Nicholas C. Makris
Naval Res. Lab., Washington, DC 20375
A variety of methods currently exist for resolving the ambiguity and blurring introduced by beamforming ocean acoustic line array measurements of ambient noise [R. A Wagstaff, J. Acoust. Soc. Am. 63, 863--869 (1978)] and reverberation [N. C. Makris, J. Acoust. Soc. Am. 94, 983--993 (1993)]. However, these methods are not necessarily optimal because they assume that the measured data are deterministic, whereas in actuality they are stochastic. An optimal estimator for resolving such blurred beamformed images produces the minimum variance possible and is unbiased in its output. Estimation theory is used to derive such a minimum variance unbiased (MVU) estimator and to determine bounds on the resolution of such blurred images. The fields measured by the array are assumed to obey circular complex Gaussian random (CCGR) statistics, which have previously been shown to describe a wide variety of ocean acoustic field measurements from towed-array reverberation, to both horizontal and vertical ambient noise. Given CCGR fields, the resulting beamformed images are corrupted with signal-dependent noise known as speckle. Coherence theory for CCGR fields is used to express the MVU estimator for resolving blurred images in terms of the temporal coherence of the received fields and the measurement time.