A Localization Algorithm Based on Improved Water Flow Optimizer and Max-Similarity Path for 3-D Heterogeneous Wireless Sensor Networks

Localization is one of the key technologies in wireless sensor networks (WSNs) because the information measured by the sensors is meaningful only if the location of the sensor nodes is known. The existing localization algorithms have low localization accuracy in 3-D heterogeneous WSNs (HWSNs) and cannot meet the user's needs well. In this article, a localization algorithm based on an improved water flow optimizer and improved max-similarity path (IWFO-IMSP) is proposed. First, based on the shortest communication path among nodes in the network, the maximum similarity path is calculated. Second, the distance between the unknown node and the anchor node is estimated using the distance of the maximum similarity path minus the distance of the dissimilar part. Third, the cosine theorem is introduced to correct the polyline distance of the path to a straight-line distance to further improve the accuracy of the distance estimation. Finally, the convergence speed and convergence ability of the water flow optimizer (WFO) are improved by fusing various strategies such as the Halton sequence and Cauchy mutation. The location of the unknown node is searched out by using the improved WFO (IWFO) to achieve accurate localization. By comparing and analyzing the simulation 3-D space and 3-D C-space with different degrees of irregularity (DOI), the localization error of IWFO-IMSP is reduced by about 70%, 80%, 12%, and 45% relative to improved DV-Hop (IDV-Hop), projection correction of closer points (CPPA), similar path-based localization algorithm (NLA-SP), and DVmaxhop, respectively. Therefore, the localization accuracy of IWFO-IMSP is much higher than the other four localization algorithms.