PRECISE ORBIT DETERMINATION OF LOW EARTH SATELLITES AT AIUB USING GPS AND SLR DATA A. J ¨ aggi 1 , H. Bock 1 , D. Thaller 1,2 , K. So´ snica 1 , U. Meyer 1 , C. Baumann 1 , and R. Dach 1 1 Astronomical Institute, University of Bern, 3012 Bern, Switzerland 2 German Federal Agency of Cartography and Geodesy, 60598 Frankfurt a.M., Germany ABSTRACT An ever increasing number of low Earth orbiting (LEO) satellites is, or will be, equipped with retro-reflectors for Satellite Laser Ranging (SLR) and on-board receivers to collect observations from Global Navigation Satellite Systems (GNSS) such as the Global Positioning Sys- tem (GPS) and the Russian GLONASS and the European Galileo systems in the future. At the Astronomical Insti- tute of the University of Bern (AIUB) LEO precise or- bit determination (POD) using either GPS or SLR data is performed for a wide range of applications for satellites at different altitudes. For this purpose the classical numeri- cal integration techniques, as also used for dynamic orbit determination of satellites at high altitudes, are extended by pseudo-stochastic orbit modeling techniques to effi- ciently cope with potential force model deficiencies for satellites at low altitudes. Accuracies of better than 2 cm may be achieved by pseudo-stochastic orbit modeling for satellites at very low altitudes such as for the GPS-based POD of the Gravity field and steady-state Ocean Circula- tion Explorer (GOCE). Key words: Low Earth orbiting (LEO) satellites; Precise orbit determination (POD); Pseudo-stochastic orbit mod- eling; GPS; SLR. 1. INTRODUCTION The Astronomical Institute of the University of Bern (AIUB) has a well-documented record concerning the scientific analysis of Global Navigation Satellite System (GNSS) data with the Bernese GNSS Software [8]. The Center for Orbit Determination in Europe (CODE) [10], a global analysis center of the International GNSS Ser- vice (IGS) [11], generates the full IGS product line such as GNSS orbits and high-rate satellite clock corrections, which are used as input for spaceborne applications re- lying on GNSS data. Spaceborne measurements of the Global Positioning System (GPS) are used at AIUB to determine precise kinematic and reduced-dynamic orbits for a variety of low Earth orbiting (LEO) satellites. For this purpose the classical dynamic orbit determination techniques are extended by so-called pseudo-stochastic orbit modeling, which is extensively used for satellites at very low orbital altitudes to efficiently cope with poten- tial force model deficiencies. The procedures described in this article are applied to different LEO satellites and are operationally used by AIUB to derive the precise sci- ence orbits (PSO) for the GOCE mission in the frame of the GOCE High-level Processing Facility (HPF) [18]. The Bernese GNSS Software has recently also been extended from a pure GNSS processing software to a package offering full capabilities for processing Satel- lite Laser Ranging (SLR) data to spherical satellites [28]. Identical orbit modeling techniques as used for GPS- based LEO precise orbit determination (POD) are applied when processing SLR data to solve for orbital parameters together with non-orbit parameters of interest, e.g., SLR station coordinates, Earth rotation parameters, SLR range biases, and geopotential coefficients. 2. ORBIT DETERMINATION The equation of motion of an Earth orbiting satellite in- cluding all perturbations reads in the inertial frame as ¨ r = −GM r r 3 + f 1 (t, r, ˙ r,q 1 , ..., q d ,s 1 , ..., s s ) . = f , (1) where GM denotes the gravity parameter of the Earth, r and ˙ r represent the satellite position and velocity, and f 1 denotes the perturbing acceleration. The ini- tial conditions r(t 0 ) = r(a, e, i, Ω,ω,T 0 ; t 0 ) and ˙ r(t 0 ) = ˙ r(a, e, i, Ω,ω,T 0 ; t 0 ) at epoch t 0 are defined by six Kep- lerian osculating elements, e.g., a, e, i, Ω,ω,T 0 . The pa- rameters q 1 , ..., q d in Eq. (1) denote additional dynamical orbit parameters considered as unknowns, e.g., spherical harmonic (SH) coefficients of the Earth’s gravity field. The parameters s 1 , ..., s s denote additional empirical pa- rameters, e.g., once-per-revolution periodic accelerations or pseudo-stochastic parameters (discussed in Sect. 2.2). Based on a numerically integrated a priori orbit r 0 (t) solving Eq. (1), dynamic orbit determination may be for- mulated as an orbit improvement process. The actual or- bit r(t) is expressed as a truncated Taylor series with re- _____________________________________ Proc. ‘ESA Living Planet Symposium 2013’, Edinburgh, UK 9–13 September 2013 (ESA SP-722, December 2013)