Exploiting sequential dilution of precision for a general framework of PPP convergence period evaluation

• DOI: 10.1016/j.asr.2021.04.033
• Publication Date: 2021-05-05T02:38:41Z
• Authors: Cheng Chi; Xingqun Zhan; Yawei Zhai; Kui Lin; Jiachao Chang; Xin Zhang; Fengwei Shao
• Keywords: Dilution of precision; Dilution

Abstract The convergence period is of critical significance in Precise Point Positioning (PPP) applications. Current criterion for determining PPP convergence period is by comparing the positioning error to the ground truth. This experiment-based criterion can be influenced by many factors like the accuracy of ephemeris and the test area. One can hardly get a consistent result of the convergence period without abundant experiments. Consequently, the criterion is not suitable for global-wide PPP specification determination and relevant GNSS service design. In response, we build a new framework of PPP convergence period evaluation based on statistical analysis, with the definition of an indicator, Sequential Dilution of Precision (SDOP). The SDOP represents the propagation from measurement errors to the filter-derived positioning errors. And the framework is established based on SDOP to connect the measurement error, confidential probability, and PPP convergence period. Furthermore, the impact factors of PPP convergence are classified into three parts, satellite geometry, satellite movement, and un-modeled measurement error, which enables researchers to focus on a specific property for analysis. Specifically, the satellite movement can be described by DOP, and we further define the Speed-Up Ratio (SUR) to represent satellite movement. The SDOP is influenced by both DOP and SUR. The proposed framework and relevant variables are examined with both real data and simulated GNSS and Low Earth Orbit (LEO) data. The results are in good agreement with public recognition. Moreover, as an example usage, the global maps of PPP convergence period are presented using the new framework, which are almost impossible to be given with traditional experiment-based criterion. The variation of PPP convergence period through latitude, longitude, and positioning directions is clearly exhibited. The plots can play a significant part in PPP analysis and GNSS service design.