  Wireless Sensor Network (WSN) localization refers to the problem of
determining the position of each of the agents in a WSN using noisy measurement
information. In many cases, such as in distance and bearing-based localization,
the measurement model is a nonlinear function of the agents' positions, leading
to pairwise interconnections between the agents. As the optimal solution for
the WSN localization problem is known to be computationally expensive in these
cases, an efficient approximation is desired. In this paper, we show that the
inherent sparsity in this problem can be exploited to greatly reduce the
computational effort of using an Extended Kalman Filter (EKF) for large-scale
WSN localization. In the proposed method, which we call the Low-Bandwidth
Extended Kalman Filter (LB-EKF), the measurement information matrix is
converted into a banded matrix by relabeling (permuting the order of) the
vertices of the graph. Using a combination of theoretical analysis and
numerical simulations, it is shown that typical WSN configurations (which can
be modeled as random geometric graphs) can be localized in a scalable manner
using the proposed LB-EKF approach.
