*2.1. Classical Method for Determining the Positioning Accuracy of a Navigation System with 95% Probability*

The classical method for determining the positioning accuracy of a navigation system is based on a statistical approach. The works of Gerolamo Cardano [38], Pierre de Fermat and Blaise Pascal [39] on gambling, as well as the works of Christiaan Huygens [40] constitute the foundation of modern statistics. In 1812, Pierre-Simon Laplace formulated the classic definition of probability [41], which was mathematically formalised in 1933 by Andrey Kolmogorov [42], who gave the basic formulas of probability calculus and its axioms. Although modern statistics is an extremely young branch of mathematics, it is widely used in many fields, ranging from engineering [43] and economics [44] to the scientific aspects of computer science [45]. In navigation, similar to other sciences, it is assumed that the position errors of navigation systems are normally distributed. Major arguments justifying the use of normal distribution in research on positioning in navigation include [46]: intuition and tradition, simplicity of the distribution [47], consistency with the central limit theorem, as well as use as an approximation [48].

Position accuracy in navigation can be defined as a degree of conformance between the estimated or measured position and its true position. Position accuracy can be determined as different types of statistic. These can be calculated related to the true values of coordinates (predictable accuracy), or, if the actual position is not known, the mean position (repeatable accuracy) is often used as an approximation to the actual position. Both position solutions must be based on the same geodetic datum, e.g., the World Geodetic System 1984 (WGS-84) [19]. The most commonly used position accuracy measures in navigation and transport are as follows: CEP (Circular Error Probable, 2D, *p* = 0.5), SEP (Spherical Error Probable, 3D, *p* = 0.5), RMS (1D, *p* = 0.632–0.683), DRMS (2D or 3D, *p* = 0.632–0.683), 2DRMS (2D or 3D, *p* = 0.954–0.982) or 3DRMS (Triple Distance Root Mean Square, 2D or 3D, *p* = 0.997). The description of individual measures is presented in detail in [34]. However, the most common accuracy measure for assessing the positioning accuracy of navigation systems is 2DRMS.
