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<p>Zenith tropospheric delay (ZTD), which is characterized by dynamic variability and strong stochasticity, is a typical contributor to the error budgets of microwave-dependent geodetic techniques. The current empirical models represent ZTD states as discretized grids and periodic harmonics, enabling rapid estimation processes but struggling to simulate short-term fluctuations and complex spatial variations, which limits the accuracy of GNSS positioning. In this work, an optimized ZTD model (GRZTD) is established using an ensemble machine learning scheme to fully account for spatiotemporal nonlinear factors. Trained on the GNSS-derived ZTD products acquired from 218 UNAVCO stations from 2018 to 2020, we first mitigate the periodic residuals of GPT3-ZTD via harmonic function fitting. The nonlinear influences of spatiotemporal factors on the remaining quadratic residuals are subsequently weakened in combination with the bidirectional gated recurrent unit (BiGRU) and random forest (RF) algorithms. The GNSS-derived ZTD data obtained from 65 external stations in 2021 are employed to verify the accuracy and applicability of GRZTD. The statistical results obtained on the postprocessed ZTD data demonstrate that the root mean square (RMS) of the GRZTD model is 26.32&#xa0;mm, which represents improvements of 26.5%, 27.1%, and 27.2% over those of the state-of-the-art GPT3, Gtrop, and IGPZWD models, respectively. The GRZTD model also exhibits optimal predictive capabilities in spatiotemporal analysis tasks, effectively capturing ZTD changes under complex climatic and terrain conditions. Moreover, when the GRZTD-derived ZTD data are introduced as a prior constraint, the convergence times of real-time precise point positioning (PPP) decrease by 4.0%, 8.6%, and 11.9% in the E, N, and U directions, respectively.</p>

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A regional area-precise ZTD forecasting model combining GPT3 and GNSS based on an ensemble learning algorithm

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Shaoni Chen,
  • Chunhua Jiang,
  • Pan Li,
  • Huizhong Zhu,
  • Junhua Kang,
  • Xiang Gao,
  • Shuaimin Wang,
  • Guangsheng Liu

摘要

Zenith tropospheric delay (ZTD), which is characterized by dynamic variability and strong stochasticity, is a typical contributor to the error budgets of microwave-dependent geodetic techniques. The current empirical models represent ZTD states as discretized grids and periodic harmonics, enabling rapid estimation processes but struggling to simulate short-term fluctuations and complex spatial variations, which limits the accuracy of GNSS positioning. In this work, an optimized ZTD model (GRZTD) is established using an ensemble machine learning scheme to fully account for spatiotemporal nonlinear factors. Trained on the GNSS-derived ZTD products acquired from 218 UNAVCO stations from 2018 to 2020, we first mitigate the periodic residuals of GPT3-ZTD via harmonic function fitting. The nonlinear influences of spatiotemporal factors on the remaining quadratic residuals are subsequently weakened in combination with the bidirectional gated recurrent unit (BiGRU) and random forest (RF) algorithms. The GNSS-derived ZTD data obtained from 65 external stations in 2021 are employed to verify the accuracy and applicability of GRZTD. The statistical results obtained on the postprocessed ZTD data demonstrate that the root mean square (RMS) of the GRZTD model is 26.32 mm, which represents improvements of 26.5%, 27.1%, and 27.2% over those of the state-of-the-art GPT3, Gtrop, and IGPZWD models, respectively. The GRZTD model also exhibits optimal predictive capabilities in spatiotemporal analysis tasks, effectively capturing ZTD changes under complex climatic and terrain conditions. Moreover, when the GRZTD-derived ZTD data are introduced as a prior constraint, the convergence times of real-time precise point positioning (PPP) decrease by 4.0%, 8.6%, and 11.9% in the E, N, and U directions, respectively.