<p>Precise modeling of the troposphere is essential for applications such as radio signal processing and weather forecasting. VMF3-FC (Vienna Mapping Functions 3 Forecast) provides high-precision real-time products, including the zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). In this study, VMF3-FC products were evaluated from 2019 to 2023 using global IGS-ZTD data from 523 IGS stations. The five-year global average RMS values of the VMF3-FC products were 1.53 cm for site-wise, 1.63 cm for 1 × 1° grid-wise, and 2.23 cm for 5 × 5° grid-wise. A highly accurate a priori variance model was proposed considering the distribution characteristics of the VMF3-FC error. The model residuals for different VMF3-FC products as 0.27, 0.32 and 0.57 cm, respectively. To validate the effectiveness of the priori variance model, globally distributed stations were selected to perform ZTD-augmented PPP with integer ambiguity resolution (PPP-IAR) reconvergence experiments. A comparative analysis was carried out on the PPP-IAR performances with and without true a priori variance, fitted variance, and empirical variance constraints. The best performance was achieved using the true variance, followed closely by the fitted variance from latitudinal fitting, where both these performances were considerably greater than that achieved using the empirical variance. Specifically, compared to the unconstrained scenario, the use of empirical variance, fitted variance, and true variance constraints respectively reduced the PPP-IAR convergence time by 7.1, 8.9 and 9.5%, and increased the ambiguity resolution success rate by 1.34, 1.49 and 1.49%. The corresponding improvement in the pre-convergence accuracy was 16.5, 17.3 and 17.1%, respectively, in the vertical component. These findings confirm that the fitted variance closely approximates the statistically determined true variance, demonstrating the global effectiveness and reliability of the proposed fitting method. Thus, the fitted variance can replace empirical values as the a priori variance used in VMF3-FC products to enhance real-time applications.</p>

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Evaluation of the VMF3-FC and prior variance modeling: implications for PPP/PPP-IAR performance

  • Xiaoting Lei,
  • Jun Tao,
  • Tianyu Yang,
  • Gaojian Zhang,
  • Qile Zhao,
  • Jing Guo

摘要

Precise modeling of the troposphere is essential for applications such as radio signal processing and weather forecasting. VMF3-FC (Vienna Mapping Functions 3 Forecast) provides high-precision real-time products, including the zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). In this study, VMF3-FC products were evaluated from 2019 to 2023 using global IGS-ZTD data from 523 IGS stations. The five-year global average RMS values of the VMF3-FC products were 1.53 cm for site-wise, 1.63 cm for 1 × 1° grid-wise, and 2.23 cm for 5 × 5° grid-wise. A highly accurate a priori variance model was proposed considering the distribution characteristics of the VMF3-FC error. The model residuals for different VMF3-FC products as 0.27, 0.32 and 0.57 cm, respectively. To validate the effectiveness of the priori variance model, globally distributed stations were selected to perform ZTD-augmented PPP with integer ambiguity resolution (PPP-IAR) reconvergence experiments. A comparative analysis was carried out on the PPP-IAR performances with and without true a priori variance, fitted variance, and empirical variance constraints. The best performance was achieved using the true variance, followed closely by the fitted variance from latitudinal fitting, where both these performances were considerably greater than that achieved using the empirical variance. Specifically, compared to the unconstrained scenario, the use of empirical variance, fitted variance, and true variance constraints respectively reduced the PPP-IAR convergence time by 7.1, 8.9 and 9.5%, and increased the ambiguity resolution success rate by 1.34, 1.49 and 1.49%. The corresponding improvement in the pre-convergence accuracy was 16.5, 17.3 and 17.1%, respectively, in the vertical component. These findings confirm that the fitted variance closely approximates the statistically determined true variance, demonstrating the global effectiveness and reliability of the proposed fitting method. Thus, the fitted variance can replace empirical values as the a priori variance used in VMF3-FC products to enhance real-time applications.