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<p>Global navigation satellite system (GNSS) plays a crucial role in ionospheric delay modeling and space weather monitoring nowadays. Recently, the so-called quasi‑4‑dimensional ionospheric model (Q4DIM) integrates global ionosphere map (GIM) and slant ionospheric delay (SID) into a unified model. Q4DIM is based on line of sight (LOS) ionosphere delay spatial gridding along latitude-longitude-elevation-azimuth. However, as the Q4DIM relies on a uniform gridding algorithm, its grid sizes and numbers are typically set empirically, without fully considering the statistical characteristics and distribution trends of the data. This lack of flexibility limits its adaptability to datasets with varying spatial scales and densities. Consequently, regardless of the geometry of satellite constellations and the distribution of tracking stations, Q4DIM may still fail to effectively utilize the increasing volume of GNSS data. Taking the great advance in machine learning into consideration, the study proposes a novel Q4DIM method based on various clustering algorithms, e.g., KMEANS, DBSCAN and Agglomerative. In the experiment, multi-GNSS measurements collected from the International GNSS Service (IGS) global network in February 2023 were processed. The result reveals that, modeling with clustering algorithm KMEANS and Agglomerative exhibits more regular clustering boundaries and greater differences between clusters, while DBSCAN has slightly poorer clustering performance but higher modeling efficiency. Moreover, since the novel Q4DIM based on clustering algorithms can elastically adapt itself to the rather un-evenly distributed GNSS network, it enables a more refined characterization of the ionosphere's actual distribution and variability, thereby significantly improving performance. Specifically, compared to the uniform grid-based Q4DIM with a STD of 0.35 TECU and a RMS of 2.16 TECU, both DBSCAN- and Agglomerative-based Q4DIM have a precision of about 0.3 TECU and 1.0 TECU for STD and RMS, respectively, while KMEANS-based Q4DIM has a STD of 0.31 TECU and a RMS of 1.3 TECU. In addition, we demonstrate that the proposed clustering-based Q4DIM maintains robust modeling accuracy even with a small number of suboptimally distributed stations, highlighting its elastic adaptability to diverse data distributions.</p>

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Quasi-4-dimensional ionospheric delay model based on clustering algorithms

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Shengfeng Gu,
  • Jiayu Hu,
  • Jiaxi Zhu,
  • Zihao Wang,
  • Xiaopeng Gong

摘要

Global navigation satellite system (GNSS) plays a crucial role in ionospheric delay modeling and space weather monitoring nowadays. Recently, the so-called quasi‑4‑dimensional ionospheric model (Q4DIM) integrates global ionosphere map (GIM) and slant ionospheric delay (SID) into a unified model. Q4DIM is based on line of sight (LOS) ionosphere delay spatial gridding along latitude-longitude-elevation-azimuth. However, as the Q4DIM relies on a uniform gridding algorithm, its grid sizes and numbers are typically set empirically, without fully considering the statistical characteristics and distribution trends of the data. This lack of flexibility limits its adaptability to datasets with varying spatial scales and densities. Consequently, regardless of the geometry of satellite constellations and the distribution of tracking stations, Q4DIM may still fail to effectively utilize the increasing volume of GNSS data. Taking the great advance in machine learning into consideration, the study proposes a novel Q4DIM method based on various clustering algorithms, e.g., KMEANS, DBSCAN and Agglomerative. In the experiment, multi-GNSS measurements collected from the International GNSS Service (IGS) global network in February 2023 were processed. The result reveals that, modeling with clustering algorithm KMEANS and Agglomerative exhibits more regular clustering boundaries and greater differences between clusters, while DBSCAN has slightly poorer clustering performance but higher modeling efficiency. Moreover, since the novel Q4DIM based on clustering algorithms can elastically adapt itself to the rather un-evenly distributed GNSS network, it enables a more refined characterization of the ionosphere's actual distribution and variability, thereby significantly improving performance. Specifically, compared to the uniform grid-based Q4DIM with a STD of 0.35 TECU and a RMS of 2.16 TECU, both DBSCAN- and Agglomerative-based Q4DIM have a precision of about 0.3 TECU and 1.0 TECU for STD and RMS, respectively, while KMEANS-based Q4DIM has a STD of 0.31 TECU and a RMS of 1.3 TECU. In addition, we demonstrate that the proposed clustering-based Q4DIM maintains robust modeling accuracy even with a small number of suboptimally distributed stations, highlighting its elastic adaptability to diverse data distributions.