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

In [1], we studied amplitude estimation of one-dimensional (1-D) sinusoidal signals from measurements corrupted by possibly colored observation noise. We herein extend the results for two-dimensional (2-D) amplitude estimation. In particular, we investigate the 2-D sinusoidal amplitude estimation within the general frameworks of least squares (LS), weighted least squares (WLS), and MAtched FIlterbank (MAFI) estimation. A variety of 2-D amplitude estimators are presented, which arc 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 2-D 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.