# A Linear Strong Constraint Joint Solution Method Based on Angle Information Enhancement
## 5 Experimental Performance Verification
### Performance of the Fusion Localization Algorithm  
The location coordinates of the base station are shown in the following Table 3:  
The layout of the base station is shown in the following Figure 11. The entire factory area is divided into three regions, each of which is affected differently by non-line of sight, resulting in different amounts of available positioning observation information received in different regions. The positioning performance of the three scenarios is compared and analyzed to verify the performance of the continuous positioning algorithm proposed in this chapter. Assuming that in region one, the propagation paths of base stations 1, 2, and 4 are direct paths, but due to hardware limitations, only the angle information of base station 1 can be measured. In Region 2, the propagation paths of base stations 2, 4, 5, and 6 are direct paths, and each direct path can obtain accurate angle information; In region three, only base station 3 has a direct path and can measure angle information. In the process of algorithm performance verification, the positions of positioning terminals are randomly generated in three different areas, and the measurement results are calculated using the algorithm in this chapter and the comparative algorithm. The positioning errors are then statistically analyzed. Figure 10: DLL tracking result. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Base 1 & [10 m, 10 m, 3 m] & Base 4 & [10 m, 30 m, 3 m] \\ Base 2 & [30 m, 10 m, 3 m] & Base 5 & [30 m, 30 m, 3 m] \\ Base 3 & [50 m, 10 m, 3 m] & Base 6 & [50 m, 30 m, 3 m] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Base station coordinate setting. To verify the progressiveness of the algorithm in this paper, the current mainstream Gauss-Newton (GN) algorithm and the Particle Swarm Optimization (PSO) algorithm are added as comparative experiments. In the positioning process, the NLOS recognition method based on comprehensive feature dynamic hierarchical optimization is first used to determine the non-line of sight path, and the LOS path is selected for high-precision measurement. The robust accurate tracking algorithm based on the PRS is used to obtain the downlink ranging information, and the efficient angle measurement algorithm based on fourth-order cumulants is used to obtain the uplink angle information. The angle and distance information are uploaded to the network side for positioning calculation. The initial position of the Gauss-Newton method is obtained through the ordinary least squares method, and the initial position of the particle swarm optimization algorithm is randomly generated and gradually iterated within the area where the positioning terminal is located. In the algorithm proposed in this article, the closed-form solution is first solved using the generalized least squares method. Since the covariance matrix of the error in the initial state is unknown, the identity matrix needs to be used as the initial weight matrix to obtain a more accurate closed-form solution through a few iterations, with the number of iterations represented by \(k_{1}\). This experiment conducted 1000 Monte Carlo experiments, using the cumulative distribution function of positioning errors as the evaluation index for positioning performance. Region 1 and Region 2 belong to areas with good wireless signal coverage performance, satisfying geometric observability and having many redundant observations. From the above Figures 12 and 13, the closed-form solution obtained after a few iterations can have good localization performance, which is superior to the PSO algorithm and GN algorithm with few iterations. With the increase in iteration times, the localization performance of both the proposed algorithm and the comparative algorithm has been improved. As the number of particles increases, PSO has higher positioning accuracy in the case of more observation information (region two).