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In this paper, we consider a simple, yet accurate approach for angle and range estimation of multiple targets in the frequency-modulated continuous-wave (FMCW) radar systems. Our new algorithm starts with estimation of time delays and ranges by the estimation of signal parameter via rotational invariance techniques (ESPRIT) algorithm. According to the estimated time delays, a group of filters is then devised to divide the received signals into a number of clusters. Finally, ESPRIT is invoked again to estimate the angles of the targets in each cluster. The new algorithm possesses some advantageous features. First, the number of the receive antennas could be less than that of the targets. Second, it is still applicable even when some targets are located at the same ranges or angles. Third, the estimated ranges and angles are automatically paired together. Both numerical simulations and practical experiments are conducted to demonstrate the superiority of our algorithm over the state-of-the-art works in terms of accuracy in various scenarios.