# A Weighted and Distributed Algorithm for Range-Based Multi-Hop Localization Using a Newton Method
## 4 A Robust and Distributed Localization Algorithm Based on the Newton Method
## 7 Conclusions

This research has investigated a range-based and distributed algorithm suitable for multi-hop network localization. The proposed scheme employs a weighted Newton method approach that minimizes errors in position estimates under anomalous pairwise range measurements between sensor nodes. Unknown sensors categorize neighboring nodes with specific weights based on the closeness to an anchor node and error distances. The algorithm has been tested at different radio ranges and noise levels in distance estimates, demonstrating robustness in presence of outliers with a small number of iterations to reach good results in accuracy. In fact, in isotropic networks, the proposed method practically matches the localization performance of the DV-HOP+DWDSCL method using far fewer iterations to converge. The best performance is carried out under anisotropic networks where the proposed scheme outperforms others providing the best accuracy in position estimates with the minimum number of iterations. Conceptualization, J.D.-R., B.M., and J.C.-R.; methodology, J.D.-R., B.M., J.C.-R., E.S., and R.G.-L.; writing-original draft preparation, J.D.-R., B.M., and J.C.-R.; validation, J.D.-R., B.M., J.C.-R., and R.G.-L.; discussion, J.D.-R., B.M., J.C.-R., and E.S., experimentation, J.D.-R., B.M., and J.C.-R.; writing-review and editing, J.D.-R., B.M., J.C.-R., E.S., and R.G.-L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this work are available on request from the corresponding author. The authors wish to express the acknowledge to PRODEP that supported this research. The authors declare no conflict of interest. Figure 12: \(RMSEavg\) vs. Iterations of algorithms using \(\Theta=20\%\) and \(nfe=0.1\) considering the average of 10 independent anisotropic networks. (**a**) Corresponds to R = 35 m and (**b**) R = 45 m.

## Acronyms and Symbols

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