Sky background noise represents a significant source of error in satellite laser ranging (SLR), its intensity and distribution directly influence the accuracy of SLR measurements. During the same observation process, fluctuations in sky background noise can vary by up to two orders of magnitude, adversely affecting both the precision and stability of the SLR-ranging results. Due to technological constraints, current SLR detection systems cannot measure the sky background noise concurrently with target observations. Consequently, a key research focus in this field is developing methods to accurately estimate the sky background noise in each observation area using readily available atmospheric parameters. Presently, there is no software on the market capable of directly calculating the sky background noise received by SLR systems. Most atmospheric radiation transmission softwares only provide simulations of atmospheric transmittance or sky background radiation intensity, which limits their ability to comprehensively analyze sky background noise. Additionally, because these tools do not account for the structural parameters of the SLR system, they cannot directly calculate the number of background noise photons, which limits their utility in optimizing and applying the SLR system.

This study utilizes the optical radiation transfer equation and the SLR system noise calculation equation in conjunction with the relationship between the distribution of atmospheric particles and meteorological parameters such as visibility and relative humidity near the surface. Key parameters, including optical thickness, scattering phase function, single scattering albedo, and scattering angle, are comprehensively considered. A satellite laser ranging atmospheric radiation transfer simulation software (SLRART) was developed using the C++ programming language. This platform was employed to estimate and analyze the sky background noise distribution as received by the 60 cm SLR system at Changchun Station. The reliability of this software was validated through experimental measurements of daytime background noise.

The experimental results demonstrate that the output from SLRART closely aligns with the actual measurement results. The average relative error for the first-level data product (atmospheric transmittance) is only 5% (Tables 1, 2), while the second-level data product (sky background noise received by the SLR system) shows an average relative error of approximately 10%, with the maximum error rate not exceeding 15% (Table 3). The above results indicate the accuracy and applicability of the SLRART software. Furthermore, the influence of different solar positions on the sky background noise received during SLR observation has been analyzed. The results indicate that the trend in the software simulation corresponds closely to the measured results, with the intensity of sky background noise generally decreasing as the solar angle increases (Table 4, Fig. 7). Finally, the impact of meteorological parameters on the detection performance of the SLR system has been examined. It has been found that, compared to visibility and relative humidity, the solar position is the primary factor driving changes in the false alarm rate of the SLR system: variations in the false alarm rate due to solar position can reach approximately 60%, significantly affecting the detection of echo signals. In contrast, the effect of seasonal meteorological factors on false alarm rates is relatively minor, with the maximum variation not exceeding 16% (Fig. 8).

This study employs the single scattering transmission equation for solar radiation, in combination with atmospheric transmittance slant transmission correction theory, to simulate the distribution of sky background noise in the SLR system. The developed SLRART software, which holds independent intellectual property rights, provides a platform for numerically calculating sky background noise using input parameters from the system and real-time meteorological data. Based on the above results, the numerical calculation of sky background noise in the SLR system has been achieved by inputting system parameters and real-time meteorological parameters. Compared with the measured results, the average relative error rate of SLRART in calculating the sky background noise of the SLR system is only about 10%, and the maximum error rate does not exceed 15%. In addition, SLR daytime background noise experiments and false alarm rate experiments have been conducted, and the experimental results are found to be in consistent with the software simulation results. The results indicate that the noise intensity decreases as the angle between the telescope and the sun increases. The developed SLRART software significantly extends the application of atmospheric transmission numerical simulation technology, addressing limitations in the theoretical calculation of sky background noise in SLR systems.