## 1 Introduction  
Position, velocity, and time accuracy, along with integrity, continuity, and availability, is the four major performance indicators of satellite navigation systems [1]. Navigation system innovations and enhancements require technical advancements. Among the many techniques for improving the Global Navigation Satellite System (GNSS) performance, inter-satellite link (ISL) technology has become a research focus in recent years. National Aeronautics and Space Administration Senior Engineer [PERSON] demonstrated the GPS III ISL. He stated that the introduction of ISLs can significantly improve the ephemeris prediction accuracy, realize autonomous integrity monitoring of satellites, increase autonomous orbit determination, and improve navigation system flexibility and expansibility [2]. Russia's new generation of navigation satellite GLONASS (GLObalnaya NAVigatsionnaya Sputnikovaya Sistema) -M also planned to improve autonomous navigation using ISLs [3, 4]. The European Space Agency has initiated several exploratory projects on the ISLs adopted in the Galileo system since 2007 [5]. Recently, with the successful launch of the new generation BeiDou (Xichang, China) navigation networking satellites, ISLs have been used in the BeiDou navigation system to achieve autonomous orbit determination [6, 7]. The introduction of ISLs has marked the emergence of a new generation of satellite navigation systems. Construction of ISLs has become an important consensus in several current GNSSs [8, 9]. The accuracy of inter-satellite ranging is crucial for determining the quality of the ISL construction, and ranging consistency is a prerequisite for ranging accuracy. [PERSON] set the precision of inter-satellite ranging to 0.5 m to simulate autonomous orbit determination [10]. [PERSON] used ISLand seven ground monitoring stations in China to achieve joint orbit determination. When the ISL pseudo-range observation error was 0.8 m, the orbit accuracy was better than 0.7 m [11]. Moreover, [PERSON] used ISL measurements in a centralized mode of the new-generation BeiDou navigation satellites to conduct autonomous orbit-determination experiments. When the standard deviation of the ISL measurement residuals was within 10.0 cm, the radial overlap differences in the autonomous orbits were less than 6.0 cm. The 24-h predicted orbital radial overlap differences were less than 10.0 cm, and the user equivalent ranging error of the 24-h predicted autonomous orbits was approximately 0.43 m [12]. According to the present notion of autonomous orbit determination and satellite-ground joint orbit determinations, the accuracy of inter-satellite ranging should be on the decimeter level. To date, most studies have focused on the ISL signal system design [13], signal dynamic characteristic analysis [14; 15], constellation design [16], and extension application [17; 18]. Few works focus on ISL ranging consistency in navigation constellation. Ranging consistency is affected by the onboard clock equipment, ISL payload device, space environment, source transmitter, etc. Ref. [19] focused on the influence of the frequency and phase characteristics of the onboard clock equipment on the ranging consistency of the ISL and proposed a phase compensation sensor design method for the phase offset of the onboard clock equipment. In addition, the ISL payload device delay is mainly affected by the device aging, light deformation, day and night temperature difference, and other space environmental factors. Device aging and light deformation have a long-term effect on the process, and the effect of intensity is very small. However, a nanosecond level of delay variations mainly caused by temperature variations is possible [20] and the influence of temperature on the equipment time-delay could not be ignored for high-precision satellite-ranging [21].