A New Ionospheric Estimation Algorithm for SBAS Combining Kriging and Tomography

One can divide the existing ionospheric methods for SBAS in two categories: tomography and methods relying on the thin shell model. At first sight, tomography appears to be the right choice. Tomography reconstructs the three dimensional density of the ionosphere from the available measurements. However, there are several drawbacks to tomography: the system of equations to be solved is often underdetermined – leading to artificial constraints -, the basis functions that are used are arbitrary, and the stochastic properties of the ionosphere – which are extremely variable – are not taken into account. The thin shell model methods on the other hand (including the planar fit that is currently used in the Wide Area Augmentation System (WAAS) and methods based on kriging) assume that the vertical density profile is an impulse function. This assumption is very limiting and gives rise to the vertical to slant error. But it allows us to transform a three-dimensional problem in a two dimensional estimation problem, and to easily characterize the stochastic properties of the ionosphere. We present an ionospheric estimation method that has elements from both categories. Like tomography, it takes into account the three dimensional nature of the ionosphere, and like in the thin shell model methods mentioned (planar fit, kriging), it relies on the measured stochastic properties of the ionosphere. This method is not a heuristic mix of both methods, but rather a natural extension of kriging in three dimensions. The technique was tested using post-processed ionospheric Total Electron Content measurements from the US and Brazil.