A directional borehole radar consists of one transmitting antenna in the borehole and four receiving antennas distributed at equal angles in a ring. The receiving antennas can determine the depth and orientation of targets beside the borehole. However, the problem of target orientation determination and 3D imaging algorithms remains a technological challenge. The MUSIC (multiple signal classification) algorithm requires a peak search, so the accuracy of the operation is limited by the angle interval. Based on the MUSIC algorithm, the Root-MUSIC algorithm is proposed and implemented. By replacing the spectral peak search with calculating the roots of the polynomials greatly improves the orientation recognition accuracy. Finally, the results obtained using the above algorithm are verified with synthetic data and compared with the results of the MUSIC algorithm. The results show that both the MUSIC algorithm and the Root-MUSIC algorithm can achieve very good orientation determination and 3D imaging results. In terms of accuracy, the Root-MUSIC algorithm has an obvious improvement compared with the MUSIC algorithm.

中文翻译：

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基于Root-MUSIC的定向钻孔雷达3D成像算法

定向钻孔雷达由一个在钻孔中的发射天线和四个等角度分布在环形中的接收天线组成。接收天线可以确定钻孔旁目标的深度和方向。然而，目标方向确定和 3D 成像算法的问题仍然是一个技术挑战。MUSIC（多信号分类）算法需要进行峰值搜索，因此运算的精度受到角度区间的限制。在MUSIC算法的基础上，提出并实现了Root-MUSIC算法。通过计算多项式的根来代替谱峰搜索，大大提高了方向识别的准确性。最后，使用上述算法得到的结果用合成数据进行验证，并与MUSIC算法的结果进行比较。结果表明，MUSIC算法和Root-MUSIC算法都可以达到非常好的方位确定和3D成像效果。在精度方面，Root-MUSIC算法相比MUSIC算法有明显的提升。