Analysis of two geolocation techniques in wireless sensor Networks

Suppose m_A location-unknown sensors out of all n sensors can be located by a localization algorithm A, then omega_A = m_A/n is defined to be the efficiency of the algorithm A. Different from the traditional trilateration technique using 3 neighbors (hence referred to as 3 neighbor algorithm, or 3NA for short), in 2004 Barbeau et al [1] proposed an algorithm, referred to as 2N+aB for short, which can locate a node only using two location-aware neighbors plus certain information from a third adjacent location-aware node. Last year the second author of this paper made an improvement to Barbeau et al´s algorithm, referred to as 2N+cB for short [6]. In this paper we analyze the efficiencies of the two algorithms, derive the formulae for omega_2N+aB and omega_2N+cBldr We also make simulations and the simulation results well match our theoretical analysis. Our results show that the efficiency of 2N+cB for sensor networks of low density is 50% higher than 2N+aB. Moreover, since 2N+cB does not overlap 3NA, we can use 2N+cB and 3NA at the same time so that simultaneously using 2N+cB and 3NA can increase the efficiency by 60% compared using trilateration 3NA alone.