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This paper presents a low complexity adaptive algorithm for two-dimensional (2-D) directions of arrival (DOA) tracking using a uniform rectangular array. The new algorithm employs three one-dimensional (1-D) subspace tracking algorithms to determine the two DOA components iteratively in a coarse-fine manner based on a single row or column of data. Also, to enhance the estimation accuracy, two orthogonal beamforming processes are invoked between the 1-D subspace tracking algorithms to partition the incoming signals into appropriate groups so that the DOAs can be well resolved even if they are very close. As such, the overall computational complexity called for is substantially less than the existing 2-D subspace tracking algorithms, which requires an update of higher-dimensional vectors. Furthermore, the estimated 2-D DOA components are automatically paired. Furnished simulations show that the new algorithm provides satisfactory tracking performance in various scenarios.