# Multi-Condition Constrained Pedestrian Localization Algorithm Based on IMU
## 3 Results
### Experimental Results  
Figure 11 shows the experimental trajectory reconstruction and pointwise error through five methods. The errors between the computed trajectories and the actual reference trajectory are shown in Table 2.  
Figure 10(a),b are the results of the traditional ZUPT pedestrian localization algorithm. Figure 10(c),d are the results using the ZC algorithm mentioned in Section 2.2. It can be observed that the result obtained by the ZC algorithm shows a noticeable improvement. In terms of the Root Mean Squared Error (RMSE), comparing the ZC algorithm to the traditional ZUPT algorithm, the positioning accuracy of the left foot improves by 21% and the right foot improves by 1%. The reason for the inconsistent improvement in accuracy between the left and right feet is that the left foot encountered a greater number of false zero-velocity interval detections during the walking experiment, which indicates the presence of substantial transient noise. Consequently, the ZC algorithm demonstrated significant effectiveness in this case. Conversely, the right foot experienced fewer false detections, and its primary source of error stemmed from considerable heading drift, which limited the improvement achieved  
Figure 11: Experimental trajectory with five different algorithms. (**a**) Traditional ZUPT algorithm. (**b**) Point-wise error values by the traditional ZUPT algorithm. (**c**) ZC algorithm. (**d**) Point-wise error values by the ZC algorithm. (**e**) ZC-SC algorithm. (**f**) Point-wise error values by the ZC-SC algorithm. (**g**) ZC-DC algorithm. (**h**) Point-wise error values by the ZC-DC algorithm (**i**) MCC algorithm. (**j**) Point-wise error values by the MCC algorithm. Based on this, the proposed MCC algorithm combines the ZC algorithm, single-foot, and dual-feet fusion constraint algorithms together. To evaluate the positioning performance, the experimental results of ZC-SC, ZC-DC, and MCC are also given in Figure 11. Figure 11e,g,i, respectively, represent the pedestrian dual-feet trajectory results by the three algorithms, while Figure 11f,h,j illustrate the pointwise error distributions between the calculated trajectories and the reference path for each algorithm. From Figure 11, it is evident that the actual trajectory by the proposed MCC algorithm is the closest to the reference trajectory, demonstrating its effectiveness in heading drift correction. Furthermore, the point-wise error plots also highlight the superiority of the MCC algorithm. To further verify the effectiveness of the proposed method, the quantitative error values by five algorithms are provided in Table 2, which includes mean error, ME, and RMSE. For left foot trajectory, the maximum mean error is 0.13 by ZC-SC, the minimum mean error 0.07 by MCC, the second smallest mean error is 0.08 by ZC-DC. The maximum ME is 0.71 by traditional ZUPT, the minimum ME 0.19 by MCC, the second smallest ME 0.23 by ZC-DC. The maximum RMSE is 0.19 by traditional ZUPT, the minimum RMSE 0.09 by MCC, the second smallest RMSE 0.11 by ZC-DC. For right foot trajectory, the maximum mean error is 0.30 by traditional ZUPT, the minimum mean error 0.12 by MCC, the second smallest mean error 0.16 by ZC-SC. The maximum ME is 1.36 by traditional ZUPT, the minimum ME 0.51 by MCC, the second smallest ME 0.66 by ZC-SC. The maximum RMSE is 0.41 by traditional ZUPT, the minimum RMSE 0.17 by MCC, the second smallest RMSE 0.21 by ZC-SC. Based on the above results, the superiority of the proposed algorithm can be observed. Taking the RMSE for example, the MCC algorithm shows a localization accuracy improvement of 42% and 20% for the left foot when compared to the ZC-SC and ZC-DC algorithms, respectively. For the right foot, the accuracy improvement is 19% and 26%, respectively. Furthermore, compared to the pedestrian localization results based solely on the traditional ZUPT algorithm, the localization accuracy is improved by 53% and 59%. These accuracy calculations and comparative results fully validate the effectiveness of the proposed MCC algorithm.