Real-Time Ionospheric Imaging of S₄ Scintillation from Limited Data with Parallel Kalman Filters and Smoothness

In this article, we propose a Bayesian framework to create 2-D ionospheric images of high spatio-temporal resolution to monitor ionospheric irregularities as measured by the $S_{4}$ index. Here, we recast the standard Bayesian recursive filtering for a linear Gaussian state-space model, also referred to as the Kalman filter, first by augmenting the (pierce point) observation model with connectivity information stemming from the insight and assumptions/standard modeling about the spatial distribution of the scintillation activity on the ionospheric shell at 350-km altitude. Thus, we achieve to handle the limited spatio-temporal observations. Then, by introducing a set of Kalman filters running in parallel, we mitigate the uncertainty related to a tuning parameter of the proposed augmented model. The output images are a weighted average of the state estimates of the individual filters. We demonstrate our approach by rendering 2-D real-time ionospheric images of $S_{4}$ amplitude scintillation at 350 km over South America with temporal resolution of 1 min. Furthermore, we employ extra $S_{4}$ data that was not used in producing these ionospheric images, to check and verify the ability of our images to predict this extra data in particular ionospheric pierce points. Our results show that in areas with a network of ground receivers with relatively good coverage (e.g., within a couple of kilometers distance) the produced images can provide reliable real-time results. Our proposed algorithmic framework can be readily used to visualize real-time ionospheric images taking as inputs the available scintillation data provided from freely available web-servers.