Topology Control for Energy-Efficient Localization in Mobile Underwater Sensor Networks Using Stackelberg Game

The characteristics of mobile underwater sensor networks (UWSNs), such as low communication bandwidth, large propagation delay, and sparse deployment, pose challenging issues for successful localization of sensor nodes. In addition, sensor nodes in UWSNs are usually powered by batteries whose replacements introduce high cost and complexity. Thus, the critical problem in UWSNs is to enable each sensor node to find enough anchor nodes in order to localize itself, with minimum energy costs. In this paper, an energy-efficient localization algorithm (EELA) is proposed to analyze the decentralized interactions among sensor nodes and anchor nodes. A single-leader-multi-follower Stackelberg game is utilized to formulate the topology control problem of sensor nodes and anchor nodes by exploiting their available communication opportunities. In this game, the sensor node acts as a leader taking into account factors such as “two-hop” anchor nodes and energy consumption, while anchor nodes act as multiple followers, considering their ability to localize sensor nodes and their energy consumption. We prove that both players select best responses and reach a socially optimal Stackelberg-Nash Equilibrium. Simulation results demonstrate that the proposed EELA improves the performance of localization in UWSNs significantly, and in particular, the energy cost of sensor nodes. Compared to the baseline schemes, the energy consumption per node is about 48% lower in EELA, while providing a desirable localization coverage, under reasonable error, and delay.