Yasyukevich Yury, Mylnikova Anna, Vesnin Artem
Institute of Solar-Terrestrial Physics SB RAS, Irkutsk 664033, Russia.
Sensors (Basel). 2020 Oct 7;20(19):5702. doi: 10.3390/s20195702.
Global navigation satellite systems (GNSS) allow estimating total electron content (TEC). However, it is still a problem to calculate absolute ionosphere parameters from GNSS data: negative TEC values could appear, and most of existing algorithms does not enable to estimate TEC spatial gradients and TEC time derivatives. We developed an algorithm to recover the absolute non-negative vertical and slant TEC, its derivatives and its gradients, as well as the GNSS equipment differential code biases (DCBs) by using the Taylor series expansion and bounded-variable least-squares. We termed this algorithm TuRBOTEC. Bounded-variable least-squares fitting ensures non-negative values of both slant TEC and vertical TEC. The second order Taylor series expansion could provide a relevant TEC spatial gradients and TEC time derivatives. The technique validation was performed by using independent experimental data over 2014 and the IRI-2012 and IRI-plas models. As a TEC source we used Madrigal maps, CODE (the Center for Orbit Determination in Europe) global ionosphere maps (GIM), the IONOLAB software, and the SEEMALA-TEC software developed by Dr. Seemala. For the Asian mid-latitudes TuRBOTEC results agree with the GIM and IONOLAB data (root-mean-square was < 3 TECU), but they disagree with the SEEMALA-TEC and Madrigal data (root-mean-square was >10 TECU). About 9% of vertical TECs from the TuRBOTEC estimates exceed (by more than 1 TECU) those from the same algorithm but without constraints. The analysis of TEC spatial gradients showed that as far as 10-15° on latitude, TEC estimation error exceeds 10 TECU. Longitudinal gradients produce smaller error for the same distance. Experimental GLObal Navigation Satellite System (GLONASS) DCB from TuRBOTEC and CODE peaked 15 TECU difference, while GPS DCB agrees. Slant TEC series indicate that the TuRBOTEC data for GLONASS are physically more plausible.
全球导航卫星系统（GNSS）可用于估算总电子含量（TEC）。然而，从GNSS数据计算绝对电离层参数仍是一个问题：可能会出现负的TEC值，并且大多数现有算法无法估算TEC的空间梯度和TEC的时间导数。我们开发了一种算法，通过使用泰勒级数展开和有界变量最小二乘法来恢复绝对非负的垂直和倾斜TEC、其导数和梯度，以及GNSS设备的差分码偏差（DCB）。我们将此算法称为TuRBOTEC。有界变量最小二乘拟合可确保倾斜TEC和垂直TEC均为非负值。二阶泰勒级数展开可提供相关的TEC空间梯度和TEC时间导数。通过使用2014年的独立实验数据以及IRI - 2012和IRI - plas模型进行了技术验证。作为TEC数据源，我们使用了Madrigal地图、欧洲定轨中心（CODE）的全球电离层地图（GIM）、IONOLAB软件以及Seemala博士开发的SEEMALA - TEC软件。对于亚洲中纬度地区，TuRBOTEC的结果与GIM和IONOLAB数据一致（均方根<3 TECU），但与SEEMALA - TEC和Madrigal数据不一致（均方根>10 TECU）。TuRBOTEC估算的垂直TEC中约9%超过（超过1 TECU）同一算法但无约束条件下的估算值。TEC空间梯度分析表明，在纬度高达10 - 15°时，TEC估算误差超过10 TECU。对于相同距离，纵向梯度产生的误差较小。TuRBOTEC和CODE的实验全球导航卫星系统（GLONASS）DCB峰值相差15 TECU，而GPS DCB一致。倾斜TEC序列表明，TuRBOTEC的GLONASS数据在物理上更合理。
