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

TL;DR

This work tackles the lack of theoretical grounding in 3D DV-Hop localization by introducing PADE, a probability-based distance estimation framework. It first derives an upper bound on anchor-detected distances using PMDE, then computes an average distance per hop via PADE, and embeds these distances into a multi-objective genetic algorithm with two distance losses to localize unknown nodes. Empirical results on random and multimodal 3D WSNs show significant localization gains over several state-of-the-art methods, with notable improvements in average localization accuracy and stability. The approach provides a rigorous foundation for distance estimation in 3D DV-Hop, enabling more accurate and robust WSN localization in complex terrains.

Abstract

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.

Figures (7)

• Figure 1: An example of deploying sensor nodes in a wireless sensor network. $a_i$: anchor node; $u_k$: unknown nodes.
• Figure 2: The example of multi hop information transmission for sensors. ${a}_{i}$: an anchor node, ${u}_{k}$: an unknown node, ${o}_{j}$ and ${o}_{\delta}$: an ordinary (anchor or unknown) node, ${r}_{\delta}$: the distance between ${o}_{\delta}$ and ${a}_{i}$, $UB_{i,m-1}$: the expected distance of the outermost node detected by node ${a}_{i}$ when $hop=m-1$.
• Figure 3: The example of node distribution detected by $a_i$ when $m=1$.
• Figure 4: An example of outermost detection node analysis. ${a}_{i}$: an anchor node, $o_\delta$: an ordinary node, $S_1$ and $S_2$: a part of the communal space, $R$: communication radius, $UB_{i,m-1}$: the expected distance of the outermost node detected by node ${a}_{i}$ when $hop=m-1$.
• Figure 5: An example of the distribution space of $u_k$ when $m=1$. $r_k$: the distance between $u_k$ and ${a}_{i}$, ${UB}_{i,m}$ and ${LB}_{i,m}$: the upper and lower bounds of $r_k$.