In Norway, as in the rest of Fennoscandia, the process of Glacial Isostatic Adjustment causes ongoing crustal deformation. The vertical and horizontal movements of the Earth can be measured to a high degree of precision using GNSS. The Norwegian GNSS network has gradually been established since the early 1990s and today contains approximately 140 stations. The stations are established both for navigation purposes and for studies of geophysical processes. Only a few of these stations have been analyzed previously. We present new velocity estimates for the Norwegian GNSS network using the processing package GAMIT. We examine the relation between time-series length and precision. With approximately 3.5 years of data, we are able to reproduce the secular vertical rate with a precision of 0.5 mm/year. To establish a continuous crustal velocity field in areas where we have no GNSS receivers or the observation period is too short to obtain reliable results, either interpolation or modeling is required. We experiment with both approaches in this analysis by using (i) a statistical interpolation method called Kriging and (ii) a GIA forward model. In addition, we examine how our vertical velocity field solution is affected by the inclusion of data from repeated leveling. Results from our geophysical model give better estimates on the edge of the network, but inside the network the statistical interpolation method performs better. In general, we find that if we have less than 3.5 years of data for a GNSS station, the

This paper demonstrates that automatic selection of the right interpolation/smoothing method in a GNSS-based network real-time kinematic (NRTK) interpolation segment can improve the accuracy of the rover position estimates and also the processing time in the NRTK processing center. The methods discussed and investigated are inverse distance weighting (IDW); bilinear and bicubic spline interpolation; kriging interpolation; thin-plate splines; and numerical approximation methods for spatial processes. The methods are implemented and tested using GNSS data from reference stations in the Norwegian network RTK service called CPOS. Data sets with an average baseline between reference stations of 60–70 km were selected. 12 prediction locations were used to analyze the performance of the interpolation methods by computing and comparing different measures of the goodness of fit such as the root mean square error (RMSE), mean square error, and mean absolute error, and also the computation time was compared. Results of the tests show that ordinary kriging with the Matérn covariance function clearly provides the best results. The thin-plate spline provides the second best results of the methods selected and with the test data used.

We present a comparative study of computational methods for estimation of ionospheric scintillation indices. First, we review the conventional approaches based on Fourier transformation and low-pass/high-pass frequency filtration. Next, we introduce a novel method based on nonparametric local regression with bias Corrected Akaike Information Criteria (AICC). All methods are then applied to data from the Norwegian Regional Ionospheric Scintillation Network (NRISN), which is shown to be dominated by phase scintillation and not amplitude scintillation. We find that all methods provide highly correlated results, demonstrating the validity of the new approach to this problem. All methods are shown to be very sensitive to filter characteristics and the averaging interval. Finally, we find that the new method is more robust to discontinuous phase observations than conventional methods.

We introduce a novel approach to the computation of network real-time kinematic (NRTK) data integrity, which can be used to improve the position accuracy for a rover receiver in the field. Our approach is based on multivariate statistical analysis and stochastic generalized linear model (SGLM). The new approach has an important objective of alarming GNSS network RTK carrier-phase users in case of an error by introducing a multi-layered approach. The network average error corrections and the corresponding variance fields are computed from the data, while the squared Mahalanobis distance (SMD) and Mahalanobis depth (MD) are used as test statistics to detect and remove data from satellites that supply inaccurate data. The variance-covariance matrices are also inspected and monitored to avoid the Heywood effect, i.e. negative variance generated by the processing filters. The quality checks were carried out at both the system and user levels in order to reduce the impact of extreme events on the rover position estimates. The SGLM is used to predict the user carrier-phase and code error statistics. Finally, we present analyses of real-world data sets to establish the practical viability of the proposed methods.

The multistate reliability theory was applied to the network real-time kinematic (NRTK) data processing chain, where the qualities of the network corrections, baseline residuals, and the associated variance-covariance matrices are considered as the system state vectors. The state vectors have direct influence on the rover receiver position accuracy. The penalized honored stochastic averaged standard deviation (PHSASD) is used to map the NRTK sensitive data, represented by the states vectors to different levels of performance. The study shows that the improvement is possible by identification of critical components in the NRTK system and implementation of some parallelism that makes the system more robust.