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. S₄ 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 S₄ 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 S₄ were deduced and analyzed. The CRB shows that the uncertainty of S₄ 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 S₄. 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 S₄ 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 S₄ 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.

中文翻译：

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GNSS接收机测量电离层闪烁指数S 4的误差分析

对于全球导航卫星系统（GNSS）来说，电离层闪烁是一个具有挑战性的问题。全球分布的GNSS接收器收集的数据提供了有关电离层的大量信息。S ₄是闪烁的最重要参数之一，可以由GNSS接收器测量。我们为GNSS接收器测量的S ₄建立了简化的概率模型。该模型充分考虑了信号强度与接收机引入的环境噪声之间的相关性。提出了揭示闪烁强度相关特征的因素。基于此模型，S ₄的克雷默-饶界（CRB）和最小方差无偏估计量被推论和分析。CRB表明，随着闪烁的加剧和去相关时间的延长，S ₄的不确定性增加。然后建立一个近似概率模型来描述S ₄的共同估计量的统计量。进行了仿真测试以验证所提出的模型。基于近似模型，分析了公共估计量的统计量。我们发现，除了环境噪声外，信号强度的变化还会导致S ₄的负偏置。测量，这在过去似乎已被忽略。提出了一种纠正这种偏差的方法。我们还发现，载噪比的增加降低了偏差，但对减小测量结果的变化几乎没有帮助。考虑到S ₄测量的准确性和跟踪环路的鲁棒性，我们发现对于弱闪烁，0.02 s是理想的相干时间。对于中度闪烁，相对理想的相干时间为0.004 s，对于重度闪烁，0.001 s是理想的相干时间。基于此分析，提出了有关GNSS接收机配置的建议。