In this paper, we review a number of algorithms for solving the problem of building a map and the problem of SLAM - Simultaneous localization and mapping - in various formulations. These tasks are solved on a graph structure that describes a mine working, in which a localization system from stationary access points is installed. To solve the SLAM problem, the FastSLAM algorithm is used in various modifications, depending on the method for estimating the positions of access points. In all the proposed solutions, it was possible to achieve an error in estimating the positions of access points of no more than 2 meters. The problem of building a map is solved as a combinatorial problem of searching for a permutation of access points by known positions. The proposed permutation search algorithm showed tangible advantages in terms of execution time over the exhaustive search method on systems with 5 or more access points.

Keywords: graph, mining, localization, map construction, SLAM, MCMC, particle filter, Kalman filter, Bayes method