## 1 Introduction
These satellites were equipped with both microwave and laser payloads for inter-satellite ranging. In 2020, [PERSON] et al. proposed a pseudo-code incoherent laser ranging scheme based on a regenerative synchronization mechanism for inter-satellite ranging scenarios involving relatively stationary satellites [17]. This scheme was validated in laboratory tests. The slave station utilized a delay-locked loop to track and regenerate the pseudo-random code from the master station. The master station determined the distance information by calculating the phase difference between the received pseudo-random code and the transmitted pseudo-random code. The compensated ranging error was \(3.47\pm 1.73\) mm, which was affected by the receiver clock error generated by the code tracking loop and the clock error produced by the clock source. In 2021, [PERSON] et al. designed an integrated solution for inter-satellite communication and ranging, successfully conducting on-orbit verification experiments with two satellites (BEIDOU-3 M21 and BEIDOU-3 M22) in the same circular orbit [18]. The ranging scheme consisted of both coarse and fine distance measurements. Coarse ranging was achieved using the header of integer frames within, per second. The synchronization of symbols and data clock recovery was then implemented in hardware using code tracking loops. Finally, the fine phase (fine range) between the transmission clock and data reception clock was determined by constructing a reference clock, ultimately achieving a ranging precision of 2.6 mm. [PERSON] et al. proposed an inter-satellite ranging scheme based on pseudo-random code amplitude modulation, in which the coarse distance measurement was performed using the cross-correlation method [19]. New early and late codes were constructed by cyclically shifting the punctual code according to the coarse measurement. The fine distance was then determined using the early-late discriminator model with theoretical characteristic parameters. A ranging precision of 0.33 mm was achieved using fiber optics. However, within a distance of 150 mm (corresponding to a time delay of 500 ps), the ranging deviation was 6 mm (corresponding to a time delay deviation of 20 ps). As the measurement range increased, particularly when the time delay exceeded the width of one chip, the ranging deviation also increased. Ranging deviation can significantly affect the application of inter-satellite laser ranging to satellite orbit determination. Although orbit determination requires multiple measurements, the deviation of each measurement cannot be directly eliminated in the orbit determination software, preventing the high-precision characteristics of laser ranging from being effectively utilized. To achieve high-accuracy ranging and reduce inter-satellite laser ranging deviations, this study proposes a pseudo-random code phase-shift coherent laser ranging phase discrimination method that employs data shifting and a discriminator with calibrated characteristic parameters, which solves the problem of mutual restriction between ranging accuracy and ranging precision in the traditional method. In contrast to the traditional method, the proposed method shifts the data according to the position determined by the punctual code correlation peak. The shifted data are then cross-correlated and normalized with fixed early and late codes to accurately determine the fine distances. Additionally, a suite of varying distances is utilized in conjunction with a real-ranging system to calibrate the characteristic parameters of the phase discrimination model. A comparison between this method and the traditional method revealed that after calibration, the characteristic parameters of the phase discrimination model for the actual system differed from the theoretical values. For static target ranging, the ranging precisions of the proposed and traditional methods were 0.34 mm and 0.38 mm, respectively, and their ranging accuracies were 0.56 mm and 51.05 mm, respectively.