Abstract. This paper proposes a new mathematical method of ionospheric delay estimation in single point positioning (SPP) using a single-frequency receiver. The proposed approach focuses on the ΔVTEC component estimation (MSPPwithdVTEC) with the assumption of an initial and constant value equal to 5 in any observed epoch. The principal purpose of the study is to examine the reliability of this approach to become independent from the external data in the ionospheric correction calculation process. To verify the MSPPwithdVTEC, the SPP with the Klobuchar algorithm was employed as a reference model, utilizing the coefficients from the navigation message. Moreover, to specify the level of precision of the MSPPwithdVTEC, the SPP with the IGS TEC map was adopted for comparison as the high-quality product in the ionospheric delay determination. To perform the computational tests, real code data was involved from three different localizations in Scandinavia using two parallel days. The criterion were the ionospheric changes depending on geodetic latitude. Referring to the Klobuchar model, the MSPPwithdVTEC obtained a significant improvement of 15–25 % in the final SPP solutions. For the SPP approach employing the IGS TEC map and for the MSPPwithdVTEC, the difference in error reduction was not significant, and it did not exceed 1.0 % for the IGS TEC map. Therefore, the MSPPwithdVTEC can be assessed as an accurate SPP method based on error reduction value, close to the SPP approach with the IGS TEC map. The main advantage of the proposed approach is that it does not need external data.

中文翻译：

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基于单历元数据的垂直总电子含量估计的单点定位

摘要。本文提出了一种使用单频接收机进行单点定位（SPP）的电离层延迟估计的新数学方法。所提出的方法着重于ΔVTEC分量估计（MSPPwithdVTEC），并假设在任何观察到的时期中初始值和恒定值均等于5。该研究的主要目的是检验这种方法的可靠性，使其在电离层校正计算过程中独立于外部数据。为了验证MSPPwithdVTEC，使用带有Klobuchar算法的SPP作为参考模型，利用了导航消息中的系数。此外，指定MSPPwithdVTEC的精度等级，采用具有IGS TEC映射的SPP作为电离层延迟确定中的高质量产品进行比较。为了执行计算测试，使用并行的两天时间来涉及来自斯堪的纳维亚半岛三个不同地区的真实代码数据。标准是电离层的变化取决于大地纬度。参照Klobuchar模型，MSPPwithdVTEC在最终的SPP解决方案中获得了15-25％的显着改善。对于采用IGS TEC图的SPP方法和对于MSPPwithdVTEC，误差减小的差异不明显，对于IGS TEC图，误差降低不超过1.0％。因此，MSPPwithdVTEC可以基于减少误差的值将其评估为一种准确的SPP方法，与IGS TEC映射的SPP方法接近。所提出的方法的主要优点在于它不需要外部数据。