On the Value of Collaboration in Location Estimation

Recently, extensive simulation-based research has shown a benefit to collaboration in wireless location estimation. However, an open question is “Is collaboration always inherently beneficial for location estimation?” In this paper, we answer this question affirmatively under very general conditions and prove that the Cramér-Rao lower bound (CRLB) is strictly decreasing when nodes attempting to determine their locations collaborate, with very mild restrictions. More specifically, for a network of arbitrary size, we establish the value of collaboration in node positioning problems by proving that the inclusion of an additional collaborator strictly reduces the CRLB of the original network nodes' position estimates. Previous work has shown a related result, but only for 1-D and 2-D positioning using pairwise observations. We generalize previous work in several ways: 1) by presenting results that apply to any dimensionality; 2) by generalizing to any observation types, including allowing for mixed observation types and models; and 3) by including nuisance parameter estimation. Several mild conditions arise during the derivation of the proof, which must be satisfied to claim a strictly decreasing lower bound, and these are discussed. Additionally, the results of our analysis allow us to draw further insights into the value of collaboration for the individual nodes in the original network and for the newly introduced collaborator. The theoretical results are supported by numerical results, considering the special case of time-of-arrival (TOA)-based positioning in both line-of-sight and non-line-of-sight conditions. Finally, we draw some qualitative insights into the factors that affect the value of collaboration.