Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

Abstract

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 1016 electrons/m2) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area.

Improving the Reconstruction Accuracy of Marine Gravity Anomaly Encrypted Reference Map Using the New Mean Sea Surface 3-D Correction Method

“…Since the NMSST-DCM has the same characteristics of unbiased and optimal as the traditional Kriging 2-D interpolation method, the weights of samping points can be obtained from the satisfied relationship as follows [50]…”

Kriging‐based ionospheric TEC, ROTI and amplitude scintillation index (S4) maps for India

“…are thoroughly studied [26–29]. Regional TEC maps for Chinese, Japanese and Turkish regions are well represented [2, 30–32]. Several researchers have developed ionospheric TEC grid estimation using various techniques such as kriging, planar‐fit, inverse distance weighted, minimum mean square error for GPS and SBAS applications over the Indian region [33–36].…”

Prediction of global ionospheric VTEC maps using an adaptive autoregressive model

“…For instance, global models are constructed by using empirical orthogonal function analysis to reproduce the major variations in TEC and the ionospheric climatology (Ercha et al 2012;Wan et al 2012;Mukhtarov et al 2013). Also, regional models are studied over many countries and regions by using different methods to capture more details of the ionosphere (Bouya et al 2010;Habarulema 2010;Chen et al 2015;Fuller-Rowell et al 2016;Huang et al 2017).…”