A Data-Driven Model for System Delay Real-Time Estimation in SLR via Window Incremental Forest

System delay is a critical parameter in Satellite Laser Ranging (SLR), typically derived from ground target calibration. However, it exhibits significant instability due to dependence on environmental factors and device operational status, which consequently impacts the overall quality of SLR data. To address the challenge posed by the non-simultaneity of calibration and satellite observations, this study presents a novel real-time estimation model based on the Window Incremental Forest (WIF) algorithm. This data-driven model learns the dynamic relationship between system delay and its influencing factors, including meteorological parameters (temperature, pressure, humidity) and the device's operational time. Leveraging data from the Kunming station's 53 cm binocular SLR system, the WIF model integrates a window increment mechanism and a temporal ensemble strategy within the random forest framework to achieve robust estimation. Experimental results demonstrate that our method significantly outperforms traditional learning models, achieving a root mean square error (RMSE) of 19.5 ps, and a mean absolute error (MAE) of 15.5 ps. We further verify the model's engineering applicability in operational SLR scenarios: it realizes real-time calibration anomaly monitoring after system state mutations, and reduces the MAE of LAGEOS-1 satellite ranging residuals by 6.32\% through real-time delay correction. Consequently, the WIF model serves as an effective tool for the real-time estimation of system delay, thereby enhancing the stability and accuracy of SLR data products.