Linear Prediction-Based DOA Estimation for Directional Borehole Radar 3-D Imaging

Directional borehole radar (BR) 3-D imaging is a challenging problem due to its limited observation space within a borehole. We present a linear prediction (LP)-based direction-of-arrival (DOA) estimation and a migration-based 3-D imaging algorithm for the directional BR, which is composed of a transmitting antenna and a uniform circular array including four small receiving antennas. Only the azimuth is estimated, while the elevation and the distance are included in the imaging process. LP is a useful tool for DOA estimation in the radar domain, but a single linear array (LA) has azimuth ambiguity in DOA estimation. The four receiving antennas are treated as two orthogonal uniform LAs. The combination of two arrays removes the ambiguity in DOA estimation. In addition, the moving window and the threshold-based estimation increase the calculation efficiency. According to the estimated azimuth angles, the measured signal at each depth is decomposed to the corresponding directions. Therefore, there is a time-series signal in each direction at each depth. After processing the measured signals at all depths, we obtain a 3-D data set that can be used for horizontal- and radial vertical-section displays. Then, the radial vertical-section data are processed by migration which transforms the time domain signal into a wavefield-based 3-D image. Simulated data from a fracture model are used to validate the algorithm, and the reconstructed image can reveal the real model well. It is concluded that the novel method we propose is an effective one with real-time processing capability.