, ranging from very costly to simple solutions based on Micro-Electro-Mechanical Systems (MEMS), which, in addition to an inertial unit, use one or two GNSS receivers. The paper presents an assessment of the accuracy of both types of solutions by testing them simultaneously in dynamic measurements. The research, due to the costs and logistics complexity, was made using a passenger car. The surveys were carried out in a complex way, because the measurement route was travelled three times at four different speeds: 40 km/h, 80 km/h, 100 km/h and 120 km/h on seven representative test sections with diverse land development. In order to determine the positioning accuracy of INS devices, two precise GNSS geodetic receivers (2 cm accuracy, p = 0.95) were used as a reference positioning system. The measurements demonstrated that only INS/GNSS systems based on two receivers can meet the requirements of most railway applications related to rail navigation, and since a solution with a single GNSS receiver has a much lower positioning accuracy, it is not suitable for many railway applications. It is noted that considerable differences between the standards defining the navigation requirements for railway applications. For example, INS/GNSS systems based on two receivers meet the vast majority of the expectations specified in the Report on Rail User Needs and Requirements. However, according to the Federal Radionavigation Plan (FRP), it cannot be used in any railway application.

The problem of the reproduction of the railway geometric layout in the global spatial system is currently solved in the form of measurements that use geodetic railway networks and also, in recent years, efficient methods of mobile positioning (mainly satellite and inert). The team of authors from the Gdańsk University of Technology and the Maritime University in Gdynia as part of the research project InnoSatTrack is looking for effective and efficient methods for the inventory of railway lines. The research is part of a wider investigation BRIK (Research and Development in Railway Infrastructure, in polish: Badania i Rozwój w Infrastrukturze Kolejowej). This paper presents a comparative analysis of the problem of the reproduction of the trajectory of the measuring system using tacheometry, satellite measurements made using a measurement trolley, and mobile satellite measurements. Algorithms enabling the assessment of the compliance of satellite measurements with classic tacheometric measurements were presented. To this end, the authors held measurement sessions using modern geodetic instruments and satellite navigation on a section of the railway line. The results of the measurements indicate the convergence of the level of accuracy achieved by different measuring techniques.

The article discusses an important issue in connection with the technique of mobile Global Navigation Satellite System (GNSS) measurements of railway track coordinates, which is digital filtering performed to precisely determine railway track axes. For this purpose, a measuring technique is proposed which bases on the use of a measuring platform with a number of appropriately distributed GNSS receivers, where two of them determine the directional base vector of the platform. The receivers used in the research had high measuring frequency in the Real Time Kinematic (RTK) operating mode and enabled correction of the obtained results in post–processing. A key problem discussed in the article is the method for assessing the quality of the measurement results obtained from GNSS receivers, and their preparation for further processing making use of geometrically constrained parameters of the base vector and specialized digital filtering, among other elements, to precisely determining the track axis. The obtained results confirm the applicability of the used method of GNSS signal processing.

When used at sea, satellite compasses are capable of determining the course of a sailing vessel with high accuracy. It is difficult to verify the accuracy declared by the device manufacturer under such conditions, as it is difficult to define a reliable reference. This study analyses the accuracy of the satellite compass in an urban setting, with the satellite signal being obscured to various extents. It is an important point in the study to refer the measurement results to a reference route, which is the axis of a tramway track, determined by the precise GNSS RTK method. The measurement data were processed in the original software developed by the authors. The results demonstrate a high 2D positioning accuracy with low height determination accuracy. The course determination errors exceed the limit values declared by the manufacturer. However, specific measurement conditions must be taken into account, which differ considerably from the typical applications of a satellite compass.

Mobile Global Navigation Satellite System (GNSS) measurements carried out on the railway consist of using satellite navigation systems to determine the track geometry of a moving railway vehicle on a given route. Their purposes include diagnostics, stocktaking, and design work in railways. The greatest advantage of this method is the ability to perform measurements in a unified and coherent spatial reference system, which effectively enables the combining of design and construction works, as well as their implementation by engineering teams of diverse specialties. In the article, we attempted to assess the impact of using three types of work mode for a GNSS geodetic network [Global Positioning System (GPS), GPS/Global Navigation Satellite System (GLONASS) and GPS/GLONASS/Galileo] on positioning availability at three accuracy levels: 1 cm, 3 cm and 10 cm. This paper presents a mathematical model that enables the calculation of positioning availability at these levels. This model was also applied to the results of the measurement campaign performed by five GNSS geodetic receivers, made by a leading company in the field. Measurements with simultaneous position recording and accuracy assessment were taken separately on the same route for three types of receiver settings: GPS, GPS/GLONASS and GPS/GLONASS/Galileo in an urban area typical of a medium-sized city. The study has shown that applying a two-system solution (GPS/GLONASS) considerably increases the availability of high-precision coordinates compared to a single-system solution (GPS), whereas the measurements with three systems (GPS/GLONASS/Galileo) negligibly increase the availability compared to a two-system solution (GPS/GLONASS).

The main aim of this paper is to assess the possibility of using non-conventional geodetic estimation methods in maritime navigation. The research subject of this paper concerns robust determination of vessel’s position using a method of parameters estimation in the split functional model (M_splitestimation). The studies performed will help in finding out if and in which situations the application of M_splitestimation as the method for determining vessel’s position is beneficial from the perspective of navigation safety. The results obtained were compared with the results of traditional estimation methods, i.e. least squares method and robust M-estimation.