Improve GNSS Orbit Determination by using Estimated Tropospheric and Ionospheric Models

Abstract

Orbit Determination is a technique used to estimate the position of a satellite from its observable measurements. Missing or incorrect modeling of troposphere and ionosphere delays is one of the major error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS). Accurate computation of these two delays is a mandatory step to cope with accuracy needs which are close to centimeter or millimeter levels. This paper presents the different steps of development of estimated tropospheric and ionospheric models. All these models are included in the Orekit open-source space flight dynamics library. Adding estimated tropospheric and ionospheric models into an orbit determination process can be a difficult procedure. Computing and validating measurement derivatives with respect to troposphere and ionosphere parameters are critical steps. To cope with this constraint, we used the Automatic Differentiation technique to avoid the calculation of the derivatives of long equations. Automatic Differentiation is equivalent to calculating the derivatives by applying chain rule without expressing the analytical formulas. Therefore, Automatic Differentiation allows a simpler computation of the derivatives and a simpler validation. This paper presents how the Jacobian measurement matrix is computed by Automatic Differentiation. It also describes the impact of using estimated tropospheric and ionospheric models. Finally, a study of different model configurations is performed in order to highlight the relevant tropospheric and ionospheric parameters to estimate. The performance of the different models is demonstrated under GPS orbit determination conditions. Both satellite state vector estimation and measurement residuals quality are used as indicator to quantify the orbit determination performance. This paper addresses that estimated tropospheric and ionospheric models are actually more accurate than empirical models to estimate satellite state vector in GNSS orbit determination. A gain of about 60% is obtained on the estimation of the satellite position when estimated models are used, without altering the computation time.