Sensor Network Localization via Nondifferentiable Optimization

Knowing the positions of nodes is essential to many wireless sensor network applications. In contrast to range-based localization methods, range-free methods are more appealing since they do not need additional expensive hardware for ranging. A range-free localization problem is a generalization of unit disk graph coordinates realization problem and in essence a feasibility problem with quadratic inequalities, which is NP- hard. In this paper, we formulate the range-free localization problem as a nondifferentiable optimization problem solved by a polynomial-time algorithm, normalized incremental subgradient (NIS) algorithm. Extensive simulations have been conducted. The simulation results show that the NIS-based localization algorithm significantly outperforms the MDS-MAP method and the SDP method, whether the network is regular or not.