Analytical problem solution of location calculation of radio source by time-difference method

The problem of calculating the coordinates of a radio source by the time-difference method based on the results of measuring the distance differences of three pairs of receiving stations is considered. In contrast to the known solutions, analytical relations have been obtained for the case when the distance differences were determined by five receiving stations, in which two pairs contain one common receiving station, and the third pair was formed by two receiving stations with arbitrary coordinates. A numerical example of calculation, illustrating the performance of the method is given.