## 8 Numerical Simulation and Experimental Testing  
### Simulation of Data Fusion Algorithm Based on TCPF  
In order to verify the performance of the proposed fusion positioning algorithm, 30 independent tests were carried out on the simulation model shown in Equations (63)-(65), and the test results were compared with the results of an Extended Kalman Filter (EKF) [29], Unscented Kalman Filter (UKF) [30], Unscented Particle Filter (UPF) [31] and Basic Particle Filter (BPF) [32] in terms of root-mean-square error (RMSE) and standard deviation (Std). \[f_{1}=\left\{ \begin{array}{l}x(k)=\sin(0.6\pi(k-1))+2x(k-1)+6+\sqrt{Q}\times randn ()\\ z(k)=0.5x^{2}(k)+\sqrt{R}\times randn()\end{array} \right. \tag{65}\]  
\[f_{2}=\left\{ \begin{array}{l}x(k)=2.2x(k-1)+\frac{3x(k-1)}{2+x^{2}(k-1)}+\cos (5(k-1))+\sqrt{Q}\times rand()\\ z(k)=0.35x^{2}(k)-8+\sqrt{R}\times rand()\end{array} \right. \tag{66}\]  
\[f_{3}=\left\{ \begin{array}{l}x(k)=x(k-1)+\frac{6x(k-1)}{1+x^{2}(k-1)}+4\cos (5(k-1))+\sqrt{Q}\times randn()\\ z(k)=0.25x^{2}(k)-3+\sqrt{R}\times randn()\end{array} \right. \tag{67}\]  
The remaining parameters of TCPF were set as follows: \(N\) was 100, \(\sigma\) was 0.75, \(\tau\) was 2; the process noise variance \(Q\) and measurement noise variance \(R\) were separately set according to different models, that is, the \(Q\) of the \(f_{1}\), \(f_{2}\) and \(f_{3}\) test models were \(Q_{1}\)-\(N\) (0,0.5), \(Q_{2}\)-\(N\) (0,1) and \(Q_{3}\)-\(N\)(0,5), respectively; and the \(R\) of the \(f_{1}\), \(f_{2}\) and \(f_{3}\) test models were \(R_{1}\)-\(N\)(0,1), \(R_{2}\)-\(N\)(0,5) and \(R_{3}\)-\(N\)(0,10), respectively. The parameters of the algorithm to be compared were taken from the corresponding references. Table 1 shows the model test results of five algorithms. From the table, it can be seen that the mean and maximum values of RSME and Std from the proposed TCPF are smaller than the corresponding performances from the other four algorithms, which indicates that the filter fusion accuracy of TCPF was the highest. The superior performances were mainly due to the fact that in the process of importance sampling in this paper, the latest positioning data were integrated into the importance function through unscented transformation, which improved the credibility of particle samples. In addition, the algorithm in this paper clustered discrete particles by constructing an adaptive threshold in the Gaussian mixture and optimized the weights of particles in the inferior layer, which improved the diversity of data samples. The performance comparison shows that compared with the other four algorithms, the mean values of RMSE and Std of data fusion based on the proposed TCPF decreased by 25.0% and 28.0%, respectively, which fully shows that the TCPF data fusion algorithm can effectively suppress the particle shortage problem and improve the filtering accuracy. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{Test Model} & \multicolumn{5}{c}{Mean Value of RMSE} & \multicolumn{5}{c}{Mean Value of Std} \\ \cline{2-11}  & EKF & UKF & BPF & UPF & TCPF & EKF & UKF & BPF & UPF & TCPF \\ \hline \(f_{1}\) & 0.493 & 0.421 & 0.646 & 0.390 & 0.345 & 0.473 & 0.393 & 0.622 & 0.381 & 0.235 \\ \(f_{2}\) & 4.433 & 2.554 & 3.972 & 3.383 & 2.485 & 4.210 & 2.574 & 2.792 & 2.893 & 2.367 \\ \(f_{3}\) & 5.456 & 3.598 & 4.812 & 4.563 & 3.487 & 5.498 & 3.702 & 3.710 & 4.236 & 3.396 \\ \hline \multirow{2}{*}{Test Model} & \multicolumn{5}{c}{Maximum Value of RMSE} & \multicolumn{5}{c}{Maximum Value of Std} \\ \cline{2-11}  & EKF & UKF & BPF & UPF & TCPF & EKF & UKF & BPF & UPF & TCPF \\ \hline \(f_{1}\) & 0.910 & 0.568 & 0.940 & 0.613 & 0.409 & 0.877 & 0.566 & 0.891 & 0.599 & 0.412 \\ \(f_{2}\) & 6.681 & 3.459 & 6.142 & 4.624 & 3.317 & 6.391 & 3.431 & 3.452 & 4.283 & 3.283 \\ \(f_{3}\) & 7.856 & 4.192 & 6.121 & 6.142 & 3.998 & 7.731 & 4.214 & 4.172 & 5.931 & 3.969 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model test results of five algorithms.