Abstract
Tropospheric delay is one of the main error sources that should be considered in global navigation satellite system (GNSS) positioning and integrity monitoring. Usually, it is first corrected by an empirical tropospheric zenith total delay (ZTD) model and an elevation-dependent mapping function during the preprocessing procedure, and then, the residual ZTDs are further compensated in the mathematical model, either functional or stochastic. Therefore, a tight and conservative stochastic model of the residual ZTDs is of great benefit to GNSS integrity monitoring. Since the residual ZTDs usually show significant geographical and seasonal variations and are not Gaussian distributed, using a spatiotemporal-invariant root mean square or standard deviation (STD) value to describe their stochastic characteristics would be either overly optimistic or overly conservative. We present a global and spatiotemporal-varying overbounding method to quantitatively assess the residual ZTDs, with a view to enhancing GNSS integrity monitoring. The proposed method combines the hierarchical clustering and Gaussian overbounding techniques to tightly envelop the residual ZTDs, by a constant bias and a periodic-varying STD in each latitude band. Modeling results of three conventionally used ZTD models (GPT2w, UNB3, and Saastamoinen) are presented. Also, we demonstrate how the proposed overbounding model can enhance the availability of GNSS integrity monitoring.
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Data availability
The VMF data were downloaded from the Vienna Mapping Functions Open Access Data Center (https://vmf.geo.tuwie-n.ac.at/); IGS ZPD products were obtained from the IGS website (https://igs.org/). The open-source software MAAST for ARAIM evaluation is available at (https://gps.stanford.edu/resources/software-tools/maast).
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Acknowledgements
This work is sponsored by the National Natural Science Foundation of China (42274030), the Shanghai Natural Science Foundation (20ZR1462000), and the Fundamental Research Funds for the Central Universities (22120210522).
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LY proposed the key idea; LY and YF jointly designed the research and wrote the paper; YF mainly processed and analyzed data; JZ jointly processed data; YS and CR advised, revised and improved the manuscript.
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Appendix: Overbounding modeling results for GPT2w and Saastamoinen
Appendix: Overbounding modeling results for GPT2w and Saastamoinen
In this section, the adaptively banding results of GPT2w and Saastamoinen models are shown in Fig. 12, and detailed parameters of each latitude band for the hydrostatic and wet components of the two models are provided in Tables 3 and 4. Graphic overbounding bias and STD values along different latitudes and DOYs of the two models are further given in Fig. 13 (GPT2s) and Fig. 14 (Saastamoinen). For demonstration and verification, upper bounds of the residual ZTDs at all DOYs and latitude bands for the two models are plotted in Fig. 15, and the corresponding Stanford diagrams are given in Fig. 16.
Adaptive banding results of GPT2w (up) and Saastamoinen (bottom) model
Overbounding bias and STD values of the residual ZTDs at all latitude bands for the GPT2w model
Overbounding bias and STD values of the residual ZTDs at all latitude bands for the Saastamoinen model
Upper bounds of the residual ZTDs at all DOYs and latitude bands for the GPT2w model (left) and Saastamoinen model (right) (unit: meters)
Stanford diagrams of the residual ZTDs, for the GPT2w model (left) and Saastamoinen model (right)
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Yang, L., Fu, Y., Zhu, J. et al. Overbounding residual zenith tropospheric delays to enhance GNSS integrity monitoring. GPS Solut 27, 76 (2023). https://doi.org/10.1007/s10291-023-01408-6
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DOI: https://doi.org/10.1007/s10291-023-01408-6