Nonparametric narrowband wavefront estimation from wavefront gradients

The wavefield sampled by a two-dimensional (2-D) planar array can he characterized by a delayed signal. This correspondence investigates the problem of the nonparametric estimation of the delay function (or wavefront) when the waveform is narrowband. The wavefront is estimated by integrating the local estimates of the differential time of delay (TOD) of the waveform between neighboring sensors. The ambiguity of the TOD estimator for the narrowband waveform can be conveniently limited by the a priori search interval for the cross correlation method. The reconstruction of the wavefronts is formulated as a least squares problem that is solved iteratively. Errors of the solution are quantified, and the contribution caused by noise is shown to be negligible.