Measuring the distance apart and speed of 2 satellites in space orbiting the earth to the width of a human hair with no margin for error [damn those drift recalculations], and taking into account unknown factors with respect to the true values for
water depth,
water weight at different salt concentrations, ice
depth magma flows, volcanic activity etc [ie making a lot of guesses], plus taking human motivation on board [like CO2 increase must melt ice surely] can give you an
accurate measurement of the volume ice in Antarctica.