Abstract

Angle-of-arrival (AOA) estimates are considered for a passive sensor array operating in atmospheric turbulence. The Cramer–Rao lower bounds (CRLBs) of the azimuth and elevation are calculated for a spherical wave assuming multiple unknown parameters, a line-of-sight propagation path, and a single monochromatic source. The received signal is modeled as a complex Gaussian random variable with a deterministic mean. Therefore, this theoretical treatment is valid for strong or weak scattering in the presence of strong diffraction. The experimental variances of the AOA estimates calculated using a spatial Fourier transform beamformer are compared to the theoretical CRLBs. The data were collected at a planar array under several distinct atmospheric conditions [D. K. Wilson et al., Acoust. Res. Lett. Online 106, L24–L29 (1999)]. The CRLBs are calculated for the meteorological conditions observed during the experiment. Models based on von Kármán’s spectrum are used to model the atmospheric turbulence. The observed experimental standard deviations are typically found to be two to three times larger than the theoretical calculations.

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