On the Spatial Information Coupling in Relative Localization Networks

High-accuracy localization techniques have been widely used in various applications such as formation control and auto-driving where the relative position information is concerned. Existing works focus on efficient algorithm design to enhance the accuracy of relative localization while the spatial information coupling effect is not well revealed. In this paper, we develop a general approach inspired by the resistance distance theorem to characterize the spatial information coupling effect in relative localization. Then a geometric interpretation for the cooperation efficiency between two agents is presented via the random walk theory. Furthermore, we develop the asymptotic analysis for large lattice networks and prove that the relative localization error grows logarithmically with both network size and spatial distance. Finally, the theoretical analysis is validated by numerical results.