On the Spatial Error Propagation Characteristics of Cooperative Localization in Wireless Networks

Cooperative localization is an important technique in wireless networks. However, there are always errors in network node localization, which will spatially propagate among network nodes when performing network localization. In this paper, we study the spatial error propagation (EP) characteristics of network localization in terms of Fisher information. First, the spatial propagation function is proposed to reveal the spatial cooperation principle of network localization. Second, the convergence property of spatial localization information propagation (SLIP) is analyzed to shed light on the performance limits of network localization through spatial information propagation. It is shown that 1) the network localization error propagates in the way of Ohm's law in electric circuit theory, where the measurement accuracy, node location accuracy, and geometric-resolution information behave like the resistances connected in parallel or series; 2) the network location error gradually diminishes with spatial localization cooperation procedures, due to the cooperative localization information propagation; and 3) the essence of spatial localization cooperation among network nodes is the spatial propagation of localization information.