ResearchResearch Projects
Abschätzung der Größe systematischer Resteffekte mit Methoden der Intervallmathematik

Assessment of remaining systematic effects by interval mathematics

Leaders:  Prof. Dr.-Ing. Steffen Schön
Year:  2006
Date:  12-01-11
Sponsors:  Deutsche Forschungsgemeinschaft (DFG)
Is Finished:  yes

A realistic assessment of the total uncertainty budget of GNSS observations and its adequate mathematical treatment is a basic requirement for all analysis and interpretation of GNSS-derived products and their temporal changes. This implies not only the random variability but also the remaining systematic errors. At present in geodesy, the main focus is on stochastic approaches in which errors are modelled by means of random variables. However an alternative approach based on interval mathematics exists. It allows us to model and to quantify the impact of remaining systematic errors (which cannot be modelled and reduced by apriori correction models) in GPS carrier-phase observations on the final results using deterministic error bands. In the observation domain the magnitude of these remaining effects are assessed by observation intervals based on influence parameters. After a complex linear transfer of this type of uncertainty to the coordinate domain, the range of variability of the estimated point positions is described by zonotopes.

« Zonotope, interval box and projections of the zonotope to the interval box for a 50-km baseline oriented in azimuth 20°. The zontope represents the three-dimensional area in which the estimated coordinate can vary due to the remaining (i.e., unmodelled) systematic errors of the observations. The vectors indicate the direction of contribution of the different groups of systematic effects. Remaining orbit errors influence the shape perpendicular to the baseline orientation (along-track (1) and cross-track (2)), while the uncertainty of propagation specific effects acts in the baseline direction (e.g. the representativity of the assumed temperature (3) and pressure (4) in the tropospheric apriori correction model)

Further investigations in this research project will be carried out concerning the following aspects:

  • Quantification of the basic influence parameters
  • Impact of physical correlations between the GNSS observations

The initial work in this research field was done in cooporation with Hansjörg Kutterer and was supported by the DFG.