A new method is proposed for estimating the parameters of two-dimensional damped/undamped harmonics. This method constructs three ESPRIT matrix pencils from the original data

combines engendecomposition filtering and the total least squares method go reduce the generalized eigenvalue problems of the noisy ESPRIT matrix pencils to the eigenvalue problems of three square matrices

and yields two sets of estimates of pole components and a set of estimates of the products of pole components. Utilizing a simple pairing algorithm

two-dimensional poles are obtained according to these three sets of estimates. The method requires quite small computations and it can be implemented by using a parallel algorithm. Simulations are provided to show the accuracy of this method.