ALBERT

Description: The four dimensional (4D) space and time dependent electron density within the ionosphere and plasmasphere needs to be accurately known for precise point positioning and satellite navigation because it strongly influences the propagation of electromagnetic waves. The electron density is a highly variable function reflecting, e.g. plasma fluctuations with periods of less than a few minutes, diurnal and seasonal variations, long-period changes corresponding to the solar cycle of 11 years as well as the impact of space weather events. If the 4D electron density would be known everywhere within the ionosphere and plasmasphere at any time moment, each measurement of space-geodetic observation techniques such as GNSS, Satellite Altimetry or DORIS could be corrected independently if single or multi-frequency measurements are used. Vice versa, all these observations including Ionospheric Radio Occultations, Langmuir probe and GRACE K-band measurement provide valuable information on the state of the ionosphere and the plasmasphere and thus, for modeling the electron density. The Multi-Layer Chapman Model developed at DGFI-TUM consists of 14 key parameters. The joint estimation of all of them means an unsolvable task. It is well-known that unrealistic estimates such as negative values for the maximum electron density value of the L2 layer, may appear in the parameter estimation procedure. To avoid this, inequality constraints must be incorporated in the estimation process. This is mathematically equivalent to solving a constrained optimization problem. We developed in this context a procedure based on the active-set method. Several numerical examples are presented mostly based on simulated input data.