Efficient Rigid Body Localization Based on Euclidean Distance Matrix Completion for AGV Positioning Under Harsh Environment

In applications for automatic guided vehicle (AGV) navigation , the positioning system based on the time-of-flight (TOF) measurements between anchors and tags is confronted with the problem of insufficient measurements caused by blockages to radio signals or lasers, etc. Mounting multiple tags at different positions of the AGV to collect more TOFs is a feasible solution. Vehicle localization by exploiting the measurements between multiple tags and anchors is a rigid body localization (RBL) problem. However, to the best of the authors' knowledge, the state-of-the-art RBL solutions do not deal with missing measurements, and thus will result in degraded localization availability and accuracy in harsh environments. In this paper, we model this problem as a sensor network localization problem with missing TOFs and propose a new efficient RBL solution based on Euclidean distance matrix (EDM) completion, abbreviated as ERBL-EDMC. Firstly, we develop a method to determine the bounds of the missing measurements to complete the EDM reliably, using the known relative positions between tags and the statistics of the TOFs. Then, based on the completed EDM, the global tag positions are obtained from a coarse estimation followed by a refinement step assisted with inter-tag distances. Finally, the optimal results are obtained iteratively based on the estimated tag positions from the previous step. Theoretical analysis and simulation results show that the ERBL-EDMC method effectively solves the RBL problem with incomplete measurements. It obtains the optimal positioning results while maintaining low computational complexity compared with the existing RBL methods based on semi-definite relaxation (SDR).