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ESPRIT is an algorithm for determining the fixed directions of arrival of a set of narrowband signals at an array of sensors. Unfortunately, its computational burden makes it unsuitable for real time processing of signals with time-varying directions of arrival. The authors develop a new implementation of ESPRIT that has potential for real time processing. It is based on a rank-revealing URV decomposition, rather than the eigendecomposition or singular value decomposition used in previous ESPRIT algorithms. The authors demonstrate its performance on simulated data representing both constant and time-varying signals. They find that the URV-based ESPRIT algorithm is effective for estimating time-varying directions-of-arrival at considerable computational savings over the SVD-based algorithm