Long arc orbit determination solutions using Encke's method

摘要

The long term tracking of geodetic satellites using laser ranging has provided an opportunity to conduct various geophysical studies by solving for continuous, dynamically consistent trajectories that span up to tens of thousands of orbital revolutions. The process of computing these long arc solutions require a reliable technique that numerically integrates the equations of motion. Previous studies have demonstrated that Encke's method can be used to reduce numerical integration errors and improve filter convergence for long arc solutions. However, current forms used to represent the reference orbit in Encke's method are not capable of maintaining the reference trajectory close to the true trajectory for the extended trajectories involved in the long arc solutions. To improve on the previous Encke reference orbit models, an expanded model has been developed and successfully applied to a 15 yr LAGEOS long are solution.