We consider cooperative position estimation in wireless networks as Bayesian inference problems in which nodes with unknown positions (agents) infer their positions based on distance measurements with respect to reference nodes (anchors) and other agents. In the indoor environment, the positions of agents can be constrained to finite geometric sets due to non-negative errors on the range estimates which arise from non-line-of-sight and multipath effects. First, we exploit the non-negativity of ranging errors in order to confine the positions of nodes to convex polygons. Subsequently, we exploit these polygons to relax the inference-based position estimation problems in terms of computational complexity. Using this two-stage approach, we show a tremendous reduction in terms of computational complexity, improvements in terms of localization accuracy, as well as the quicker convergence of the inference algorithm.
