The angular position measurement of an array antenna based on a wireless signal has high accuracy in an indoor no-occlusion environment. However, due to the high complexity of indoor environments, signal occlusion, multipath, and other interfering factors are inevitable when users move randomly, which can greatly reduce the positioning accuracy. In addition, different directions of the positioning source signal can also affect the positioning result. The switching wheels of the dual-polarization antenna array are collected in channel 1, the fast Fourier transform (FFT) is applied to the data of channel 2 to estimate the frequency offset, and the phase of the data is compensated. Using the FFT frequency offset estimation, the high-precision positioning of a single base station is realized using the dual-channel switch and dual-polarization antenna array in turn. Aiming at analyzing the affecting factors of the positioning system accuracy, the strong tracking kalman filter algorithm is studied. At the same time, the singular value decomposition of the covariance matrix is performed to improve the robustness of the strong tracking kalman filter, and the adaptive factor is introduced to improve the filtering accuracy. The proposed positioning algorithm can achieve the positioning accuracy within 1 m in the coverage area in a line-of-sight (LOS) environment, while the dynamic positioning accuracy within 1 m cannot be guaranteed in the coverage area in a non-line-of-sight (NLOS) environment. On this basis, the analysis of the static, rotational, and dynamic positioning accuracies of the source in the LOS and NLOS environments shows that the proposed singular value decomposition strong tracking kalman filter (SVD-STKF) algorithm can improve the overall positioning accuracy of the system by 0.03 m, and the maximum error in the LOS environment can be reduced by 0.08 m. The proposed SVD-STKF algorithm can correct the Hausdorff distance of dynamic positioning by up to 0.513 m in the NLOS environment where the system’s positioning accuracy decreases sharply due to the signal shielding. Also, it can make the positioning results smoother and achieve a good correction effect for the points far away from the true trajectory.