"Using a Kalman Filter to Improve the Accuracy of Satellite Orbital Parameter Determination Using Laser Range Finding"

"Determining the orbital parameters of artificial Earth satellites with centimeter and millimeter accuracy is a fundamental task in modern space geodesy, navigation, and space monitoring. Laser range finders (SLRs) provide the most accurate method for measuring satellite ranges, achieving millimeter-level accuracy. However, traditional data processing based on polynomial interpolation ignores the physical nature of orbital motion and exhibits instability during extrapolation. This paper proposes an algorithm for processing SLR data based on a Kalman filter, integrating a dynamic model of satellite motion with a sequence of range measurements. A comparative analysis with the cubic spline method was conducted on data from the Simeiz-1873 station for LAGEOS-1\/2 satellites. The results demonstrate a 35\u201342% reduction in the root-mean-square extrapolation error and provide a physically based estimate of the covariance matrix of state errors in real time."