Noise-aware localization algorithms for wireless sensor networks based on multidimensional scaling and adaptive Kalman filtering

The range-based MDS-MAP (multidimensional scaling-MAP) localization algorithm has been widely applied to the estimation of node position in wireless sensor networks (WSNs). However, the range for the MDS-MAP is often influenced by measurement noise so that there is an error, which will greatly reduce the positioning precision of MDS-MAP. Although the current improved MDS-MAP algorithms, such as MDS-MAP(P) and MDS-MAP(P,R), and the algorithms based on the theory of the rigid graph can obtain higher accuracy compared to the MDS-MAP, they are not suitable for the occasion where there are large errors in distance measurements between most nodes, namely the non-rigid graph. Therefore, Kalman filter (KF) is employed to refine the node coordinates from the MDS-MAP on this occasion, but it requires obtaining accurate noise statistics in advance and cannot adapt to the change of noise statistics. In the real WSN localization scenario with unknown or time-varying noise statistics, the inaccurate statistical parameter of noise will seriously weaken the refinement effect of KF on the MDS-MAP, especially under large noise-statistic bias. In this work, we propose two types of two-stage noise-aware localization algorithms for WSNs based on MDS-MAP and adaptive KF (AKF), i.e. an existing adaptive extended KF and an innovative adaptive unscented KF. The positioning accuracy and the time complexity of the AKF for the proposed algorithms are better than those of the spring relaxation for the rigid-graph based localization and the least square optimization for the improved MDS-MAP in the noisy environment. The results of extensive simulations show that compared with the present algorithms for refining the MDS-MAP, our proposed algorithms can always achieve higher positioning accuracy and lower time complexity regardless of the placement way of node, the shape of network topology, the communication radius of node, the node degree of network, and the deviation of noise statistics.