Coordinate Measurement Method of the Earth Station Based on the Two Spacecraft Use

Relevance. The existing methods of coordinate measurement, such as goniometric, goniometric-range-measuring, difference-range-measuring, total-range-measuring are well studied and optimized. However, the application of these methods is not always possible or advisable, which stimulates the development and study of new methods and their integration with the existing ones. The article presents the developed method of coordinate measurement of the earth station, based on the use of two spacecraft. The derivation of analytical relationships for calculating the coordinates of earth stations based on the values of mutual time delays and frequency shifts is shown. The specified time delays and frequency shifts are due to different distances and Doppler frequency shifts of the same implementations of radio signals on different radio paths. The main expressions for time delays and frequency shifts of radio signals of earth stations retransmitted by spacecraft are presented. A system of three independent equations is composed. The first equation is the difference-range equation, the second is the difference-radial-velocity equation, and the third is the equation of the Earth's reference ellipsoid. The result of solving the system of equations is the coordinates of the earth station. The study used the methods of modeling and mathematical analysis. When solving the second-order equation, the iterative Newton-Raphson method was used with the expansion of functions in Taylor series with an accuracy of up to the first derivatives. A particular example of calculation is given as an illustration of the developed method. The developed method of coordinate measurement is invariant to the type of orbits of spacecraft used to determine the coordinates of earth stations. Two spacecraft are given as an example: the first is in geostationary orbit, the second is in low orbit. The scientific novelty of the developed technical solution is the unambiguous one-time determination of the coordinates of earth stations located on the surface of the Earth's reference ellipsoid, based on the use of only two spacecraft. In this case, there is no need for synchronization with the radiation of radio signals of earth stations, which is a necessary condition for most existing methods of coordinate measurement. The practical significance of the proposed combined (difference-range and difference-Doppler) method of coordinate measurement of earth stations lies in the possibility of its application in existing and prospective radio monitoring complexes for assessing the coordinates of earth stations that illegally use the frequency-time resource of a spacecraft, as well as being sources of intentional or unintentional radio interference.