Physically-Informed Fuzzy Clustering of Vertical Sounding Ionograms
This paper presents a physically-informed fuzzy clustering of vertical sounding ionograms for automatically separating the ionogram into tracks suitable for further interpretation and determining their optimal number. The model is designed for use not only in conditions where the number of tracks is known, but also in disturbed ionospheric conditions where the number of tracks is preliminary unknown. The method is based on an expectation-maximization algorithm, used for clustering, and on parametrically specified distributions of distances from points to parametrically specified curves. The curves used as track models are close to model tracks in the parabolic ionospheric layer model. The resulting model of each track has six parameters: three standard ones (the critical frequency, the lower boundary of the layer, and its half-width), and three additional ones to take into account possible underlying layer effects. By sequentially increasing the number of tracks and optimizing their parameters, the model finds the optimal number of tracks on the ionogram by minimizing the modified Bayesian information criterion. The Sequential Least Squares Quadratic Programming algorithm is used to find the parameters of a single track. The width of each single track is assumed to be unknown constant found during fitting process. To improve the quality of ionogram clustering, automatic adaptive noise filtering is performed before clustering. This filtering is based on a combination of the DBSCAN and Gaussian Mixture algorithms. Also, to improve clustering quality on an ionosonde without hardware separation of the ordinary and extraordinary components, a preliminary approximate removal of points belonging to the extraordinary mode is performed.