Exploiting sparsity for localisation of large-scale wireless sensor networks

Wireless Sensor Network (WSN) localisation 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 localisation, the measurement model is a non-linear function of the agents' positions, leading to pairwise interconnections between the agents. As the optimal solution for the WSN localisation problem is known to be computationally expensive in these cases, an efficient approximation is desired. The authors 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 localisation. In the proposed method, which the authors call the L-Banded Extended Kalman Filter (LB-EKF), the measurement information matrix is converted into a banded matrix by relabelling (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 modelled as random geometric graphs) can be localised in a scalable manner using the proposed LB-EKF approach.