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Stoica, Li and Li, (see IEEE Trans. Signal Processing, vol.48, p.338-52, 2000) introduced an amplitude estimation based scheme for one-dimensional (1-D) system identification that overcomes several drawbacks (e.g., computational complexity, local convergence, and statistical inefficiency when spectrally colored noise is present) suffered by the conventional output error method (OEM). Along the same line, we herein propose a two-dimensional (2-D) system identification scheme that makes use of 2-D amplitude estimation. In particular, we consider the recently introduced 2-D amplitude and phase estimation (APES) amplitude estimator, which has been shown to yield superior performance over its competitors. To benchmark the proposed scheme, we also derive the Cramer-Rao bound (CRB) for the 2-D system identification problem.