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Space-time adaptive processing (STAP) for range-dependent clutter rejection in airborne radar is considered. Indeed, radar antenna architectures or configurations that are different from the conventional uniform linear antenna array (ULA) and side-looking (SL) configuration have consequences on the clutter properties. The authors here investigate the use of Taylor series expansions (TSEs) of the space-time covariance matrix in the classical sample matrix inversion (SMI) STAP method in order to mitigate the range non-stationarity of the clutter and they compare it to the derivative-based updating (DBU) already proposed in the literature. The authors also propose a new algorithm based on a TSE of the clutter plus noise subspace in conjunction with the eigencanceler-based (EC) STAP, which improves the performance in term of signal-to-interference plus noise ratio (SINR) loss, compared to the DBU method. In this study, the particular cases of a ULA and a uniform circularly curved antenna (UCCA) array in SL and non-SL monostatic configurations as well as a ULA in some bistatic configurations are considered for the test and the comparison of the presented algorithms.