Nonlinear estimation to assimilate GPS TEC data into a regional ionosphere model

A new method of is being developed to estimate the ionosphere's 3-dimensional electron density distribution based on GPS slant TEC data. The goal of this effort is to develop a generalized parametric ionospheric model that is amenable to data assimilation using powerful nonlinear least-squares batch filtering techniques and related techniques. In addition to assimilating GPS TEC data, this method will eventually be targeted at assimilating additional data types in order to implement true data fusion for ionospheric characterization. The parameterized ionosphere model uses a latitude/longitude bi-quintic spline model to characterize the horizontal variations of parameters of a vertical electron density profile. The result is a truly 3-dimensional electron density distribution. It is parameterized by vertical profile parameter values at latitude/longitude spline nodes and by various latitude and longitude partial derivatives of these parameters at the nodes. This electron density distribution is used in conjunction with quadrature numerical integration to determine slant TEC along line-of-sight paths to tracked GPS satellites. A nonlinear batch estimation algorithm compares the modeled GPS slant TEC values predicted by its current parameter estimates with corresponding measured values. It then updates its parameter estimates to improve its fit to the measurements while balancing a need to use parameters that remain relatively near reasonable a priori values, as dictated by an International Reference Ionosphere calculation. A truth-model simulation study shows that the vertical TEC map is observable as part of a latitude/longitude-dependent Chapman profile. The height of peak electron density and the scale height of the Chapman profile are only weakly observable from slant TEC data alone. Tests of this method have also been made with slant TEC data from an array of over 900 dual-frequency GPS receivers distributed over the continental U.S. The method demonstrates an equal or better ability to predict slant TEC at other GPS receivers than that of a traditional thin-shell, fixed-altitude ionosphere data assimilation model like the one used for WAAS.