An Evaluation of Interpolation Techniques for Reconstructing Ionospheric TEC Maps

Abstract

Maps of the total electron content (TEC) of the ionosphere can be reconstructed using data extracted from global positioning system (GPS) signals. For historic and other sparse data sets, the reconstruction of TEC images is often performed using a multivariate interpolation technique. Although there are many interpolation methods available, only a limited number, for example kriging, have been applied to TEC data. This paper presents a quantitative comparison of various commonly used algorithms for scattered-data interpolation over a range of sparsities. Techniques evaluated include a relatively new approach called Adaptive Normalized Convolution (ANC) that has not previously been applied to ionospheric reconstruction. The proposed evaluation scheme employs a quantitative methodology applied to both simulated and real TEC data. Results show that, although the performance of kriging is good in many cases, it is several times worse than the best performing techniques at some sparsities. Natural-neighbor interpolation has a better overall performance than kriging for both simulated and TEC data. Although its performance is a few percent worse than other methods for the simulated data, ANC produces the best performance for the TEC reconstructions. He has published over 50 papers in journals and refereed conference proceedings. His current research interests include nonlinear image processing, feature extraction and motion estimation in application to remotely sensed, color and multispectral images, and video compression.

L-band scintillations and calibrated total electron content gradients over Brazil during the last solar maximum

“…This choice follows what was found by Foster & Evans (2008), that demonstrated how, in the case of local maps of TEC, the natural neighbour interpolation technique gives better results with respect to other commonly used methods (linear, inverse distance weighting, kriging, etc.). Details on the natural neighbour interpolation technique applied can be found in Okabe et al (1994) and Lee & Schachter (1980).…”

Extending Ionospheric Correction Coverage Area By Using A Neural Network Method

“…For this reason only the BHS is considered in this research. The BHS is a method of finding the minimum-curvature surface, which passes through a set of points [8]. For N data points in m dimensions the interpolation problem is [9] LATION METHODS ethods are tested for the extrapolation function f of Eq.…”

“…For this reason only the BHS is considered in this research. The BHS is a method of finding the minimum-curvature surface, which passes through a set of points [8]. For N data points in m dimensions the interpolation problem is [10] ( ) where ( ) x φ is a Green's function which is the impulse response of an inhomogeneous differential equation [9], and j α is a weighting factor.…”

“…Therefore, the extrapolation becomes the function of observed TEC only as follows where i s is a unit vector in the direction i n . The BHS method can be numerically unstable for large numbers of points and has a tendency to drastically overshoot when points are close together [8]. The BHS utilizes the observed TEC only and does not require the environmental parameters.…”

A terrain-based hybrid approach towards DEM interpolation

“…However, it may result in an undeserved rough surface generation causing higher values near the points. Spline method fits suitable mathematical function (say, radial basis function) over comparatively lesser number of sampled data points to create smooth surface preserving small features (Foster and Evans 2008). KRG approach is based on spatial autocorrelation and uses semi-variogram (plot of semi-variance versus separation distance) that captures the spatial structure of the sample points for interpolation.…”