Probability-based Distance Estimation Model for 3D DV-Hop Localization in WSNs

Localization is one of the pivotal issues in wireless sensor network applications. In 3D localization studies, most algorithms focus on enhancing the location prediction process, lacking theoretical derivation of the detection distance of an anchor node at the varying hops, engenders a localization performance bottleneck. To address this issue, we propose a probability-based average distance estimation (PADE) model that utilizes the probability distribution of node distances detected by an anchor node. The aim is to mathematically derive the average distances of nodes detected by an anchor node at different hops. First, we develop a probability-based maximum distance estimation (PMDE) model to calculate the upper bound of the distance detected by an anchor node. Then, we present the PADE model, which relies on the upper bound obtained of the distance by the PMDE model. Finally, the obtained average distance is used to construct a distance loss function, and it is embedded with the traditional distance loss function into a multi-objective genetic algorithm to predict the locations of unknown nodes. The experimental results demonstrate that the proposed method achieves state-of-the-art performance in random and multimodal distributed sensor networks. The average localization accuracy is improved by 3.49\%-12.66\% and 3.99%-22.34%, respectively.