Consensus-Based Distributed Source Term Estimation with Particle Filter and Gaussian Mixture Model

Source term estimation (STE) techniques provide an effective way of understanding the key parameters of an atmospheric release in different scenarios. Following the Bayesian inference framework, this paper investigates the distributed STE problem over a sensor network based on a consensus-based particle filtering scheme. Among different consensus strategies, the posterior-based consensus method is selected, so that all the sensor nodes can reach the same belief of the source term. To effectively approximate the local posterior density functions (PDFs) and share them over the sensor network, the Gaussian mixture model (GMM) is constructed at each node by resorting to the expectation-maximization method, and the parameters of the GMMs are exchanged between the sensor nodes. The consensus between the GMMs from different nodes is realised in the sense of Kullback-Leibler average (KLA). To provide a numerical solution to this process, an importance sampling method with a novel importance density function is proposed to draw particles at each node with respect to the GMMs from the neighboring nodes. Finally, the effectiveness of the proposed distributed STE solution is demonstrated with an experimental dataset.