Graph-topology-learning-based IoT positioning under incomplete measurement data

Obtaining location information of the multi-sensor internet of things (IoT) is a fundamental requirement. But, two kinds of the incomplete measurement data enhance the difficulty of positioning: 1) The location information is partially missing. 2) The errors of the measurement. Furthermore, the complex environmental impact and the characters of the measurement methods make the error model more changeable at the same time. This paper tries to study a universal method to address these problems, through combining IoT positioning and affinity graph assessment with arbitrary model of the measurement errors or the missing measurement data. First of all, the relationship between the graph signal and the combinatorial graph Laplacian matrix is constructed to link the graph topology learning and the IoT localization problem. Later, the Gaussian mixture model is applied to describe the measurement errors as a general model. Then, the calculations of the graph signal, Laplacian matrix and hyper parameters are obtained via variational Bayesian inference and message passing. The numerical results show the superiority of the proposed algorithm.