On the Value of Collaboration in Non-Line-of-Sight Location Estimation

In this paper, we investigate the benefit of inter-node collaboration in multidimensional location estimation under nonline-of-sight signal propagation conditions using time-of-arrival range observations. Specifically, for a network of arbitrary size, we establish the value of collaboration for node positioning by proving that the inclusion of an additional collaborator strictly reduces the Cramér-Rao lower bound of the original network nodes´ position estimates. During the derivation of the proof, several conditions arise which must be satisfied in order to claim a strictly-decreasing lower bound. Following the proof, these conditions are discussed and the result of the proof is verified with numerical results showing both the theoretical reductions in the lower bound as well as the reductions observed in the mean square error performance of the maximum a posteriori implementation of the collaborative positioning estimator. While in the line-of-sight case, the observed improvement in estimation performance matches well with that predicted by the Cramér-Rao lower bound, the relationship is much less tight in the nonline-of-sight case. However, the simulation results show that the benefit of collaboration is often greater with the maximum a posteriori estimator than the Cramér-Rao lower bound analysis would indicate.