## 4 Experimental Validation
### Empirical Tracking Algorithm  
#### 4.3.1 Empirical Source Rotation Positioning  
In the source rotation test, two representative points were used, point (0, 0) that was directly below the antenna, and point (2, \(-1.5\)) that was far away from the antenna on the non-coordinate axis. During the test, 200 frames of data were collected at each point. The error diagram of 200 frame data and the CDF graph corresponding to the single-frame data are presented in Figures 10 and 11. In the error graph, the yellow horizontal line represents the coordinate value of the current position, the blue curve represents the positioning value obtained by the system, the horizontal axis is the number of sampled frames, and the vertical axis is the error value. In the CDF graph, the horizontal axis represents positioning error of this point, the vertical axis represents CDF. The precision in \(x\)-direction was about 0.124 m, and that in \(z\)-direction was about 0.109 m. The positioning result was good, and there was no jump point. It can be seen from the CDF diagram that the positioning errors are all within 0.3 m. The positioning result in the \(x\)-direction was strongly affected by the source rotation, which showed a trend of first decreasing, then increasing, and finally, decreasing. The positioning results in the \(z\)-direction were stable under the source rotation. Since point (2, \(-1.5\)) was far away from the base station, its positioning error increases. The precision in the \(x\)-direction was about 0.255 m, and that in the \(z\)-direction was about 0.125 m. Thus, when the source was far away from the base station, the positioning accuracy of some frames fluctuated significantly, with the maximum value exceeding 0.5 m. The CDF diagram shows that the positioning errors are all within 0.8 m.  
Figure 9: The static test location results for the source location of (2, \(-1.5\)). (**a**) Average error in the \(x\)-direction. (**b**) Average error in the \(z\)-direction. (**c**) Location distribution. (**d**) CDF. Figure 11: _Cont_. Figure 10: The source rotation test positioning results at the point (0, 0). (**a**) Error in the \(x\)-direction. (**b**) Error in the \(z\)-direction. (**c**) CDF. In addition, the STKF was applied to the above two points. The positioning results after the STKF optimization are shown in Figures 12 and 13. The positioning accuracy of the point (0, 0) in the \(x\)-direction was about 0.122 m, and that in the \(y\)-direction was about 0.106 m. Compared with the results before the optimization, the accuracies in the \(x\)- and \(y\)-directions were improved by approximately 0.002 m and 0.003 m, respectively. The positioning accuracies of the point (2, \(-\)1.5) in the \(x\)- and \(z\)-directions were approximately 0.239 m and 0.119 m, respectively. Compared with the results before the optimization, the positioning accuracies in the \(x\)- and \(z\)-directions were improved by approximately 0.006 m and 0.005 m, respectively. Due to the instability of the positioning result caused by the source rotation, the STKF could only slightly improve the positioning accuracy; the accuracy improvement was small, by only a few millimeters. The positioning result was smoother than before the modification, but there was no significant correction for the mutation of point (2, \(-\)1.5). Figure 11: The source rotation test positioning results at the point (2, \(-\)1.5). (**a**) Error in the \(x\)-direction. (**b**) Error in the \(z\)-direction. (**c**) CDF. Figure 12: The strong tracking kalman filter (STKF) positioning results under the source rotation for the point (0, 0). (**a**) Error in the \(x\)-direction. (**b**) Error in the \(z\)-direction. As shown in Figures 14 and 15, in the case of source rotation, the strong tracking kalman filter could make the positioning result smoother, but the accuracy improvement was small. The singular value decomposition strong tracking kalman filter (SVD-STKF) was performed for the above two points.