ESPRIT is a successful algorithm for determining the constant directions of arrival of a set of narrowband signals on an array of sensors. Unfortunately, its computational burden makes it unsuitable for real time processing of signals with time-varying directions of arrival. In this work we 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. We demonstrate its performance on simulated data representing both constant and time-varying signals. We find that the URV-based ESPRIT algorithm (total least squares variant) is effective for time- varying directions-of-arrival using either rectangular or exponential windowing techniques to diminish the effects of old information.