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In this paper, we develop a novel reduced-rank space-time adaptive processing (STAP) algorithm based on joint iterative optimization of filters for adaptive radar applications. The proposed algorithm consists of a joint iterative optimization of a bank of full-rank adaptive filters that forms the projection matrix and an adaptive reduced-rank filter that operates at the output of the bank of filters. We describe constrained minimum variance (CMV) expressions for the design of the projection matrix and the reduced-rank filter. Adaptive algorithms including normalized least-mean-squares (NLMS) and recursive least square (RLS) are derived for its efficient implementation. Simulations for a clutter-plus-jamming suppression application show that the proposed STAP algorithm outperforms the state-of-the-art reduced-rank schemes in convergence and tracking at significantly lower complexity.