Introduction. Currently, there is a significant increase in the number of relay satellites in geostationary orbit. However, frequent incidents of illegal use of the satellites frequency resource, as well as unintentional and deliberate interference with other users are fixed. In this regard, it becomes necessary to evaluate accuracy and applicability of various methods for determining the location of sources of illegal and interfering radio emission with different signal parameters and with different levels of uncertainty for relay satellite coordinates and velocities.Aim. To study and to evaluate the accuracy of methods of geolocation of radio emission sources operating through geostationary relay satellites, with different signal parameters and with different levels of uncertainty for relay satellite coordinates and velocities.Materials and methods. Imitation modeling and the theory of digital signal processing were used.Results. Factors influencing the accuracy of the estimation of TDOA and FDOA parameters when determining the position of radio emission sources, which operate via relay satellites located in geostationary orbit, were considered. As a result of simulation, the estimate of the accuracy of the considered geolocation methods was obtained. It depends on the bandwidth of radio emission source signal, on the recording duration and on the level of a priori uncertainty relatively the relay satellites coordinates and velocities. Recommendations for the application of the considered methods in various conditions were formulated.Conclusions. Conclusions and recommendations formulated as a result of the study, will allow one to choose the most appropriate geolocation method to improve the accuracy of radio emission sources locating depending on conditions and signal parameters.

Introduction.  There  are  incidences  of  jamming  the  users  of  satellite  communication  systems,  who  apply  e.g. geostationary relay satellites, and the illegal use of such satellite resources. These actions can be both intentional and unintentional, and, among other things, be caused by non-compliance with electromagnetic compatibility standards on part of other users of satellite communication systems. For a prompt and high -quality response of radio monitoring services and satellite operators to these illegal  actions, it seems urgent to develop methods for accurate determination of the geolocation of radio emission sources.Aim.  To develop a method for improving the accuracy of determining the coordinates of ground-based radio emission sources operating via geostationary relay satellites based on shared operation of a barrage jammer and reference signal sources.Materials and methods.  The research was conducted using the statistical theory of radio engineering systems, the theory of digital signal processing and the method of simulation.Results.  A  method  was  developed  for  improving  the  geolocation  accuracy  of  ground-based  radio  emission sources operating via geostationary relay satellites based on shared operation of a barrage jammer and reference signal sources. A method for resolving ambiguity regarding the true correlation peak of a reference source signal using a signal from a barrage jammer was described. An expression was obtained for the probability of a correct  solution  when  resolving  such  ambiguity.  As  a  result,  the  estimates  of  geolocation  accuracy  obtained using the developed method were compared with those obtained by a conventional method relying on the usage of 3 different reference stations.Conclusions. The method proposed in this paper makes it possible to achieve a relatively high accuracy when determining the geolocation of ground-based radio emission sources in the Earth’s regions of interest, at the same time as involving no organizational and financial costs for the installation of a large number of reference stations.

Currently, there are often cases of illegal use of the resource of relay satellites located in geostationary orbit, and the creation of unintentional and deliberate interference with legal users of satellite communication systems, for example due to non-compliance with the power standards of radio transmitting devices and antenna radiation patterns, as well as the rules for the frequency spectrum regulating. One of the possible stages of the response by the radio frequency service and satellite systems operators to such situations may be an operational assessment of locating of the interference ground radio emission sources that violate the established requirements. The existing methods for estimating the coordinates of radio emission sources operating through geostationary satellites-repeaters involve calculating the Cross-Ambiguity Function (CAF) of signals received from several satellites that relay the signals of the main and side lobes of the antenna pattern of the geolocated source. In the case of a low received signals SNR, it is required to record signals for a long time, and in such cases, to achieve a sufficient SNR at the correlator output, it is necessary to take into account not only the Doppler frequency shift between the signals, but also the change in the frequency shift caused by the change in the velocity vectors of the repeater satellites. The aim of this work is to study the recording duration, at which it is required to take into account phase distortions caused by a change in the speed of the repeater satellite and their effect on the SNR at the correlator output, as well as to develop a method for accounting for such distortions. The theory of digital signal processing and the method of simulation were used as research methods. As a result of the study, an assessment was made of the duration of the signal recording, at which the Doppler frequency shift can be considered constant; introduced the concept of a modified CAF, which takes into account the change in the Doppler frequency shift due to its approximation by a linear function; the maximum duration of signal recording was estimated, at which the proposed linear approximation is valid. It is concluded that in the case of using the modified CAF, the minimum duration of signal recording, at which the absence of correlator output SNR degradation will be guaranteed, is 8.1 times greater than when using the traditional CAF.

Unintentional and intentional interference of terrestrial radio sources operating via geostationary relay satellites to legal users of satellite communication systems requires accurate determination of their location. Methods of terrestrial radio sources location are based on the calculation of an cross-аambiguity function by additive mixtures of signals and noise received from relay satellites. In the presence of frequency-phase instability of relay satellites heterodynes the retransmitted signals have phase distortions, which lead to a decrease in the signal-to-noise ratio (SNR) when calculating the cross- ambiguity function. The paper is aimed to study the effect of phase distortions caused by the instability of relay satellites heterodynes on SNR at the correlator output and to develop methods for their compensation based on statistical radio engineering and digital signal processing. The study of the proposed compensation methods was carried out by statistical simulation modeling. The SNR dependences at the correlator output on the duration of correlated signals for the model with a domi-nant frequency noise and frequency random walk have been obtained and a method for compensat-ing phase distortions caused by the instability of the relay satellites heterodynes has been developed. The energy gain has been estimated by applying the proposed compensation method. It has been shown that the developed method of compensation of relay satellites heterodynes instability allows achieving a significant gain in the SNR at the correlator output and contributes to increasing the probability of radio source signal detection from auxiliary relay satellites.