Tatjana Gerzen

Application of SWACI products as ionospheric correction for single-point positioning: a comparative study

In Global Navigation Satellite Systems (GNSS) using L-band frequencies, the ionosphere causes signal delays that correspond with link related range errors of up to 100 m. In a first order approximation the range error is proportional to the total electron content (TEC) of the ionosphere. Whereas this first order range error can be corrected in dual-frequency measurements by a linear combination of carrier phase- or code-ranges of both frequencies, single-frequency users need additional information to mitigate the ionospheric error. This information can be provided by TEC maps deduced from corresponding GNSS measurements or by ionospheric models. In this paper we discuss and compare different ionospheric correction methods for single-frequency users. The focus is on the comparison of the positioning quality using dual-frequency measurements, the Klobuchar model, the NeQuick model, the IGS TEC maps, the Neustrelitz TEC Model (NTCM-GL) and the reconstructed NTCM-GL TEC maps both provided via the ionosphere data service SWACI (http://swaciweb.dlr.de) in near real-time. For that purpose, data from different locations covering several days in 2011 and 2012 are investigated, including periods of quiet and disturbed ionospheric conditions. In applying the NTCM-GL based corrections instead of the Klobuchar model, positioning accuracy improvements up to several meters have been found for the European region in dependence on the ionospheric conditions. Further in mid- and low-latitudes the NTCM-GL model provides results comparable to NeQuick during the considered time periods. Moreover, in regions with a dense GNSS ground station network the reconstructed NTCM-GL TEC maps are partly at the same level as the final IGS TEC maps.

Comparing different assimilation techniques for the ionospheric F2 layer reconstruction

From the applications perspective the electron density is the major determining parameter of the ionosphere due to its strong impact on the radio signal propagation. As the most ionized ionospheric region, the F2 layer has the most pronounced effect on transionospheric radio wave propagation. The maximum electron density of the F2 layer, NmF2, and its height, hmF2, are of particular interest for radio communication applications as well as for characterizing the ionosphere. Since these ionospheric key parameters decisively shape the vertical electron density profiles, the precise calculation of them is of crucial importance for an accurate 3-D electron density reconstruction. The vertical sounding by ionosondes provides the most reliable source of F2 peak measurements. Within this paper, we compare the following data assimilation methods incorporating ionosonde measurements into a background model: Optimal Interpolation (OI), OI with time forecast (OI FC), the Successive Correction Method (SCM), and a modified SCM (MSCM) working with a daytime-dependent measurement error variance. These approaches are validated with the measurements of nine ionosonde stations for two periods covering quiet and disturbed ionospheric conditions. In particular, for the quiet period, we show that MSCM outperforms the other assimilation methods and allows an accuracy gain up to 75% for NmF2 and 37% for hmF2 compared to the background model. For the disturbed period, OI FC reveals the most promising results with improvements up to 79% for NmF2 and 50% for hmF2 compared to the background and up to 42% for NmF2 and 16% for hmF2 compared to OI.

An NP-Completeness Result of Edge Search in Graphs

Consider the following generalization of the classical sequential group testing problem for two defective items: suppose a graph G contains n vertices two of which are defective and adjacent. Find the defective vertices by testing whether a subset of vertices of cardinality at most p contains at least one defective vertex or not. What is then the minimum number cp(G) of tests, which are needed in the worst case to find all defective vertices? In Gerzen (Discrete Math 309(20):5932–5942, 2009), this problem was partly solved by deriving lower and sharp upper bounds for cp(G). In the present paper we show that the computation of cp(G) is an NP-complete problem. In addition, we establish some results on cp(G) for random graphs.