Geostatistical interpolation applied to tracking jitter variance maps

This paper focuses on the development of tools to mitigate ionospheric scintillation effects in both real time and in post mission GNSS positioning computation by a method based on the improvement and validation of the stochastic model applied in a (Recursive) Least Squares or Kalman filter solution. One method of obtaining the input for the stochastic model is the use of tracking jitter variance maps. The method of least squares collocation/ordinary kriging has been often used in physical geodesy and within the field of GNSS it has been successfully applied to Network RTK and for the interpolation of TEC maps. The paper will introduce the method of collocation/kriging applied to the interpolation of tracking errors for the creation of tracking jitter variance maps. The concept of tracking jitter variance maps and collocation/kriging will be introduced and a brief overview of the various methods (e.g. Conker model) for tracking jitter estimation will be described, followed by the actual construction of the maps. Then a short introduction into the used geostatistical interpolation method will be given. Further, the paper will show the calculation route (e.g. used variograms) and the results of the geostatistical interpolation method used for the creation of tracking jitter variance maps. A network of stations (the Canadian High Arctic Ionospheric Network (CHAIN) is used to calculate the maps, through ordinary (co)kriging. Verification of the performance of the interpolation method is obtained by leaving one of the stations in the network outside the calculation, and comparing the interpolation results with the actual tracking jitter obtained at this station. Ordinary (co)kriging interpolates the tracking jitter, but also provides an estimate of the accuracy of the interpolation, so that an ';interpolation confidence' parameter can be plotted together with the interpolated and directly obtained values. Finally the paper describes the application of the tracking jitter variance maps, through a Precise Point Positioning (PPP) solution for the station left out in the construction of the tracking jitter map. Four solutions will be shown: 1) the stochastic model improved based of the tracking jitter from the geostatistical interpolation technique and furthermore through additional statistical testing 2) the stochastic model improved based on the tracking jitter from the geostatistical interpolation technique, 3) the stochastic model improved based on the actual tracking jitter variances from the station and 4) no improvement to the stochastic model, i.e. the use of the standard stochastic model.