Sensor Network Localization via Alternating Rank Minimization Algorithms

Sensor network localization (SNL) is to determine physical coordinates of all sensors in a network given global coordinates of anchors and available measurements among sensors and anchors. Two challenges related to SNL are to find conditions leading to a uniquely localizable network and develop effective and efficient methods to solve SNL problems. This work first proves that infinitesimal rigidity, together with some mild conditions, is sufficient for unique localizability of a network considering additional relationships between nonadjacent sensors. On the other hand, solving an SNL problem is generally NP-hard due to its nonconvex constraints. Instead of ignoring the rank constraint used in existing relaxation methods, we convert the rank constraint in the SNL problem into its equivalent constraints and solve it alternatively by proposing the alternating rank minimization algorithm (ARMA). We start with the centralized ARMA to solve the exact SNL problem. Next, to improve the scalability for solving large-scale SNL problems, ARMA is extended in a distributed manner by decomposing the original problem into a group of subproblems, which can be solved independently. Finally, simulation cases are provided for both centralized and distributed ARMA to validate the improved localization accuracy, efficiency, and robustness by being compared to the state-of-the-art localization methods.