Error analysis on ionospheric scintillation index S-4 measured by GNSS receiver

Ionospheric scintillation is a challenging issue for the Global Navigation Satellite System (GNSS). Data collected by the globally distributed GNSS receivers provide abundant information about the ionosphere. S-4 is one of the most important parameters of the scintillation, which can be measured by the GNSS receivers. We established a simplified probability model for S-4 measured by the GNSS receiver. This model fully considers the correlation of the signal intensity and the ambient noise introduced by the receiver. A factor that reveals the correlation feature of scintillated intensity was proposed. Based on this model, the Cramer-Rao bound (CRB) and the minimum-variance unbiased estimator for S-4 were deduced and analyzed. The CRB shows that the uncertainty of S-4 increases as the scintillation becomes severe and the decorrelation time becomes longer. Then an approximate probability model was established to describe the statistics of the common estimator of S-4. Simulation tests were carried out to validate the proposed model. Based on the approximate model, the statistics of the common estimator was analyzed. We found that, apart from ambient noise, the variation of signal intensity leads to a minus bias for S-4 measurements, which seems to have been neglected in the past. A method to correct this bias was proposed. We also found that the increase in the carrier-to-noise ratio decreases the bias but helps little in reducing the variance of the measurements. Considering the accuracy of S-4 measurements and the robustness of the tracking loop, we found that for weak scintillation, the value 0.02 s is an ideal coherent time. For moderate scintillation, a relatively ideal coherent time is 0.004 s and for severe scintillation, 0.001 s is an ideal coherent time. Based on this analysis, suggestions for GNSS receiver configurations were proposed.