Two-Dimensional Sub-Sample Shift Estimation Using Plane Phase Fitting

This paper investigates the problem of two-dimensional shift estimation between two sinusoids, proposing a method based on a least square plane fitting of the phases of two complex functions. The complex functions are defined using the cross-correlation and its Hubert transforms. This estimation method is shown to be unbiased for long signals and high signal-to-noise ratios. The case of truncated signals is considered and an iterative version of the estimator, giving more accurate results in these situations, is proposed