## 1 Introduction  
The Global Navigation Satellite System (GNSS) has been widely applied in many fields and has become an essential infrastructure for societal development. The four major GNSSs all employ constellations primarily composed of Medium-Earth Orbit (MEO) satellites. The MEO satellites of the global positioning system (GPS) are unevenly distributed across six orbital planes, whereas the MEO satellites of Russia's Global Navigation Satellite System (GLONASS), the European Union's Galileo, and China's BeiDou Navigation Satellite System (BDS) form Walker constellations, which are distributed across three orbital planes [1]. The GNSS orbits are primarily tracked by ground stations, which usually need to be evenly distributed throughout the globe to ensure a suitable observation geometry. However, because of limitations in the number and distribution of ground stations, not all GNSS satellites can be tracked at a sufficiently high accuracy. Currently, the 1D accuracy of GPS and GLONASS orbits, based on ground station observations provided by the InternationalGNSS Service (IGS), is better than 3 cm [2]. In contrast, the orbital accuracy of the BDS is lower because of its relatively small number of unevenly distributed ground stations [3]. Inter-satellite ranging can enhance the orbital accuracy of navigation satellites by combining the orbital data obtained from ground stations. This capability also enables GNSSs to navigate autonomously without requiring the support of ground stations, thereby improving their survivability in extreme conditions. In 2011, [PERSON] [4] described a GNSS exploratory project conducted by the European Space Agency (ESA), which analyzed the effects of introducing inter-satellite microwave ranging and communication links to improve GNSS and signal propagation performance. The results indicated that inter-satellite links (ISLs) are able to more effectively maintain the accuracy of satellite orbits and clocks. In practical applications, from the early 1990s, GPS satellites of the IIR series were already equipped with cross-link capabilities as part of the so-called Autonomous Navigation (AUTONAV) mode [5]. The GPS IIR satellites determined inter-satellite distances using a time-division, dual-frequency two-way mode of the ultra-high frequency (UHF) band [6]. However, the UHF band was prone to significant multipath errors and noise [7]. Therefore, subsequent GPS ISLs used the Ka-band [8]. The second generation of GLONASS satellites, GLONASS-M, employed inter-satellite microwave links to measure distances and to improve ephemeris and clock accuracy [1]. The BDS also primarily used Ka-band ISLs to autonomously determine satellite orbits and synchronize inter-satellite times, achieving inter-satellite ranging errors of less than 0.25 ns [9]. Compared to microwaves, optical waves have shorter wavelengths, superior directionality, higher signal-to-noise ratio gain, and greater modulation bandwidth. Therefore, laser ranging has a very high potential for ISLs as a high-precision ranging method, and it has been used to achieve favorable results in fiber-based time-frequency synchronization and satellite orbit determination [10; 11; 12; 13]. Inter-satellite ranging carriers are also beginning to shift from microwaves to optical waves to enhance clock synchronization and ranging capabilities between satellites. In 2013, [PERSON] et al. reported on a verification experiment for laser communication ranging technology conducted between the GLONASS-728 and GLONASS-747 satellites, which achieved an inter-satellite ranging precision of 3 cm [14]. Furthermore, the next-generation satellite GLONASS-K2 incorporated laser ISLs to further enhance the accuracy of its orbit determination and clock synchronization [1; 15]. [PERSON] et al. introduced the Kepler navigation system proposed by the German Aerospace Center (DLR) [16]. The space segment of this system was comprised of 24 Galileo-like MEO satellites and six Low-Earth Orbit (LEO) satellites equipped with ultra-stable optical clocks.