Abstract
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.
Highlights
Localization is an essential tool in many sensor network applications
stable suboptimal equilibrium (SSE) exist for the three body model in 1D space, they can be eliminated by dimension expansion, which, in this case, is to allow the 1D system to evolve in a 2D space
If we expand the space from 1D to 2D, all the SSE configurations become unstable and the system will evolve into the unique globally optimal configuration
Summary
Localization is an essential tool in many sensor network applications. Over the years, a rich literature has been developed to solve the sensor localization problem from different perspectives [1-3]. The most prominent problem is the “folding” phenomenon in which the spring system falls into an energy local minimum and cannot unfold itself To tackle this problem, many pre-processing methods have been proposed, such as the first stage of the AFL algorithm, which may fail due to an insufficient number of nodes or to measurement noise. But requires many iterations, incurring significant communication cost Another problem with the spring model (with Hooke’s law) is that the potential energy, measured by the squared error between the true distance and the estimated distance, is sensitive to measurement error, and is not robust enough for many applications.
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