Signal Strength-Based Cooperative Sensor Network Localization Using Convex Relaxation

In a wireless sensor network (WSN), locations of a few sensor nodes are assumed to be known at the time of deployment (known as anchor nodes) and localization techniques are used to estimate the locations of the other sensor nodes (known as target nodes). We consider a received signal strength (RSS) based localization problem for which the maximum likelihood (ML) formulation is non-convex, non-linear, and discontinuous. We propose a novel technique to convexify the ML problem by constructing a function that underestimates the ML cost function and solve the resulting localization problem using the gradient descent technique. We also derive the Lipschitz constant for gradient of the convexified ML function and convergence rate of the proposed algorithm. Performance evaluation of the proposed method and comparison with state of the art methods, in terms of localization accuracy, execution time, and convergence rate, are presented. Results show superiority of the proposed technique.