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

In a companion paper [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 twodimensional (2-D) amplitude estimation, which is of interest in various applications, including medical imaging, synthetic aperture radar (SAR), seismology, and many others. In particular, we investigate 2D sinusoidal amplitude estimation under the general frameworks of least-squares (LS), weighted-leastsquares (WLS), and MAtched-FIlterbank (MAFI) estimation. A variety of 2-D amplitude estimators are presented, which 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 Cramér-Rao bound (CRB), the lower variance bound for any unbiased estimators. Making use of amplitude estimation techniques, we introduce a new scheme for 2-D system identification, which has a closed-form expression. The proposed 2-D system identification scheme is shown to be computationally simpler and statistically more accurate than the conventional output error method (OEM), when the observation noise is colored. The CRB for the 2-D 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. ∗This work was supported by the New Jersey Center for Wireless Telecommunications (NJCWT), the Senior Individual Grant Program of the Swedish Foundation for Strategic Research, and the National Science Foundation under Grant MIP-9457388. †Hongbin Li and Wei Sun are with the Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA (e-mail: {hli,wsun}@stevens-tech.edu). ‡Petre Stoica is with the Department of Systems and Control, Uppsala University, P.O.Box 27, SE–751 03, Uppsala, Sweden (e-mail: [email protected]). §Jian Li is with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA (e-mail: [email protected]).