2D sinusoidal amplitude estimation with application to 2D system identification

We previously studied amplitude estimation of one-dimensional (1D) sinusoidal signals from measurements corrupted by possibly colored observation noise (see Stoica, P. et al., IEEE Trans. on Sig. Proc., vol. 48, p.338-52, 2000). We extend those results for two-dimensional (2D) amplitude estimation. In particular, we investigate the 2D sinusoidal amplitude estimation within the general frameworks of least squares (LS), weighted least squares (WLS), and MAtched FIlterbank (MAFI) estimation. A variety of 2D amplitude estimators are presented, which are all asymptotically statistically efficient. The performances of these estimators in finite samples are compared numerically with one another. Making use of amplitude estimation techniques, we introduce a new scheme for 2D system identification, which is shown to be computationally simpler and statistically more accurate than the conventional output error method (OEM), when the observation noise is colored