Reduced dynamic orbit determination using GPS code and carrier measurements

Abstract

The three-dimensional nature of Global Positioning System (GPS) measurements provides a unique opportunity for accurately determining the position and velocity of satellites in low Earth orbit (LEO). For optimum results a reduced dynamic technique is commonly preferred, which combines the merits of kinematic positioning techniques with those of a fully dynamic trajectory modeling. As part of the present study two different approaches to reduced dynamic orbit determination are compared, both of which involve the estimation of empirical accelerations on top of a precise deterministic force model. In the batch least-squares estimator piece-wise constant accelerations are adjusted in consecutive sub-intervals that are sufficiently short compared to the orbital period. The extended Kalman filter/smoother approach, on the other hand, estimates the empirical accelerations using a first-order Gauss–Markov process noise model. Software implementations of both estimation methods have been used with GPS measurements of the GRACE mission to assess the individual merits of the different filtering schemes. Both approaches are shown to provide accurate and compatible results, which match an external reference solution to better than 5 cm when processing dual-frequency data and better than 10 cm when using single-frequency measurements. While the extended Kalman filter/smoother requires less computer resources in terms of memory and processing time, the batch least-squares estimator ensures a better smoothness of the resulting trajectory and was found to be more robust in case of data gaps.