## 1 Introduction  
Nowadays, due to a rapid development of global navigation satellite system (GNSS) [1] the problem of rail routes reconstruction in a global reference system turns out to be increasingly possible. Knowing the coordinates of longitudinal track centerline, it is possible to work with so called Absolute Track Geometry. The essence of the process is determining the axis of railway tracks in the form Cartesian coordinates of a global or local coordinate system. The pioneering studies with a use of satellite measurements on railway tracks using a mobile measuring trolley were conducted in the 1990s at the University of Graz in cooperation with the Plasser & Theurer company [2]. In the early 2000s, a research on the application of precise GNSS measurements to determine track position was conducted at Marshall University [3]. Since then, the mobile measurements and analysis of real time kinematic data (RTK) have been developed by researchers and engineers. The current methods being developed for determining coordinates using GNSS techniques allow engineers for an accurate survey of a railway or tram tracks in a practical and economically effective manner [3; 4; 5; 6; 7; 8; 9]. In 2009, an interdisciplinary scientific team of the Gdansk University of Technology, Gdynia Maritime University, and Polish Naval Academy joined to this investigations and started to develop a method for mobile measurements of a track centerline [10; 11; 12; 13; 14; 15; 16]. The method was called a mobile satellite measurement (MSM) method, which included typical solutions, like differential global positioning system (DGPS) and RTK, but also original measurement data processing algorithms adapted for railway geometry specifics. From the beginning, it was certain that the accuracy of obtained track positions is significantly affected by a horizontal shift of the antennas centres in relation to the track axis. That occurs while the platform runs through circular curves and transition curves. This shift results from the tilting of the measuring platform due to the rail height differences, the so-called cant, which is commonly constructed on the length of these track sections. So, the lack of compensation for the measurement signal results with an inaccuracy in the identification of the track absolute geometry. Although the earlier work of the authors took into account the influence of the track cant on the measurements and the estimation of the track axis coordinates, the corrections have been determined with the knowledge of the track inclination value from independent measurements [17]. This means that the relevant corrections were calculated based on the cant measurements conducted by the methods commonly used in diagnostics and maintenance of the railway track. A subject matter of data fusion of inertial navigation system (INS) and GNSS signals have been discussed for example in papers [3; 4; 5; 9]. The algorithms currently presented in the literature are often based on the data-fusion process using Kalman filters [4; 9]. This data fusion is commonly implemented for combining the GNSS and INS signals, especially when the quality of GNSS is disturbed by terrestrial obstacles or even when the signal is interrupted (i.e., in tunnels or under viaducts). On the other hand, INS is subject to the control of the GNSS signal, especially to avoid the influence of drift. Such redundancy certainly improves reliability of the measurement system [3]. In this paper, the integration of INS and GNSS signals is focused on the previously mention problem, i.e., on calculating the corrections for a track inclination impact on the measured positions. However, the integration of both measurements into the multisensory platform results in an increase of measurement efficiency, and therefore makes the entire process faster and cheaper. Also, a crucial issue in such measurements is to improve the quality of track axis identification in a sense of measurement speed.