Assessment of Single-difference Ionospheric Residuals in a Regional Network for GBAS (2014)

In current Global Navigation Satellite System (GNSS) differential single-frequency data processing, ionospheric delays are considered to be considerably reduced for short baselines in regional network. However, under strong ionosphere activities the remaining ionospheric effects on the single-difference level and their short-term variations may not be neglected and may become critical for, e.g., the approach and landing of airplanes using a Ground Based Augmentation System (GBAS).

In this paper, the single-difference ionospheric residuals and spatial gradients are studied as a function of the Ionosphere Pierce-Point (IPP) distance under diverse ionosphere activities using data of the Automated GNSS Network for Switzerland (AGNES) over 15 years. A similar study has been performed by Lee et al. (2006) using the Wide Area Augmentation System (WAAS) “supertruth” data and the Jet Propulsion Laboratory (JPL) post-processed Continuously Operating Reference Stations (CORS) data by leveling the carrier-phase-based ionospheric measurements with the help of the code observables. Here, we provide an alternative method to estimate the single-difference ionospheric residuals and spatial gradients based on double-difference phase observations with resolved ambiguities.

After pre-processing of the phase observations, the phase ambiguities can be resolved with the help of the Bernese GPS Software. The geometry-free (GF) linear combination of the phase observations is then generated on the double-difference level without the code-related error sources like differential code biases (DCBs) and arc-wise biases resulting from code smoothing. Only the ionospheric delay, the phase noise and biases like multipath remain in the residuals. However, singularities exist when deriving single-difference ionospheric delays from double-difference residuals. This is corrected for by imposing, e.g., a zero-mean condition on the single-difference residuals per baseline and per observation epoch. In order to correct for the lack of absolute information in the double-difference residuals mentioned above, model values of the ionospheric delays are generated for each observation using the CODE’s global ionosphere maps. A mean model ionospheric offset is then added epoch-wise to the estimated single-difference ionospheric delays per baseline to supply absolute information and the zero-mean condition is then applied to the deviations from the mean ionospheric offset. Local ionosphere maps may be considered in the future to produce more appropriate mean model ionospheric offset. It should be mentioned that small epoch-wise biases may still exist in each of the ground baselines because of the spatial and temporal smoothing effects of the ionosphere model.

The single-difference spatial ionospheric gradients are estimated with the single-difference ionospheric delays and the pierce-point baseline length, namely the distance between the two pierce points of the “thin-shell” ionosphere model. We categorize the ionosphere activity into different levels based on geomagnetic indices, e.g., the Kp and Dst Index (see Lee et al. 2006), and analyze the correlation between the slant differential ionospheric delays and the geomagnetic indices as well as the daily Total Electron Content (TEC) provided by the Center for Orbit Determination in Europe (CODE). Using an elevation-dependent mapping function, the vertical single-difference ionospheric delays and gradients are also calculated and studied for all available days except the very stormy days. Very short ground baselines for the purposes of investigation of the non-ionospheric biases and ground baselines longer than 300 km are included in the study.

Studies with long-term time series and the entire network of the AGNES stations have delivered a general relationship between the ionospheric delays, gradients and the ionosphere activity. The differential slant and vertical ionospheric delays and gradients were calculated and analyzed from 1999 to 2013. We see that the change of the differential ionospheric delays and gradients corresponds to the ionosphere activities. For very short baselines, the mean single-difference ionospheric residuals are at mm-level with a standard deviation at cm-level.

In the end, the vertical ionospheric gradients are normalized in specific distance bins and an inflated sigma which bounds all the outliers and non-Gaussian tails of the normalized vertical ionospheric gradients has been determined. This part of the analysis is based on the work of Lee et al. (2006) for all the ionosphere nominal and active days. The daily peak slant ionospheric gradients are further analyzed for all available days under different ionosphere conditions with the help of the Conterminous United States (CONUS) ionosphere anomaly threat model (see Pullen et al. 2009).

This work has been financed by Flughafen Zurich AG as part of the Skyguide (Swiss Air Navigation Services Ltd.) project of Ionospheric Activities onto GNSS Signal during Approach and Landing within the frame of the Swiss-wide program to implement new technologies (CHIPS). We would also like to thank swisstopo for providing the AGNES data for the processing.

References:
Lee J., Pullen S., Datta-Barua S. and Enge P.: Assessment of Nominal Ionosphere Spatial Decorrelation for LAAS; Position, Location, and Navigation Symposium, 2006 IEEE/ION, Coronado, CA, USA, pp. 506-514, April 2006.
Pullen S., Park Y.S. and Enge P.: Impact and mitigation of ionospheric anomalies on ground-based augmentation of GNSS, Radio Science 44, 2009, doi:10.1029/2008RS004084.