In this paper, a generalized likelihood ratio test (GLRT) detector, based on support estimation (Sup-GLRT), for multiple scatterers detection in SAR Tomography, is proposed. It incorporates, in the statistical model, a sparsity assumption of the signal in the elevation direction, which is always verified in practical cases for scarcely vegetated areas. The test consists of sequential steps: first the presence of scatterers is detected; then, the determination of the number of scatterers and the estimation of their positons is performed sequentially, one by one, by means of a signal support detection-estimation operation. The test proposed follows an approach similar to SGLRT, where decisions are taken based on subspace energy measurements, but it is derived following a different testing order and is investigated both at the nominal system resolution and in the super-resolution cases, showing in the latter case, a detection gain with respect to SGLRT. Sup-GLRT performance is evaluated in terms of receiver operating characteristic (ROC) curves for different signal-to-noise ratio values. Experimental results obtained on real COSMO-SkyMed data are shown.