Further Relaxations of the SDP Approach to Sensor Network Localization

Recently, a semidefinite programming (SDP) relaxation approach has been proposed to solve the sensor network localization problem. Although it achieves high accuracy in estimating sensor’s locations, the speed of the SDP approach is not satisfactory for practical applications. In this paper we propose methods to further relax the SDP relaxation; more precisely, to decompose the single semidefinite matrix cone into a set of small-size semidefinite matrix cones, which we call the smaller SDP (SSDP) approach. We present two such relaxations or decompositions; and they are, although weaker than SDP relaxation, tested to be both efficient and accurate in practical computations. The speed of the SSDP is much faster than that of the SDP approach as well as other approaches. We also prove several theoretical properties of the new SSDP relaxations.