A Data-Driven Method for Real-Time Estimation of System Delay in Satellite Laser Ranging Using the Window Incremental Forest

System delay is a critical parameter in Satellite Laser Ranging, typically derived from ground target calibration. However, it shows significant instability because of dependence on environmental factors and device operational status, which consequently impacts the overall quality of the 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 algorithm. This data-driven model learns the dynamic relationship between system delay and its influencing factors, including meteorological parameters (such as temperature, pressure, and humidity) and the device's operational time. Using data from the 53~cm binocular Satellite Laser Ranging system at Kunming Station, the chosen model integrates a window increment mechanism and a temporal ensemble method, within the random forest framework, for robust estimation. Experimental results demonstrate that our method significantly outperforms traditional learning models, achieving a root mean square error of 19.5~ps, and a mean absolute error of 15.5~ps. We verify the applicability of the model in operational Satellite Laser Ranging scenarios, demonstrating real-time calibration anomaly monitoring after system state mutations, and reduction of the mean absolute error of satellite ranging residuals by 6.32% through real-time delay correction. Consequently, the Window Incremental Forest model serves as an effective tool for the real-time estimation of system delay, enhancing the stability and accuracy of Satellite Laser Ranging data.