Robust distributed positioning algorithms for cooperative networks

Abstract

The problem of positioning targets based on distance estimates is studied for cooperative wireless sensor networks when there is limited a priori information about measurements noise. To solve this problem, two different methods of positioning are considered: statistical and geometrical. Based on a geometric interpretation, we show that the positioning problem can be rendered as finding the intersection of a number of convex sets. To find this intersection, we propose two different methods based on projection onto convex sets and outer-approximation. In the statistical approach, a partly novel two-step linear estimator is proposed which can be expressed in a closed-form solution. We also propose a new constrained non-linear least squares algorithm based on constraints derived in the outer-approximation approach. Simulation results show that the geometrical methods are more robust against non-line-of-sight measurements than the statistical approaches while in dense networks with line-of-sight measurements statistical approaches outperform geometrical methods.