We have developed a Kalman filter to estimate accurate Eotvos corrections and horizontal ship accelerations from Global Positioning System (GPS) fixes. High-resolution shipboard gravity measurements are obtained with a newly designed, linear phase, Finite Impulse Response (FIR) low-pass filter. Both filters are combined to yield accurate, near-real time, Eotvos-corrected underway gravity estimates. Error ranges that reflect uncertainty in navigation for these estimates are calculated from autocovariances of Kalman velocity estimates by means of variance propagation expressions for time-invariant linear digital filters. Estimates of horizontal ship acceleration are combined with a simplified instrument impulse response model in an attempt to remove transient noise from the gravimeter output.We apply the technique to data collected by two shipboard gravimeters, a LaCoste and Romberg Model S Air-Sea Gravity Meter and a Bell Aerospace BGM-3 Marine Gravity Meter System, operated side-by-side on the Scripps R/V Thomas Washington during Leg 1 of the Roundabout expedition.In the absence of significant horizontal accelerations due to course or speed changes, both instruments yield data with good repeatability, characterized by rms differences of less than 1 mGal. Horizontal accelerations generate transient signals that cannot be modeled at present to an accuracy of better than 5 mGal. Difficulties in removing these transients are primarily due to insufficient quantitative knowledge of the response of the instrument, including the gyro-stabilized platform. This can be determined analytically or empirically.