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Estimation of signal parameters via rotational invariance techniques (ESPRIT) appears to be the best of the known spectral-analysis methods. It has the highest resolution, has no spectral splatter and is robust in the presence of noise. It answers immediately and explicitly the question "What frequencies, real or complex, are present and what are their amplitudes?" Fourier methods (and other high-resolution methods), answer the less direct question "What amplitudes, applied to a set of regularly-spaced real frequencies, best represent the data?" They then present the problem of interpreting the amplitudes. These attributes of ESPRIT, in the two-dimensional (2-D) version described here, make it a natural for radar signal processing, where it answers the need for high-resolution imaging, free of sidelobes in range and range rate, and for high-fidelity feature extraction. The paper starts with the mathematical data model, describes a "resampling" procedure to fit the data better to the model, summarizes the 2-D ESPRIT algorithm itself, and presents examples of its performance. The paper covers the details of this least-squares version of ESPRIT, including an enhancement that allows the scatterers to be tracked individually. The algorithm properly distinguishes between scatterers having one coordinate in common, and it automatically pairs correctly the range and range-rate of each scatterer.