Satellite gradiometry data provide the framework for estimating and validating Earth's gravity field from second and third order derivatives of the Earth's gravitational potential. Such procedures are especially useful when applied locally, as they relate to local and regional characteristics of the real gravity field. In this study a joint inversion procedure is proposed for the estimation of gravity anomalies at sea surface level from second and third order potential derivatives, based on a standard Gauss–Markov estimation model. The estimation procedure is applied for a test area stretching over Iran involving simulated grids from GOCE-only model GGM_TIM_R05 at GOCE altitude and gravity anomalies recovered at sea level. In order to validate the proposed estimation three different reductions have been considered independently, namely the removal of the long-wavelength part of the observed field through a global gravity model, the removal of the high-frequency part of the field through the incorporation of a topographic/isostatic gravity model and the application of variance component estimation. The application of a global gravity model leads to an improvement in the individual component estimation of the order of magnitude 3–73 per cent, with a significant reduction in bias to 4 mGal. Smoother gradient components can come out according to removing the topography and taking into account for isostasy that improved up results of recovery to 25 per cent for the radial second order derivative. Finally, the implementation of variance component estimation leads to no significant improvement in results of recovered gravity anomalies.