## 1 Introduction

Table 1: The current status of the autonomous navigation system constellations (as of 26 August 2021). Error (URE) and the User Equipment Error (UEE). In view of the above, the formula for positioning accuracy can be represented by the following relationship:  
\[DRMS=UEE\cdot DOP=\sqrt{URE^{2}+UEE^{2}}.DOP, \tag{1}\]  
where:  
\(DRMS\)--Distance Root Mean Square (m),  
\(UEE\)--User Equivalent Range Error (m),  
\(URE\)--User Range Error (m),  
\(UEE\)--User Equipment Error (m),  
\(DOP\)--the appropriate geometric coefficient of the satellite location in relation to the receiver: Geometric Dilution Of Precision (GDOP), Position Dilution Of Precision (PDOP), Horizontal Dilution Of Precision (HDOP), Vertical Dilution Of Precision (VDOP), and Time Dilution Of Precision (TDOP) (-). The above equation for the positioning accuracy in the GNSS system has a simplified form, which makes it sufficient and universal for multiple applications. It is correct since all the errors of the pseudorange measurement are subject to normal (Gaussian) distribution. Based on relationship (1), it should be concluded that, at present, the main parameter whose value can be influenced by the system user is the DOP [26; 27; 28; 29]. Its value is determined by the following: the instantaneous location of satellites in relation to the observer, i.e., to the azimuth and the elevation, the number of satellites used to determine the position coordinates, the min. elevation cut-off that is set in the user's receiver to prevent the multipath of satellite signals, the observer's coordinates, etc. [30; 31; 15; 32]. Reducing the DOP value, i.e., increasing the positioning accuracy is possible through the planning of a GNSS measurement campaign to select the optimum time for test performance [33; 34; 35]. There are many free of charge and commercial programs for the planning of a GNSS measurement campaign:  
* Trimble Planning--free, proprietary software from Trimble Inc. It is the most popular product in the field of GNSS planning. Currently distributed as a web application, previously available in a slightly more extensive form as a program for Windows. It enables the determination of DOP values for specific coordinates and at a specific time. The previous version allowed to set a height mask, the current one only enables you to enter the min. elevation cut-off. The application takes into account all GNSS constellations, it also allows the filtration of individual satellites. The simulation results are presented in a series of simple graphs. It is not possible to read the exact values of all of them;
* SKYPLOT DEM--software described in [36]. Not available for download on the Internet. It was supposed to be a console tool for simulating DOP values for specific coordinates and at a specific time. The authors showed in their work the influence of the number of GNSS constellations used and terrain fields on the DOP. They used the height model;
* SatNav Toolbox--paid toolkit for the MATLAB package. They allow reading orbit data of navigation systems. The graphs drawn by them enable a simple analysis of the state of GNSS constellations for specific coordinates and at a specific time;
* GeoPAL--software described on the website of the European Union Agency for the Space Programme (EUSPA) [37], which was the beneficiary of the grant. The project website no longer exists, and no other information is available about it. It was supposed to be a program for the planning of a GNSS measurement campaign dedicated to farmers and supporting crop efficiency. It made it possible to plan operations in an arable land when geometric coefficients have the best values. In addition to the above-mentioned comprehensive solutions, smaller components and tools should be mentioned. These include high-quality libraries designed to work with navigation data, such as GAMIT, GPS Toolkit and RTKLIB. There is also softwarespecialised in calculating and simulating the availability of satellite data (e.g., Bernese GNSS Software and MAAST).