## 1 Introduction  
Global navigation satellite system (GNSS) signals are employed in various fields of terrestrial application to obtain position, navigation, and time (PNT) information, and several studies to expand its applications to space have been conducted with the goal of utilizing GNSS signals in space [1]. With the modernization of the global positioning system (GPS) and the development of additional global satellite navigation systems such as Russia's GLONASS, Europe's GALILEO, and China's BEIDOU (BDS), and regional satellite systems such as Japan's Quasi-Zenith Satellite System (QZSS) and India's Navigation with Indian Constellation (NavIC), the utilization of multi-constellation GNSS in space has been discussed. The use of the multi-constellation consisting of more than 100 active GNSS satellites will provide a great improvement in terms of signal coverage and system diversity, thereby improving the overall PNT performance and resiliency even in space [2, 3]. Additionally, South Korea is also planning a satellite navigation system called the Korea Positioning System (KPS) to provide an RNSS service over the Korean Peninsula [4, 5]. For development of these infrastructure systems, research on the use of GNSS technology for deep space exploration has been carried out by the National Aeronautics and Space Administration (NASA) [6], the European Space Agency (ESA) [7, 8, 9], and other projects [10]. The orbit of the GNSS satellites is located at an altitude of about 20,000 km. The GNSS satellites orbit around the earth and transmit signals in the direction of the center of the earth. For GPS L1 signals, the beam width of the main lobe is about 47\({}^{\circ}\), which transmits signals to areas including the ground and Low-Earth Orbit (LEO). Thus, by employing this characteristic, GNSS signals can be utilized in LEOs through the same method used on the terrestrial region. However, when GNSS signals are utilized at higher altitudes than LEOs, a limitation occurs due to the geometric structure between the GNSS satellite and receiver, and this should be taken into consideration. The geometric structure when GNSS satellite signals are received at geostationary orbits is shown in Figure 1. When a receiver is located at a higher position than the GNSS satellite orbit, no GNSS satellites are present in the zenith direction. Thus, GNSS signals transmitted from the opposite of the earth in the nadir direction should be received. In this case, the visibility of GNSS satellites is considerably degraded due to the blockage produced by the earth [11]. As is well known, at least four satellites should be observed simultaneously in order to achieve the position, and more satellites can improve the position accuracy. However, due to the signal blockage by the earth, the satellite visibility and geometry problem occurs when only individual GNSS is utilized [12]. Moreover, the propagation distance of the signals transmitted from the opposite of the earth is increased followed by an increasing free space loss, resulting in a weakening of the signal strength. For this reason, it is necessary to study minimal receivable signal strength in order to utilize GNSS signals at the geostationary orbit. In relation to this, NASA defined the concept of space service volume (SSV) based on the characteristics of GNSS signals at different altitudes. That is, a section from the ground's surface up to an altitude of 3000 km is classified as the terrestrial service volume (TSV), and a section from an altitude of 3000 km up to 36,000 km is classified as the SSV. For an example of the LEO in the TSV, almost constant signal strength can be received, and PNT can be estimated using the GPS alone, with no signal outage. GPS receivers, which are utilized in the ground, can be employed by the satellites in the TSV with only minor modifications. That is, only the Doppler Effect due to the high-speed rotation is taken into consideration in the design of the signal tracking unit in the GPS receiver.