An Efficient Bayesian Integration Technique to Densify Global Ionospheric Maps using Observations of Local GNSS Networks

Global ionosphere maps (GIM) are generated on daily basis at the Center for Orbit Determination in Europe (CODE) using data from about 200 GNSS sites of the International GNSS Service (IGS) and other institutions. These measurement are used to numerically model the vertical total electron content (VTEC) in a solar-geomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. In this study, an efficient method is developed and applied to densify the GIM model in a region of interest using the TEC measurements of local networks. Our approach follows a Bayesian updating scheme, where the GIM data are utilized as a prior information in the form of Slepian-coefficients in the region of interest. These coefficients are then updated by the GNSS measurements in a Bayesian framework that considers both the uncertainty of a priori information and the new measurements. Numerical application is demonstrated using a GNSS network in South America. Our results indicate that by using 62 GNSS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the Bayesian-derived VTEC estimates in a Standard Point Positioning (SPP) experiment improved the positioning accuracy compared to the usage of GIM/CODE and Klobuchar models. The reductions in the root mean squared of errors were found to be ∼23% and 25% for a day with moderate solar activity while 26% and ∼35% for a day with high solar activity, respectively.Key words: Bayesian densification, Slepian Functions, Spherical Harmonics, Ionospheric modelling, VTEC, SPPs