Impact of colinearity of sensors selected for location estimation

We consider estimating the location of a target moving in a 2D plane by combining distance measurements from multiple sensors. Given that available energy in sensors is at a premium, it is desirable that energy be conserved by selecting fewer number of sensors that measure distance and communicate to the central tracker. We propose heuristics on the basis of which a handful of sensors may be selected. In this paper, we present one of the heuristic. The particular heuristic discussed at length is based on colinearity of sensors. In this paper, we provide a formal and theoretical basis for arriving at the heuristic and evaluate its utility.