## 1 Introduction  
The inter-satellite link (ISL), as an integrated dynamic network between satellites and between satellites and ground stations, combines measurement and data transmission functions, bringing significant changes to the traditional operation mode of the Global Navigation Satellite System (GNSS) [1, 2]. The primary functions of navigation ISLs can be summarized as follows: (1) achieving precise inter-satellite ranging, improving the geometric configuration of the network, and enhancing the accuracy of orbit determination and time synchronization; (2) utilizing real-time inter-satellite data transmission to increase the update frequency of navigation broadcast ephemeris; (3) enabling autonomous inter-satellite navigation in the absence of ground station support, enhancing the system's survivability and wartime operational capabilities; (4) addressing the limitations of regional tracking station monitoring capabilities, ensuring global service performance; and (5) real-time monitoring of the integrity of navigation information, improving the system's availability and reliability [3, 4, 5]. Currently, major spacefaring nations are accelerating the construction and refinement of ISL systems, striving to provide higher-quality navigation service performance on a global scale [6]. The development of the Global Positioning System (GPS) inter-satellite links began early and has reached the highest level of maturity. As early as the 1980s, the United States initiated research on ISL for the GPS, driven initially by the need for real-time monitoring of global nuclear tests and to enhance the survivability of GPS during wartime [7]. In 1984, [PERSON], [PERSON] et al. first proposed the fundamental framework for autonomous navigation, providing theoretical analysis results that were subsequently adopted by the U.S. military [2]. By 1990, the theoretical design and data simulation for the GPS Block IIR ISL were completed, demonstrating that, without ground support, the user range error (URE) could be maintained below 6 m for up to 180 days [7]. In 1997, the first GPS Block IIR satellite equipped with ISL payloads was developed, tested, and launched. [PERSON] et al. conducted orbit determination experiments using inter-satellite ranging data from four GPS Block IIR satellites, with results showing that the URE could be better than 3 m over 75 days [8]. To date, GPS has launched four types of satellites: GPS IIR, GPS IIR-M, GPS IIF, and GPS III, with their corresponding operational characteristics summarized in Table 1[9]. GPS satellites utilize UHF-band wide-beam antennas to establish ISLs, employing a polling-based time-division ranging system, where only one satellite transmits at any given time while the others receive [10]. Currently, the United States is developing third-generation navigation satellites, divided into three phases: GPS IIIA, GPS IIIB, and GPS IIIC. Although GPS III was originally planned to use Ka-band (22.55-23.55 GHz) and V-band (59.3-64 GHz) frequencies, the currently launched satellites of GPS III still operate in the UHF band due to various reasons [11]. Additionally, ongoing projects are exploring the integration of laser payloads into future GPS satellites [12]. Facing intense competition in the global navigation arena and challenges in establishing foreign ground stations, Russia has made significant investments in developing inter-satellite link (ISL) technologies for its GLONASS system. The current implementations primarily serve GLONASS-M and GLONASS-K satellites, each demonstrating distinct technological approaches. The GLONASS-M series satellites utilize S-band wide-beam antennas to establish ISLs and employ a simplex time-division mode to measure inter-satellite pseudo-range values, achieving systematic and random errors of 0.3 m and 0.4 m, respectively [13]. The GLONASS-K ISLs adopt a pulsed laser system, enabling centimeter-level inter-satellite ranging accuracy and medium data transmission rates (50 kbit/s), with the fastest link establishment time being less than 10 s [14].