Different approaches in determining global geodetic parameters from SLR data - a simulation study

Satellite laser ranging (SLR) is currently one of the four space geodetic techniques that provide a relevant contribution to the International Terrestrial Reference Frame (ITRF) realization as well as to the determination of global geodetic parameters including the low-degree harmonics of the Earth's gravity potential. ITRF realizations are mostly based on the observations to the two LAGEOS and two Etalon satellites, however, the impact of observations to Etalon satellites is marginal when compared to LAGEOS. Currently under consideration is an extension of the ITRF solution to include the LAser RElativity Satellite (LARES) and LARES-2 developed by the Italian Space Agency ASI and launched on July 13, 2022. The contribution of other satellites with retroreflectors is still being investigated.

This study aims to verify various approaches to estimating geodetic parameters depending on the number of determined empirical once-per-revolution parameters for satellite orbits and different approaches of parametrization for the Earth rotation parameters (ERP), including piecewise linear and piecewise constant parametrization. We analyze six parametrizations, where three of them are proposed in this study and the other three are used by research centers, such as the Center for Space Research (CSR), the International GNSS Service (IGS), and the International Laser Ranging System (ILRS). For IGS and ILRS, these are the approaches used in determining the ERPs based on GNSS and SLR data, respectively. To the constellation of geodetic satellites such as LAGEOS-1/-2, Etalon-1/-2, and LARES-1/-2, we add hypothetical SLR satellites such as LARES-3/-4 and LARES-5/-6 which supplement the current constellation in the simulation study. We check whether satellite parameters, such as satellite altitudes and inclination angles affect individual global geodetic parameters when using different approaches to ERP parameterization and the set of estimated empirical orbit parameters.

The obtained results show that the value of the obtained formal errors may depend not only on the choice of the estimated geodetic parameters but also on the number of satellites or satellite orbit parameters involved in the calculations.