Joint Multiple Sources Localization Using TOA Measurements Based on Lagrange Programming Neural Network

Multiple sources’ localization using the time-of-arrival (TOA) measurements in the presence of sensor position uncertainty is studied in this paper. The non-cooperative scenario where the clock between the source and sensors is not synchronized is also considered. First, we theoretically prove that the Cramér–Rao lower bound of multi-source joint localization is lower than that of the single source case when the TOA measurements from different sources possess the same sensor position errors. Moreover, different from the conventional numerical algorithms, we propose to employ a neural circuit named Lagrange programming neural network (LPNN) to fulfill this non-trivial task of jointly locating multiple sources. The maximum likelihood problem of multi-source localization is reformulated by utilizing the LPNN framework, and then we build up a neural model, which is proved to be asymptotically stable through both mathematical analysis and numerical experiments. The simulation results show that the proposed method is superior to other positioning algorithms, and it has excellent localization performance and robustness even in the case of large measurement noise, synchronization error, and sensor position displacements.