Geometric triangulation uncertainty for sustainable urban underwater localization in presence of malicious virtual node

Abstract

Sustainability of urban underwater sensor networks (uUWSNs) depends critically on the efficient triangulation during the localization process. There is very limited literature on sustainable range-free localization in uUWSNs. To address this issue, we improve localization method based on triangulation approach through convex optimization with Geometric Dilution of Precision (GDOP). We define “geometric triangulation uncertainty”. A sustainable scheme is proposed for identification of underwater nodesto modify a two-mode Gaussian Mixture Model. The proposed method is then compared to a weighted least square model for different threshold levels of maximum node range and associated triangulation uncertainties. The convex formulation is then solved using semidefinite programming to obtain optimal position of target in presence of a malicious virtual node. Theproposed method is verified using Cramer’s Rao lower bound in terms of RMS errors and cumulative errors. It exhibits close to ideal performance whenever perturbations associated with geometric triangulation uncertainty is bounded. The performance of the proposed method exceeds that of the weighted least squares method, which means that the proposed technique shall find immense application in intelligent computation of urban underwater scenarios, where the amount of sensor information exchange critically depends upon terrain environment and surrounding disturbances.