We present a new approach (AWI-ICENet1), based on a deep convolutional neural network, for analysing satellite radar altimeter measurements to accurately determine the surface height of ice sheets. Surface height estimates obtained with AWI-ICENet1 (along with related products, such as ice sheet height change and volume change) show improved and unbiased results compared to other products. This is important for the long-term monitoring of ice sheet mass loss and its impact on sea level rise.