The Electric Field DOA Estimation of Low Frequency With Small Aperture Arrays via the Sparse Bayesian Focusing Method

The direction-of-arrival (DOA) estimation is a relatively popular research area, and most studies are biased toward electromagnetic and acoustic fields in high-frequency situations. The DOA estimation at low frequency is more challenging using electrode sensor arrays, which is the main focus of this article. An electrode array with a limited array aperture is considered for electric field signal measurements and DOA estimation at low frequencies. The sparse focusing method called iterated Bayesian focusing (IBF) is then proposed to be applied to electric field DOA estimation, in which the focusing mechanism is explained from the physical level of the electric field. The applicability of the IBF algorithm at all frequencies is theoretically demonstrated, which expands the spatial frequency of the algorithm and, thus, overcomes the array aperture limitation problem. Finally, an electric field DOA estimation experiment is designed in the rock formation to validate the feasibility of electric field DOA estimation at low-frequency conditions and the performance of the proposed algorithm. The experimental results show that DOA estimation at 1-Hz frequency can be achieved using three electrode sensors with limited apertures (2/11 wavelength aperture). The IBF algorithm can overcome the aperture limitation problem at the algorithmic level, and the error range of DOA estimation is controlled within 4°.