**N**OWADAYS, wireless sensor networks are developed to provide fast, cheap, reliable, and scalable hardware solutions to a large number of industrial applications, ranging from surveillance and tracking to exploration monitoring , robotics, and other sensing tasks . Distributed Maximum Likelihood Sensor Network Localization From the software perspective, an increasing effort is spent on designing distributed algorithms that can be embedded in these sensor networks, providing high reliability with limited computation and communication requirements Distributed Maximum Likelihood Sensor Network Localization for the sensor nodes. Estimating the location of the nodes based on pair-wise distance measurements is regarded as a key enabling technology in many of the aforementioned scenarios, where GPS is often not employable. From a strictly mathematical standpoint, this sensor network localization problem can be formulated as determining the node position in or ensuring their consistency with the Distributed Maximum Likelihood Sensor Network Localization given inter-sensor distance measurements and with the location of known anchors. As it is well known, such a fixed-dimensional problem often phrased as a polynomial optimization is NP-hard in general. Consequently, there have been significant research efforts in developing algorithms and heuristics that can accurately and efficiently localize the nodes in a given dimension . Besides heuristic geometric schemes, such as multi-lateration, typical methods encompass multi-dimensional scaling , belief propagation techniques and standard non-linear filtering . Distributed Maximum Likelihood Sensor Network Localization A very powerful approach to the sensor network localization problem is to use convex relaxation techniques to massage the non-convex problem to a more tractable yet approximate formulation. First adopted in, this modus operandi has since been extensively developed in the literature example for a comprehensive survey in the field of signal processing. Distributed Maximum Likelihood Sensor Network Localization Semidefinite programming (SDP) relaxations for the localization problem have been proposed in. Theoretical properties of these methods have been discussed in, while their efficient implementation has been presented in. Further convex relaxations, namely second-order cone programming relaxations (SOCP) have been proposed in to alleviate the computational load of standard SDP relaxations, at the price of some performance degradation. Highly accurate and highly computational demanding sum of squares (SOS) convex relaxations have been instead employed in .