LITM: Localization With Insufficient TOA Measurements for Unsynchronized Mobile Nodes in Underwater Acoustic Networks

Underwater acoustic networks (UWANs) play a vital role in the Internet of Underwater Things (IoUT), enabling critical functions such as communication, data collection, and navigation. Among the applications of the IoUT, localizing a mobile node (MN) via a UWAN is particularly promising. However, the existing localization algorithms are ineffective when faced with an insufficient number of time of arrival (TOA) measurements for an unsynchronized MN due to the presence of sparsely deployed anchor nodes and signal reception issues. Although tracking methods can offer position predictions, their accuracies are compromised over time due to the movement of MNs. To overcome these challenges, we propose a methodology that combines the departure time of a beacon signal (DOB) with limited TOA measurements. This methodology enables an MN to be localized using a TOA-based method, which typically requires fewer measurements than a time difference of arrival (TDOA)-based method. Based on this methodology, we introduce an algorithm called localization with insufficient TOA measurements (LITM), which comprises two subalgorithms: one for estimating and tracking the DOBs and the other for localizing MNs through a closed-form solution. Together, these subalgorithms provide accurate MN position estimates under the constraint of insufficient TOA measurements. To validate the performance of our proposed algorithm, we conduct both simulation studies and sea experiments. The results demonstrate the superior effectiveness and position estimation accuracy of our algorithm compared to those of the existing methods.