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The contribution of Satellite Laser Ranging (SLR) to the definition of the origin of the reference frame (geocenter coordinates), the global scale, and low degree coefficients of the Earth's gravity field is essential due to the remarkable orbit stability of geodetic satellites and the accuracy of laser observations at a level of a few millimeters. Considering these aspects, SLR has an exceptional potential in establishing global networks and deriving geodetic parameters of the supreme quality. SLR faces today the highest requirements of the Global Geodetic Observing System (GGOS) yielding 1 mm of long-term station coordinate and 0.1 mm/y of station velocity stability. The goal of this work is to assess the contribution of the latest models and corrections to the SLR-derived parameters, to enhance the quality and reliability of the SLR-derived products, and to propose a new approach of orbit parameterization for low orbiting geodetic satellites. The impact of orbit perturbations is studied in detail, including perturbing forces of gravitational origin (Earth's gravity field, ocean and atmosphere tides) and perturbing forces of non-gravitational origin (atmospheric drag, the Yarkovsky effect, albedo and Earth's infrared radiation pressure). A multi-satellite combined solution is obtained using SLR observations to LAGEOS-1, LAGEOS-2, Starlette, Stella, and AJISAI. The quality of the SLR-derived parameters from the combined solution is compared with external solutions. The Earth rotation parameters are compared to the IERS-08-C04 series and the GNSS-derived series, whereas the time variable Earth's gravity field coefficients are compared to the CHAMP and GRACE-derived results.