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Due to the lack of accurate labels for the airborne synthetic aperture radar altimeter (SARAL), the use of deep learning methods is limited for estimating the above ground level (AGL) of complicated landforms. In addition, the inherent additive and speckle noise definitely influences the intended delay/Doppler map (DDM); accurate AGL estimation becomes more challenging when using the feature extraction approach. In this paper, a generalized AGL estimation algorithm is proposed, based on a fully supervised altimetry enhancement network (FuSAE-net), where accurate labels are generated by a novel semi-analytical model. In such a case, there is no need to have a fully analytical DDM model, and accurate labels are achieved without additive noises and speckles. Therefore, deep learning supervision is easy and accurate. Next, to further decrease the computational complexity for various landforms on the airborne platform, the network architecture is designed in a lightweight manner. Knowledge distillation has proven to be an effective and intuitive lightweight paradigm. To significantly improve the performance of the compact student network, both the encoder and decoder of the teacher network are utilized during knowledge distillation under the supervision of labels. In the experiments, airborne raw radar altimeter data were applied to examine the performance of the proposed algorithm. Comparisons with conventional methods in terms of both qualitative and quantitative aspects demonstrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]