This Master’s thesis contains an overview of determining measurement uncertainties of direct and indirect measurements. It describes a way of creating a magnetic field with the help of Helmholtz coil and a more detailed description of some principles of magnetic field sensors. This thesis also contains a description of the experiments and the factors influencing them. The last part deals with the quantification of uncertainties from measured experiments and with the discussion of the results from these measurements.

This master's thesis focuses on the utilization of an artificially created weak magnetic field for navigation in 3D space. The theoretical part of this work deals with the general properties of the magnetic field and with its description. The next section of the theoretical part contains an overview of measuring principles for magnetic field measurements. Based on various types of measuring principles, the thesis elaborates on commercially available miniature sensors for magnetic field measurement with a measuring range up to 10 mT. The work focuses mainly on the magnetoresistive principle and fluxgate sensors. Furthermore, the theoretical part contains descriptions of methods for modeling the magnetic field of simple permanent magnets and various magnet assemblies. Lastly, the theoretical part involves a patent search of devices used for locating magnets that are installed in an intramedullary nail, which is used in intramedullary stabilization used on fractures of human bones. By locating the magnet in the nail, it is possible to precisely determine the position of the mounting holes. The practical part of the thesis deals with the analysis of magnetic field behavior in the vicinity of various magnetic assemblies, which were modeled in COMSOL Multiphysics using the finite element method. The models were created with the aim of analysing the behaviour of the magnetic field in the vicinity of the magnets and at the same time to find possible analytical functions that could be used to determine the position of the magnet in space relative to the probe. The result of this work is an analysis of various assemblies, which contains graphs of different dependencies and prescription of polynomial functions that approximate these dependencies. Another part of the thesis is the design of a probe that serves to locate the magnetic target. The work describes two possible methods of localization. For the differential method, a user interface in LabVIEW was created. The probe based on this method is fully capable of locating the magnet in the 2D plane. The state space search method is described only in theory.