Improved PSA for 3D WSN Localization Algorithm

Objective This study proposes an improved 3D WSN localization algorithm with an enhanced particle swarm algorithm (PSA) to address the high positioning errors and instability encountered with the traditional 3D DV–Hop localization algorithm in locating wireless sensor network nodes. The proposed improved particle localization algorithm (IPLA) specifically targets and mitigates the error steps inherent in the traditional 3D DV–Hop localization process.Methods Firstly, in the traditional method, the nodes within the communication radius were considered as 1-hop, which caused the hop count calculation to be insufficiently refined and produced a significant error. In contrast, this study adopted a dual communication radius, broadcasted at <italic>R</italic> and <italic>R</italic>/2, respectively, to refine the hop count calculation and obtain the minimum hop count with a much smaller error. Secondly, the calculation of the average hopping distance in the traditional method was based on the topology of a linearly distributed wireless sensor network. The average hopping distance calculated by this method affected the accuracy of the localization. Therefore, a fitness function with a distance weighting factor was established. The improved PSA algorithm with meta-starting was used for the solution, and the introduction of chaotic mapping into the PSA algorithm enhanced the algorithm’s optimization capability and reduced the error in obtaining the average hopping distance.Finally, for the problem of large errors in obtaining node coordinates by the least squares method of the traditional method, an adaptation function with weights was established to reduce the error existing in the topology. The improved PSA algorithm was again employed in this paper instead of the least squares method, which was the traditional method, to further improve the accuracy of locating the nodes. Simulation experiments were conducted in different scenarios to compare the proposed IPLA algorithm with the traditional 3-dimensional DV–Hop algorithm, DBO algorithm, and WBOA algorithm in terms of localization performance. The results showed that the IPLA algorithm has good effects and a better convergence ability in improving the localization error of wireless sensors.Results and Discussions Comparative experiments on algorithm iteration performance and localization simulation were conducted using the IPLA algorithm, the traditional 3-dimensional DV–Hop algorithm, and other algorithms. The comparative analysis demonstrated the advantages of the IPLA algorithm. It achieved convergence in approximately five iterations, which is faster than the PSA, the adaptive weighted butterfly optimization algorithm (WBOA), and the dung beetle optimization algorithm (DBO). In addition, the IPLA algorithm exhibited lower fitness values at the convergence point, indicating a more efficient search for optimal solutions. In positioning simulation experiments, the IPLA algorithm was compared to the 3D DV–Hop algorithm optimized by the traditional 3D DV–Hop, DBO, and WBOA algorithms. It was found that with an anchor node ratio of 0.15 and a communication radius of 35 m, the IPLA algorithm performed better in reducing the positioning error as the total number of nodes increased. When the total number of nodes reached approximately 150, the localization errors of all algorithms stabilized, and the IPLA algorithm exhibited the lowest error value. With a further increase in the total number of nodes, the localization errors of the WBOA and DBO algorithms fluctuated, while those of the IPLA algorithm remained stable, demonstrating its superiority in complex topologies. In tests with different communication radii, when the anchor node ratio and the total number of nodes were set to 0.15 and 100, respectively, the normalized localization errors of all algorithms stabilized around 40 m with the increase in the communication radius. In contrast, the IPLA algorithm exhibited the lowest error, which could reach 0.17. This indicates that the IPLA algorithm can maintain stable localization performance despite increases in the communication radius and complexity of the topology. Finally, in the anchor node ratio test, when the total number of nodes and the communication radius were set to 100 and 35 meters, respectively, the IPLA algorithm outperformed the other three algorithms at different anchor node ratios. The performance of the IPLA algorithm started to stabilize at an anchor node ratio of about 0.2, and its normalized localization error was lower than that of the other algorithms. This demonstrated that the IPLA algorithm can maintain a low localization error across different anchor node ratios and maintain good performance even with changes in topology. Conclusions This study proposes the IPLA algorithm to solve the 3-dimensional DV–Hop algorithm based on non-ranging WSN positioning algorithms, which are characterized by significant errors and instability. This algorithm utilizes the dual communication radius, the distance weighting factor, and the improved PSA algorithm to optimize the positioning nodes and obtain coordinates with lower positioning errors. Simulation experiments demonstrated that the IPLA algorithm has superior convergence ability and provides better positioning accuracy and stability than the DV–Hop, DBO, and WBOA algorithms. The PSA algorithm is used twice, and although it increases energy consumption, it improves the positioning accuracy and will be the focus of future research.