## Abstract

The knowledge of the electron density is the key point in correcting electromagnetic measurements for ionospheric disturbances. In the last 15 years, the space-geodetic observation techniques such as the Global Positioning System (GPS) or radar altimetry have become a promising tool for monitoring the electron distribution in the ionosphere. This chapter gives a detailed overview of the mathematical modeling of ionospheric parameters such as the electron density by means of B-spline expansions. B-splines - which are locally supported basis functions - allow for optimal handling of unevenly distributed observations and data gaps. By combining the one-dimensional basis functions by means of tensor products, multidimensional models can be constructed easily. The unknown model coefficients are estimated based on observations from a number of space-geodetic techniques. In addition to the mathematical model and the basis functions used, the estimation process including variance component estimation (VCE) and multi-scale representation (MSR) is introduced. The feasibility of the approach is shown for one example modeling the vertical total electron content (VTEC) for 24 h in South America.

Original language | English |
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Title of host publication | Handbook of Geomathematics |

Subtitle of host publication | Second Edition |

Publisher | Springer Berlin Heidelberg |

Pages | 939-983 |

Number of pages | 45 |

ISBN (Electronic) | 9783642545511 |

ISBN (Print) | 9783642545504 |

DOIs | |

State | Published - 15 Sep 2015 |

Externally published | Yes |