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In this paper, parameter estimation of a two-dimensional (2-D) single damped real/complex tone in the presence of additive white Gaussian noise is addressed. By utilizing the rank-one property of the 2-D noise-free data matrix, the damping factor and frequency for each dimension are estimated in a separable manner from the principal left and right singular vectors according to an iterative weighted least squares procedure. The remaining parameters are then obtained straightforwardly using standard least squares. The biases as well as variances of the damping factor and frequency estimates are also derived, which show that they are approximately unbiased and their performance achieves Crame??r-Rao lower bound (CRLB) at sufficiently large signal-to-noise ratio (SNR) and/or data size conditions. We refer the proposed approach to as principal-singular-vector utilization for modal analysis (PUMA) which performs estimation in a fast and accurate manner. The development and analysis can easily be adapted for a tone which is undamped in at least one dimension. Furthermore, comparative simulation results with several conventional 2-D estimators and CRLB are included to corroborate the theoretical development of the PUMA approach as well as to demonstrate its superiority.