Dimension expansion and customized spring potentials for sensor localization

The spring model algorithm is an important distributed algorithm for solving wireless sensor network (WSN) localization problems. This article proposes several improvements on the spring model algorithm for solving WSN localization problems with anchors. First, the two-dimensional (2D) localization problem is solved in a three-dimensional (3D) space. This "dimension expansion" technique can effectively prevent the spring model algorithm from falling into local minima, which is verified both theoretically and empirically. Second, the Hooke spring force, or quadratic potential function, is generalized into L _p potential functions. The optimality of different values of p is considered under different noise environments. Third, a customized spring force function, which has larger strength when the estimated distance between two sensors is close to the true length of the spring, is proposed to increase the speed of convergence. These techniques can significantly improve the robustness and efficiency of the spring model algorithm, as demonstrated by multiple simulations. They are particularly effective in a scenario with anchor points of longer broadcasting radius than other sensors.