Practical navigation is far from an exact science because the navigator in his daily routine uses too many approximations which would be unacceptable in careful scientific work. These approximations will not be referred to in detail, or elaborated upon, since the matter is adequately dealt with in standard navigation manuals and textbooks. The laws that govern the distribution of random errors, however, their occurrence and frequency, will be discussed in this paper in terms of the theory of probability and mathematical statistics. The main objective will be the quantitative error analysis of random structures. We shall also formulate mathematical models and use them for computer simulations of practical navigation problems.