Background: The systems of positioning on the base of radiowaves are widely used both in a global scale and for the exact position-finding of objects indoors. Global systems of positioning usually need valuable high-quality time synchronization, assume substantial errors at improper weather, at falling of radio waves on the earth surface at small angles, shading of transceivers by large obstacles, and at presence of radio electronic interferences of different nature. Objectives Investigation of the new system of positioning on the ultrawideband impulse electromagnetic fields and their analysis by an artificial neural network is proposed. Materials and methods: The phenomenon of the pulse form change on angle of radiation by antenna is used for the determination of the position of ultrawideband receiver. At first, the two-dimensional case of the problem is considered. Exciting two antennas separated at known distance by means of different impulse signals it is possible to define the place of location of receiver if we know the angles of arrival of impulses from each antenna. The ultrawideband bow-tie antennas excited by the Gaussian impulses of different durations are used as irradiators. The forms of the received impulses are calculated by method of Finite Differences in Time Domain (FDTD). The classification of the time forms of the received electromagnetic waves from different antennas at different angles of radiation is carried out by a deep neural network. Results: It is shown that for the classification the artificial neural network pays special attention to the intervals of time where the received impulse changes quickly. The four-layer network faultlessly distinguishes the obtained signals from different antennas. The numerical calculation of the electromagnetic problem and artificial neural network training show the possibility of determination of angles of radiation by the network with the accuracy of one degree excepting some cases. Using the basis between antennas of 50 meters the precision of receiver position determination is not worse than 62 cm in the square domain of 50 meter size eliminating some angles where the accuracy falls to 2 meters. Conclusion: Property of antennas to change the form of radiated ultrawideband impulses for different angles can be used for the construction of the new system of positioning that does not need the time synchronization with transmitters. The proposed system can be effectively employed indoors. The distinctive feature of the impulse electromagnetic wave positioning system is its immunity to the existent narrowband electromagnetic waves.