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<p>Fractional Cycle Biases (FCB) and Integer Recovery Clocks&#xa0;(IRC) are two essential phase bias estimation models to facilitate ambiguity resolution (AR) in Precise Point Positioning (PPP). For a long time, they have been considered equivalent or similar and viewed as two different product forms to achieve PPP–AR. However, previous comparisons relied on high-precision final orbit and clock products, neglecting the impact of product errors on these models. In practice, not all orbit and clock products maintain long-term stability, especially real-time (RT) products. This study analyzes and compares these two models, especially the influence of RT product errors on phase bias estimation are considered. Firstly, integrating into orbit and clock product error items, the FCB and IRC estimation formulas are developed, and the response and compensation capabilities of the two models to product errors are analyzed. Then, these two kinds of phase bias products are determined and compared using the GPS/BD3/Galileo data from the regional GNSS station network from Shaanxi, China, and the global MGEX network, respectively. By analyzing NL residual distribution and PPP-AR performance with RT orbit and clock products, the results show that the IRC model outperforms the FCB model in terms of recovering ambiguity integer characteristics since the former can provide timely corrections to orbit and clock product errors. With a regional network, corrections with IRC-generated phase biases lead to NL residuals for GPS, BD3, and Galileo within ± 0.15 cycles, improving by 17.75%, 34.31%, and 19.41% respectively, compared to FCB-generated phase biases. Moreover, IRC-generated phase biases reduce the root mean square (RMS) error of positioning for GPS, BD3, and GPS/BD3/Galileo by approximately 65%, 73%, and 72%, respectively. With a global network, although the ability to compensate for orbit and clock product errors declined for both models, the IRC-generated products still demonstrate superior performance compared to those from the FCB model.</p>

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Analysis and comparison of FCB and IRC models considering effect of real-time orbit and clock product errors

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Yunqing Tian,
  • Bao Shu,
  • Yang Gao,
  • Guanwen Huang,
  • Pan Li,
  • Qin Zhang,
  • Li Wang

摘要

Fractional Cycle Biases (FCB) and Integer Recovery Clocks (IRC) are two essential phase bias estimation models to facilitate ambiguity resolution (AR) in Precise Point Positioning (PPP). For a long time, they have been considered equivalent or similar and viewed as two different product forms to achieve PPP–AR. However, previous comparisons relied on high-precision final orbit and clock products, neglecting the impact of product errors on these models. In practice, not all orbit and clock products maintain long-term stability, especially real-time (RT) products. This study analyzes and compares these two models, especially the influence of RT product errors on phase bias estimation are considered. Firstly, integrating into orbit and clock product error items, the FCB and IRC estimation formulas are developed, and the response and compensation capabilities of the two models to product errors are analyzed. Then, these two kinds of phase bias products are determined and compared using the GPS/BD3/Galileo data from the regional GNSS station network from Shaanxi, China, and the global MGEX network, respectively. By analyzing NL residual distribution and PPP-AR performance with RT orbit and clock products, the results show that the IRC model outperforms the FCB model in terms of recovering ambiguity integer characteristics since the former can provide timely corrections to orbit and clock product errors. With a regional network, corrections with IRC-generated phase biases lead to NL residuals for GPS, BD3, and Galileo within ± 0.15 cycles, improving by 17.75%, 34.31%, and 19.41% respectively, compared to FCB-generated phase biases. Moreover, IRC-generated phase biases reduce the root mean square (RMS) error of positioning for GPS, BD3, and GPS/BD3/Galileo by approximately 65%, 73%, and 72%, respectively. With a global network, although the ability to compensate for orbit and clock product errors declined for both models, the IRC-generated products still demonstrate superior performance compared to those from the FCB model.