Nonparametric narrowband wavefront estimation from wavefront gradients

The wavefield sampled by a two-dimensional (2-D) planar array can be charac terized by a delayed signal. This correspondence investigates the problem o f the nonparametric estimation of the delay function (or wavefront) when th e waveform is narrowband. The wave front is estimated by integrating the lo cal estimates of the differential time of delay (TOD) of the waveform betwe en neighboring sensors. The ambiguity of the TOD estimator for the narrowba nd waveform can be conveniently limited by the a priori search interval for the cross correlation method. The reconstruction of the wavefronts is form ulated 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.