V.A. Ufaev, A.V. Ufaev, D.V. Ufaev

Completed one-step synthesis of algorithms for locating the sources of short-wave radiation by maximum likelihood. The variant of the reception signal ground source radiation reflected from different layers of the ionosphere on the background of additive Gaussian noise with spatially separated DF antenna, forming a circular array antenna. A priori uncertainty about the number of rays and angles where they are coming off suggested by the calculation of propagation paths of radio waves in the geometrical optics approximation. Defining in this way the number of rays and angles of the place of their arrival, as a function of distance, eliminates the need for a separate independent measurement of angles of arrival of radio waves with unknown among them, reducing the problem of synthesis of the well-known version of the estimates of the unknown complex amplitudes of the signals of each of the beams from the site of a possible source. The resulting solution consists in determining the minimum of the function of spatial uncertainty on the bearing and distance from the compensation calculated raids phase-rays, taking into account the calculated propagation paths for each of the possible values of range and bearing to the source of radiation. To eliminate bias minimum of uncertainty associated with an increase in the number of simultaneously received signals, it is proposed to introduce a penalty function that increases linearly with the number of received signals and the order of the analyzed model. Results of statistical modeling showed the possibility of determining the distance to the source with a relative error of up to 5% for the range to 400-1250, 2400-2650 km. The presence of the boundary values of elevation angles of arrival of all the rays equal to about 15 degrees, below which the error increases to 30%.