# A Robust Tracking Algorithm Based on a Probability Data Association for a Wireless Sensor Network
## 4 Experiment and Result Analysis
### Gaussian Distribution  
It was assumed that the NLOS errors obeyed the Gaussian distribution \(N\left(\mu_{NLOS},\sigma_{NLOS}^{2}\right)\), the measurement noise obeyed the Gaussian distribution \(N\left(0,\sigma_{L}^{2}\right)\), and the range measurements were irrelevant. The default parameters of the Gaussian distribution simulation experiment are shown in Table 1.  
Figure 3: The trajectory of the mobile node. As shown in Figure 4a, with the number of beacon nodes increasing from 4 to 9, the RMSEs of the four algorithms decreased. This indicates that increasing the number of beacon nodes was helpful for reducing the NLOS errors and improving the positioning accuracy of the algorithms. When the number of beacon nodes varied from 4 to 7, the RMSEs of the IMM-EKF, MPDA, and the proposed algorithm decreased rapidly. When the number of beacon nodes increased to 7, the RMSEs of the MPDA and the proposed algorithm decreased slowly, and the RMSE of the IMM-EKF hardly changed. The RMSE of the EKF decreased slowly. From Figure 4a, we can see that the positioning accuracy of the proposed algorithm was better than that of the EKF, IMM-EKF, and MPDA. When the number of beacon nodes was 9, the proposed algorithm had a higher positioning accuracy than the EKF, IMM-EKF, and MPDA at about 65.70%, 59.97%, and 25.16%, respectively. Figure 4b shows the impact of the NLOS errors probability on RMSE. Compared with the EKF and IMM-EKF algorithms, the RMSE of the proposed algorithm increased slowly when the probability of the NLOS error was less than 0.4. However, when the probability of the NLOS error was greater than 0.4, the RMSE of the proposed algorithm increased rapidly with the increase of the NLOS errors probability. The change of root mean square error of the MPDA algorithm was similar to that of the proposed algorithm, but its growth rate was faster than that of the proposed algorithm. When compared with EKF, IMM-EKF, and MPDA, the proposed algorithm had a higher positioning accuracy. Figure 4c shows the relationship between the RMSE and the mean value of the NLOS errors. As the mean value of the NLOS error varied from 3 to 10, the RMSE of the EKF, IMM-EKF, and MPDA increased. Although the RMSE of the proposed algorithm also increased, its RMSE was always smaller than that of the EKF, IMM-EKF, and MPDA. From Figure 5, we can see that the growth rate of the root mean square error of the proposed algorithm was obviously less than that of other three algorithms. When the mean value of NLOS error was 3, the proposed algorithm improved the positioning accuracy by about 47.22%, 32.72%, and 28.98% compared with the EKF, IMM-EKF, and MPDA, respectively. When the mean value of the NLOS error was 10, the proposed algorithm had a higher positioning accuracy than the EKF, IMM-EKF, and MPDA at about 35.76%, 36.67%, and 30.06%, respectively. Figure 4d shows the impact of the standard deviation of NLOS errors on the RMSE. The RMSE of the EKF clearly increased with the increase of the standard deviation, which led to a rapid decline in its positioning accuracy. When the standard deviation was 10, the RMSE of the EKF, IMM-EKF, MPDA, and the proposed algorithm were 5.3948 m, 3.9240 m, 3.2254 m, and 2.0257 m, respectively. Compared with the EKF, IMM-EKF, and MPDA, the proposed algorithm improved the positioning accuracy by about 62.45%, 48.38%, and 37.20%, respectively. Figure 4e shows the error cumulative distribution function of the localization errors, which shows that the 90 th percentile of the errors of the proposed algorithm was less than 3.263 m. In contrast, the 90 th percentile of errors of the EKF, IMM-EKF, and MPDA were 6.668 m, 5.494 m, and 4.191 m, respectively.