# A Robust Tracking Algorithm Based on a Probability Data Association for a Wireless Sensor Network
## 4 Experiment and Result Analysis
### Uniform Distribution  
It was assumed that the measurements' noise obeyed a Gaussian distribution \(N\big{(}0,\sigma_{L}^{2}\big{)}\) and the NLOS errors obeyed a uniform distribution \(U(a,b)\). The default parameters for the uniform distribution simulation experiment are shown in Table 2.  
Figure 5a shows the relationship between the RMSE and the number of beacon nodes when the NLOS errors took on a uniform distribution. It can be seen that the number of beacon nodes varied from 4 to 9, and the RMSEs of the EKF and IMM-EKF algorithms decreased slowly in a similar trend. The change in the number of beacon nodes had a great impact on the positioning results of the MPDA and the proposed algorithm. The proposed algorithm had a higher positioning accuracy than the EKF, IMM-EKF, and MPDA with about 39.70%, 34.81%, and 18.33%, respectively, on average.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Default Values** \\ \hline The number of beacon nodes & \(M\) & 6 \\ \hline The NLOS error probability & \(P_{NLOS}\) & 0.5 \\ \hline The measurements’ noise & \(N\big{(}0,\sigma_{L}^{2}\big{)}\) & \(N\big{(}0,1^{2}\big{)}\) \\ \hline The NLOS errors & \(U(a,b)\) & \(U(0,14)\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Uniform distribution parameter.  
Figure 5: **(a)** Performance comparison between the EKF, IMM-EKF, MPDA, and the proposed algorithm under a different number of beacon nodes \(M\), where \(P_{NLOS}=0.5\), \(N\big{(}0,1^{2}\big{)}\), and \(U(0,14)\). **(b)** Performance comparison between the EKF, IMM-EKF, MPDA, and the proposed algorithm under different NLOS error probabilities \(P_{NLOS}\), where \(M=6\), \(N\big{(}0,1^{2}\big{)}\), and \(U(0,14)\). **(c)** Performance comparison between the EKF, IMM-EKF, MPDA, and the proposed algorithm under different maximum values \(b\) of uniform distribution, where \(M=6\), \(P_{NLOS}=0.5\), and \(N\big{(}0,1^{2}\big{)}\). **(d)** The CDF of the localization error.  
As shown in Figure 4(b), increasing the probability of the NLOS error aggravated the interference of the NLOS factors for positioning, which resulted in increasing the RMSE of the EKF, IMM-EKF, MPDA, and the proposed algorithm. We can see that the RMSE of the proposed algorithm increased slowly with the increase of the probability of the NLOS errors when the probability of the NLOS errors was not more than 0.4, but the growth rate increased gradually. On the whole, the proposed algorithm showed a significant improvement in positioning accuracy compared with the EKF and IMM-EKF algorithms when the NLOS error probability was not higher than 0.6. Compared with the MPDA, the proposed algorithm had a higher positioning accuracy.  
Figure 4(c) shows how the RMSE varied with the maximum value of the NLOS errors. The RMSEs of the EKF, IMM-EKF, MPDA, and the proposed algorithm increased almost linearly as the maximum value of the NLOS errors gradually increased. Compared with the EKF and IMM-EKF algorithms, the proposed algorithm had a greatly improved positioning accuracy. When the maximum of the NLOS error was 15 m, the proposed algorithm had a higher positioning accuracy than the EKF, IMM-EKF, and MPDA with about 39.90%, 34.89%, and 21.67%, respectively. It can be seen from Figure 4(c) that the proposed algorithm significantly outperformed the other three algorithms in terms of inhibiting NLOS errors.  
The error cumulative distribution function of the localization errors for the same example is depicted in Figure 4(d), which shows that the 90 th percentile of the proposed algorithm was less than 5.555 m. In contrast, the 90 th percentile of the EKF, IMM-EKF, and MPDA were 8.566 m, 8.228 m, and 7.829 m, respectively.