Two-dimensional sinusoidal amplitude estimation with application to two-dimensional system identification

In a companion paper we studied amplitude estimation of one-dimensional (I D) sinusoidal signals from measurements corrupted by possibly colored observation noise. We herein extend the results to two-dimensional (2D) amplitude estimation, which is of interest in various applications, including medical imaging, synthetic aperture radar, seismology, and many others. In particular, we investigate 2D sinusoidal amplitude estimation under the general frameworks of least-squares (LS), weighted least-squares, and matched-filterbank estimation. Various 2D amplitude estimators are presented. They do not model the observation noise exactly, but are all asymptotically (for large samples) statistically efficient. The performances of these estimators in finite samples are compared numerically with one another as well as with the Cramer-Rao bound (CRB), the lower variance bound for any unbiased estimators. Making use of amplitude estimation techniques, we introduce a new scheme for 2D system identification, which has a closed-form expression. The proposed 2D system identification scheme is computationally simpler and statistically more accurate than the conventional output error method, when the observation noise is colored. The CRB for the 2D system identification problem is also investigated in this paper. Close-to-CRB performances are observed for the proposed system identification scheme for both white and colored noise with moderate numbers of data samples.