3-D localization of wireless sensor nodes using near-field magnetic-induction communications

This paper proposes two localization methods for wireless sensor nodes that utilize an arbitrarily oriented tri-directional coil as both magnetic induction (MI) transmitter and receiver for wireless communications. Taking advantage of magnetic field measurements of a tri-directional coil antenna in the near-field, the two localization algorithms use only two anchor nodes to locate a sensor node in the 3-D space. Assuming each anchor node transmits the communication signals by three coils sequentially, which are received by the three coils at a sensor node simultaneously, this paper derives closed-form formulas for estimating the transmission distance and the polar angles to yield eight possible location points based on the signals of each anchor node. Then a rotation matrix (RM)-based method derives the orientation rotation matrix between the transmitter and receiver to find two possible location vectors with opposite directions in each anchor node. Then, we use maximum likelihood to estimate the location with two anchor nodes assisted. Another method called the distance-based method, taking into account the locations of the two anchor nodes and the two sets of eight possible location estimates of the sensor node, estimates the location by minimizing the distance. The RM-based method can achieve high localization accuracy while the distance-based method has less computational complexity. However, the distance-based method may encounter location ambiguity when the orientations of the two anchor nodes are the same. Simulations were performed to compare these two algorithms and the existing localization algorithm in this scenario. The results show that the proposed two localization algorithms and the derived closed-form formula of distance achieve good accuracy under large measurement errors. (C) 2018 Published by Elsevier B.V.