The TOPEX/Poseidon satellite (inclination 65¿, period 113 min) is scheduled for launch in 1992 to study the world's ocean topography through precise altimetric measurements. It will also carry an experimental Global Positioning System (GPS) receiver to demonstrate precise orbit determination with GPS. Data for the GPS experiment will be collected by the on-board receiver and a worldwide network of ground receivers. These data may also be used to improve the knowledge of the Earth's gravitational field. The GPS data are especially useful for improving the gravity field over the world's oceans, where the current tracking data are sparse. Using a realistic scenario for processing 10 days of GPS data, we perform a covariance analysis to obtain the expected improvement to the GEM-T2 gravity field. The large amount of GPS data and the large number of parameters (1979 parameters for the gravity field, plus carrier phase biases, etc.) require special filtering techniques for efficient solution. We have used the gravity bin technique introduced earlier to compute the covariance matrix associated with the spherical harmonic gravity field. The covariance analysis shows that the GPS data from one 10-day arc of TOPEX/Poseidon with no a priori constraints can resolve medium degree and order (3--26) parameters with sigmas (standard deviations) that are an order of magnitude smaller than the corresponding sigmas of GEM-T2. When the information from GEM-T2 is combined with the TOPEX/Poseidon GPS measurements, an order of magnitude improvement is observed in low- and medium-degree terms with significant improvements spread over a wide range of degree and order. ¿ American Geophysical Union 1992