Distributed Cooperative Positioning in Mobile Wireless Networks: A GNN-Aided Joint Model- and Data-Driven Framework With High-Accuracy Closed-Form Message Representation

Future mobile wireless networks will catalyze substantial demand for precise distributed cooperative positioning (DCP), especially when the global navigation satellite systems are unavailable. However, conventional message passing based DCP methods may suffer considerable performance degradation due to message approximation and sparsity/mobility of nodes. In this paper, we first present a high-accuracy parametric message approximation method, which achieves closed-form representations of all types of messages involved and reduces the computational complexity of message passing procedures. Using these representations, we propose a model- and data-driven hybrid inference approach, dubbed graph neural network enhanced spatio-temporal message passing (GNN-STMP), which fine-tunes parametric messages passed on factor graph and obtains more accurate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> distribution of nodes’ positions by exploiting GNN-generated messages. Furthermore, we develop a universal framework for the parametric message passing based DCP problem, by integrating GNN-STMP with the extend Kalman filter based node’s state prediction and refinement. This framework significantly reduces the positioning ambiguity caused by insufficient spatial ranging measurements from neighbor nodes. Simulation results and analyses demonstrate that, compared with state-of-the-art methods, our proposed approaches achieve the best and near-best positioning accuracy when insufficient and sufficient spatial ranging measurements are available, respectively, while incurring modest computational complexity.