Development of an adequate variance model for GNSS carrier phase observations based on turbulence theory
Final Report Abstract
Tropospheric fluctuations create correlations between GPS carrier phase measurements that limit the precision of the least-squares results. Based on Kolmogorov turbulence theory and the concept of eddies, Schön and Brunner (2008) developed the so called SIGMA-C model However, this model, as the Treuhaft and Lanyi (1987) one used in VLBI, are involving a numerical double integration, making its concrete use in least-squares estimation time consuming. Thus until now, no simple, physically derived and easily to handle model for GPS phase correlations due to the troposphere is available. In this project, two major steps forward were realized: (i) The computation of covariance matrices based on the Mátern covariance family without numerical double integration and thus less time consumption. (ii) Use of an equivalent diagonal kernel that allows to take correlations into account thanks to diagonal covariance matrices. Thus, this makes the commonly used normal equation stacking also possible for correlated data. The equivalence is mathematically given for the mean estimator case, yielding possible applications for calibration purposes. Thanks to the special structure of the design matrix these findings could be successfully extended to GPS point positioning. A study of the impact of the atmospheric parameters that have to be taken in consideration was carried out. Our model being based on physical considerations and approximations, the wind velocity or the outer scale length could be fixed. Parameters such as the structure constant were taken constant in a first step. The data of the Seewinkel network, specially designed to study the influence of the troposphere on GPS carrier phase observations was processed in a least-squares adjustment with the developed fully populated covariance matrices. Improvements of the parameter estimates for short baselines were not found, however a more realistic coordinate precision was noticed. For long baselines (up to 500 km), first tests were carried out with data from the IGS network. Here, the Mátern parameters sets has to be adapted since further correlating effects remain. This allows to improve the parameter estimates up to the cm level.
Publications
- (2014) On taking correlations into account in least-squares adjustment with a diagonal covariance matrix. Intergeo 2014 Geodätische Woche, October 7-9th
Schön S, Kermarrec G
- (2014) On the Mátern covariance family: a proposal for modeling temporal correlations based on turbulence theory. Journal of Geodesy, 88:1061–1079
Kermarrec G, Schön S
(See online at https://doi.org/10.1007/s00190-014-0743-7) - Turbulence Theory In:In: Freeden W., Nashed M., Sonar T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg, 2014, pp 1-45.
Schön S, Kermarrec G
(See online at https://doi.org/10.1007/978-3-642-27793-1_77-3)
