To address high deployment complexity and cost associated with antenna-array-based radio frequency identification (RFID) positioning systems, this paper proposes a 3D positioning algorithm based on tag arrays. First, the RFID phase backscatter model is analyzed, and the coupling effect is experimentally investigated to reveal their potential impact on angle estimation accuracy. Second, to mitigate the mutual coupling within the tag array, we propose a virtual tag construction method considering the tag arrangement. By optimizing the tag array with sparse configurations, an angle of arrival (AOA) estimation method for sparse tag arrays based on virtual tag construction is developed. Furthermore, to address the interference caused by potential target pose variations in practical applications, an angle-search-based attitude estimation method is incorporated. This method employs a spatial coordinate transformation model to achieve precise estimation of the tag array′s true orientation relative to a known antenna, effectively reducing the negative impact of attitude angles on angular measurement precision. Subsequently, a 3D positioning model is established using one-dimensional angle measurements, where azimuth and elevation angles after attitude compensation are obtained from sparse tag subarrays in two orthogonal directions to achieve 3D positioning through triangulation. Finally, a systematic evaluation of the proposed sparse tag array AOA estimation and localization algorithms was performed on a test platform built with the commercial Impinj R420 reader and tags. Experimental results demonstrate that the proposed system achieves positioning in three-dimensional space, with a median positioning error of 23.5 cm and a standard deviation of 12.5 cm, validating the effectiveness of the proposed algorithm.