Satellite laser ranging is one of the most accurate astronomical and geodynamic measurements. At present, the detectors used by most stations in the world are single-photon avalanche diodes. Due to the detection characteristics of single-photon avalanche diodes, energy fluctuations will cause walk errors in each ranging data during every daily observation. The existence of walk error limits the development of satellite laser ranging to higher precision, so it needs to be studied. This study first introduces the detection principle of single photon avalanche diodes, and explains why walk error exists in single photon avalanche diodes:the fluctuation of the number of echo photons. Secondly, based on the detection principle of the single photon avalanche diode, the theoretical calculation of the walk error and the calculation method of the photon number of the laser ranging echo are deduced. The method for calculating the number of photons can calculate the number of echo photons corresponding to the satellite laser ranging original data. According to the data processing protocol of satellite laser ranging, the data processing of satellite ranging data should be combined with the ground target ranging data. However, satellite echo photon numbers and the ground target echo photon numbers cannot be guaranteed to be strictly consistent, so there will still be walk error in the processed data. The simulation result of laser ranging of LAGEOS satellite and ground target can show the difference in echo photon numbers and walk error of two targets, which can explain the question above. Furthermore, a compensation method for the walk error of the satellite laser ranging measured data combined with the theoretical model is proposed. The operation process of the method is as follows:first, signal identification, photon number calculation, and walk error calculation are performed on the ground target laser ranging data;then, signal identification, photon number calculation and walk error calculation are performed on the satellite laser ranging data;at last, the difference between the two walk errors is added to the satellite laser ranging results. Combining the proposed method of calculating the number of echo photons with the simulation based on the 53 cm binocular laser ranging telescope of the Yunnan Astronomical Observatory of the Chinese Academy of Sciences, the calculation results of the echo photons numbers are obtained. Then we apply the walk error compensation method to the data processing process of the corresponding data. In this way, walk errors in the satellite laser ranging data can be compensated. We select the satellite laser ranging data from the laser ranging data of 6 satellites to practice this method and analyze the results. The data is part of the laser ranging data of Ajisai, Jason-3, KOMPSAT-5, LARES, Stella, and Swarm-B from 2017 to 2022. Among them, the five-year average compensation value of Ajisai is 41.9 ps (1.257 cm), Jason-3 is 28.5 ps (0.855 cm), KOMPSAT-5 is 28.7 ps (0.861 cm), LARES is 34.7 ps (1.041 cm), Stella is 22.6 ps (0.678 cm), Swarm-B is 450.7 ps (13.521 cm). At the same time, the maximum correction value appeared in the Swarm-B ranging data on January 5, 2020, which was 770 ps. This means the data exists a distance deviation of 23.1 cm. The reason is that Swarm-B satellite owns a low orbit altitude and its running speed is fast, which lead to low tracking accuracy of the telescope. As a result, the echo photon numbers will fluctuate more than other High-Orbit Satellite. In this study, we analyze and study the cause, simulation of walk error and how to compensate for it. The results show that using the proposed walk error compensation method in this study to process satellite laser ranging data can reduce the distance measurement value fluctuation caused by the fluctuation of the number of echo photons in the laser ranging data of each satellite. As a result, it can correct walk errors caused by energy changes in the data and improve data quality.
